[ { "text": "NNLO BFKL Pomeron eigenvalue in N=4 SYM: We obtain an analytical expression for the Next-to-Next-to-Leading order of\nthe Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4\nusing Quantum Spectral Curve (QSC) integrability based method. The result is\nverified with more than 60 digits precision using the numerical method\ndeveloped by us in a previous paper. As a byproduct we developed a general\nanalytic method of solving the QSC perturbatively.", "category": "hep-th" }, { "text": "Quantum properties of the polytopic action in some simple geometries: The partition function corresponding to the \"polytopic\" action, a new action\nfor the gravitational interaction which we have proposed recently, is computed\nin the simplest two-dimensional geometries of genus zero and one. The\nfunctional integral over the Liouville field is approximated by an ordinary\nintegral over the constant zero mode. We study the dependence on both the\ncoupling constant and the cosmological constant, and compare with recent\nscaling results in standard 2D quantum gravity.", "category": "hep-th" }, { "text": "On the density of states in a free CFT and finite volume corrections: Results from spectral geometry such as Weyl's formula can be used to relate\nthe thermodynamic properties of a free massless field to the spatial manifold\non which it is defined. We begin by calculating the free energy in two cases:\nmanifolds posessing a boundary and spheres. The subextensive contributions\nallow us to test the Cardy-Verlinde formula and offer a new perspective on why\nit only holds in a free theory if one allows for a change in the overall\ncoefficient. After this we derive an expression for the density of states that\ntakes the form of a Taylor series. This series leads to an improvement over\nknown results when the area of the manifold's boundary is nonzero but much less\nthan the appropriate power of its volume.", "category": "hep-th" }, { "text": "Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds: The problem of computing the anomalous dimensions of a class of (nearly)\nhalf-BPS operators with a large R-charge is reduced to the problem of\ndiagonalizing a Cuntz oscillator chain. Due to the large dimension of the\noperators we consider, non-planar corrections must be summed to correctly\nconstruct the Cuntz oscillator dynamics. These non-planar corrections do not\nrepresent quantum corrections in the dual gravitational theory, but rather,\nthey account for the backreaction from the heavy operator whose dimension we\nstudy. Non-planar corrections accounting for quantum corrections seem to spoil\nintegrability, in general. It is interesting to ask if non-planar corrections\nthat account for the backreaction also spoil integrability. We find a limit in\nwhich our Cuntz chain continues to admit extra conserved charges suggesting\nthat integrability might survive.", "category": "hep-th" }, { "text": "Quantum Background Independence of Closed String Field Theory: We prove local background independence of the complete quantum closed string\nfield theory using the recursion relations for string vertices and the\nexistence of connections in CFT theory space. Indeed, with this data we\nconstruct an antibracket preserving map between the state spaces of two nearby\nconformal theories taking the corresponding string field measures $d\\mu\ne^{2S/\\hbar}$ into each other. A geometrical construction of the map is\nachieved by introducing a Batalin-Vilkovisky (BV) algebra on spaces of Riemann\nsurfaces, together with a map to the BV algebra of string functionals. The\nconditions of background independence show that the field independent terms of\nthe master action arise from vacuum vertices $\\V_{g,0}$, and that the overall\n$\\hbar$-independent normalization of the string field measure involves the\ntheory space connection. Our result puts on firm ground the widely believed\nstatement that string theories built from nearby conformal theories are\ndifferent states of the same theory.", "category": "hep-th" }, { "text": "An explicit construction of Wakimoto realizations of current algebras: It is known from a work of Feigin and Frenkel that a Wakimoto type,\ngeneralized free field realization of the current algebra $\\widehat{\\cal G}_k$\ncan be associated with each parabolic subalgebra ${\\cal P}=({\\cal G}_0+{\\cal\nG}_+)$ of the Lie algebra ${\\cal G}$, where in the standard case ${\\cal G}_0$\nis the Cartan and ${\\cal P}$ is the Borel subalgebra. In this letter we obtain\nan explicit formula for the Wakimoto realization in the general case. Using\nHamiltonian reduction of the WZNW model, we first derive a Poisson bracket\nrealization of the ${\\cal G}$-valued current in terms of symplectic bosons\nbelonging to ${\\cal G}_+$ and a current belonging to ${\\cal G}_0$. We then\nquantize the formula by determining the correct normal ordering. We also show\nthat the affine-Sugawara stress-energy tensor takes the expected quadratic form\nin the constituents.", "category": "hep-th" }, { "text": "Electrified branes: A geometrical form of the supersymmetry conditions for D-branes on arbitrary\ntype II supersymmetric backgrounds is derived, as well as the associated BPS\nbounds. The treatment is general and allows to consider, for instance,\nnon-static configurations or D-branes supporting a non-vanishing electric flux,\nhence completing previous partial results. In particular, our discussion\nclarifies how the notion of calibration can be extended in order to be\napplicable to the most general supersymmetric configurations. As an\nexemplifying preliminary step, the procedure followed is first applied to\nfundamental strings.", "category": "hep-th" }, { "text": "Simplifying the Tree-level Superstring Massless Five-point Amplitude: We use the pure spinor formalism to obtain the supersymmetric massless\nfive-point amplitude at tree-level in a streamlined fashion. We also prove the\nequivalence of an OPE identity in string theory with a subset of the\nBern-Carrasco-Johansson five-point kinematic relations, and demonstrate how the\nremaining BCJ identities follow from the different integration regions over the\nopen string world-sheet, therefore providing a first principles derivation of\nthe (supersymmetric) BCJ identities.", "category": "hep-th" }, { "text": "Exploring SU(3) Structure Moduli Spaces with Integrable G2 Structures: We study the moduli space of SU(3) structure manifolds X that form the\ninternal compact spaces in four-dimensional N=1/2 domain wall solutions of\nheterotic supergravity with flux. Together with the direction perpendicular to\nthe four-dimensional domain wall, X forms a non-compact 7-manifold Y with\ntorsionful G2 structure. We use this G2 embedding to explore how X(t) varies\nalong paths C(t) in the SU(3) structure moduli space. Our analysis includes the\nBianchi identities which strongly constrain the flow. We show that requiring\nthat the SU(3) structure torsion is preserved along the path leads to\nconstraints on the G2 torsion and the embedding of X in Y. Furthermore, we\nstudy flows along which the torsion classes of X go from zero to non-zero\nvalues. In particular, we present evidence that the flow of half-flat SU(3)\nstructures may contain Calabi-Yau loci, in the presence of non-vanishing\nH-flux.", "category": "hep-th" }, { "text": "Universality of the Holographic Angular Momentum Cutoff: The AdS/CFT dual description of a peripheral heavy ion collision involves an\nasymptotically AdS rotating black hole. The explicitly known black holes of\nthis kind, with planar event horizon topology [the \"KMV$_0$\" spacetimes], have\nbeen shown to be unstable when string-theoretic effects are taken into account.\nIt has been argued that this implies a \"holographic\" angular momentum cutoff\nfor peripheral collisions at very high energies. However, the KMV$_0$ black\nhole corresponds to a specific velocity distribution in the aftermath of a\nperipheral collision, and this distribution is not realistic at all points of\nthe interaction zone. It could therefore be argued that the angular momentum\ncutoff is an artefact of this particular choice of bulk geometry. We\ndemonstrate that, on the contrary, a Quark-Gluon Plasma with any physically\nreasonable internal velocity distribution corresponds to a black hole which is\nstill unstable, in the same way as the KMV$_0$ spacetime. The angular momentum\ncutoff is therefore a universal prediction of the holographic description of\nthese collisions.", "category": "hep-th" }, { "text": "M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory: A self-contained review is given of the matrix model of M-theory. The\nintroductory part of the review is intended to be accessible to the general\nreader. M-theory is an eleven-dimensional quantum theory of gravity which is\nbelieved to underlie all superstring theories. This is the only candidate at\npresent for a theory of fundamental physics which reconciles gravity and\nquantum field theory in a potentially realistic fashion. Evidence for the\nexistence of M-theory is still only circumstantial---no complete\nbackground-independent formulation of the theory yet exists. Matrix theory was\nfirst developed as a regularized theory of a supersymmetric quantum membrane.\nMore recently, the theory appeared in a different guise as the discrete\nlight-cone quantization of M-theory in flat space. These two approaches to\nmatrix theory are described in detail and compared. It is shown that matrix\ntheory is a well-defined quantum theory which reduces to a supersymmetric\ntheory of gravity at low energies. Although the fundamental degrees of freedom\nof matrix theory are essentially pointlike, it is shown that higher-dimensional\nfluctuating objects (branes) arise through the nonabelian structure of the\nmatrix degrees of freedom. The problem of formulating matrix theory in a\ngeneral space-time background is discussed, and the connections between matrix\ntheory and other related models are reviewed.", "category": "hep-th" }, { "text": "Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex\n Models: Boundary conditions compatible with integrability are obtained for two\ndimensional models by solving the factorizability equations for the reflection\nmatrices $K^{\\pm}(\\theta)$. For the six vertex model the general solution\ndepending on four arbitrary parameters is found. For the $A_{n-1}$ models all\ndiagonal solutions are found. The associated integrable magnetic Hamiltonians\nare explicitly derived.", "category": "hep-th" }, { "text": "Symmetry enhancement in 4d Spin(n) gauge theories and compactification\n from 6d: We consider a known sequence of dualities involving $4d$ ${\\cal N}=1$\ntheories with $Spin(n)$ gauge groups and use it to construct a new sequence of\nmodels exhibiting IR symmetry enhancement. Then, motivated by the observed\npattern of IR symmetries we conjecture six-dimensional theories the\ncompactification of which on a Riemann surface yields the $4d$ sequence of\nmodels along with their symmetry enhancements, and put them to several\nconsistency checks.", "category": "hep-th" }, { "text": "An eight-dimensional approach to G_2 manifolds: We develop a systematic approach to G_2 holonomy manifolds with an\nSU(2)xSU(2) isometry using maximal eight-dimensional gauged supergravity to\ndescribe D6-branes wrapped on deformed three-spheres. A quite general metric\nansatz that generalizes the celebrated Bryant-Salamon metric involves nine\nfunctions. We show that only six of them are the independent ones and derive\nthe general first order system of differential equations that they obey. As a\nbyproduct of our analysis, we generalize the notion of the twist that relates\nthe spin and gauge connections in a way that involves non-trivially the scalar\nfields.", "category": "hep-th" }, { "text": "MHV-Vertices for Gravity Amplitudes: We obtain a CSW-style formalism for calculating graviton scattering\namplitudes and prove its validity through the use of a special type of\nBCFW-like parameter shift. The procedure is illustrated with explicit examples.", "category": "hep-th" }, { "text": "Yukawa Corrections from Four-Point Functions in Intersecting D6-Brane\n Models: We discuss corrections to the Yukawa matrices of the Standard Model (SM)\nfermions in intersecting D-brane models due to four-point interactions.\nRecently, an intersecting D-brane model has been found where it is possible to\nobtain correct masses and mixings for all quarks as well as the tau lepton.\nHowever, the masses for the first two charged leptons come close to the right\nvalues but are not quite correct. Since the electron and muon are quite light,\nit is likely that there are additional corrections to their masses which cannot\nbe neglected. With this in mind, we consider contributions to the SM fermion\nmass matrices from four-point interactions. In an explicit model, we show that\nit is indeed possible to obtain the SM fermion masses and mixings which are a\nbetter match to those resulting from experimental data extrapolated at the\nunification scale when these corrections are included. These corrections may\nhave broader application to other models.", "category": "hep-th" }, { "text": "Quantizing the non-linear graviton: We consider holomorphic Poisson-BF theory on twistor space. Classically, this\ndescribes self-dual Einstein gravity on space-time, but at the quantum level it\nis plagued by an anomaly. The anomaly corresponds to the fact that\nintegrability of the self-dual vacuum Einstein equations does not survive in\nself-dual quantum gravity. We compute the anomaly polynomials in the Poisson-BF\ntheory, as well as in this theory coupled to a holomorphic BF theory on twistor\nspace describing self-dual Yang-Mills. We show that all anomalies may be\ncancelled by further coupling to a twistor field representing a type of axion\non space-time. When the twistor anomalies are cancelled, all $n\\geq4$-pt\namplitudes vanish and integrability is restored.", "category": "hep-th" }, { "text": "Superconducting Source of the Kerr-Newman Electron: Regular superconducting solution for interior of the Kerr-Newman (KN)\nspinning particle is obtained. For parameters of electron it represents a\nhighly oblated rotating bubble formed by Higgs field which expels the\nelectromagnetic (em) field and currents from interior to domain wall boundary\nof the bubble.\n The external em and gravitational fields correspond exactly to Kerr-Newman\nsolution, while interior of the bubble is flat and forms a `false' vacuum with\nzero energy density. Vortex of the KN em field forms a quantum Wilson loop on\nthe edge of the rotating disk-like bubble.", "category": "hep-th" }, { "text": "Area-preserving structure of 2d-gravity: The effective action for 2d-gravity with manifest area-preserving invariance\nis obtained in the flat and in the general gravitational background. The\ncocyclic properties of the last action are proved, and generalizations on\nhigher dimensions are discussed.", "category": "hep-th" }, { "text": "Electrically Charged Einstein-Born-Infeld Black Holes with Massive\n Dilaton: We numerically construct static and spherically symmetric electrically\ncharged black hole solutions in Einstein-Born-Infeld gravity with massive\ndilaton. The numerical solutions show that the dilaton potential allows many\nmore black hole causal structures than the massless dilaton. We find that\ndepending on the black hole mass and charge and the dilaton mass the black\nholes can have either one, two, or three horizons. The extremal solutions are\nalso found out. As an interesting peculiarity we note that there are extremal\nblack holes with an inner horizon and with triply degenerated horizon.", "category": "hep-th" }, { "text": "Spontaneous symmetry breakings in the singlet scalar Yukawa model within\n the auxiliary field method: The aim of this work is to investigate the occurrence of two different\nspontaneous symmetry breakings {at} two levels of the description of\nfermion-scalar field model, by means of a set of gap equations and {with} a\nbackground field effective action. For that, we consider the Yukawa model, as a\ntoy model for interactions between non-massive fermions intermediated by a\nself-interacting real scalar field. This model has at stakes two symmetries at\nthe classical level that, as we know, might be spontaneously or dynamically\nbroken with mass generation for the particles. The auxiliary field method is\nconsidered and it produces coupled renormalized gap equations. The effective\naction is then written with quantum contributions by {the} external background\n{field} method. We brought to light how the renormalization procedure affects\nthe physical gaps, investigate its properties, and discuss the connection\nbetween the auxiliary fields not only to define composite states but also to\ncompute the effective action.", "category": "hep-th" }, { "text": "3d $\\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes: We study CFT data of 3-dimensional superconformal field theories (SCFTs)\narising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via\nso-called 3d/3d correspondence, central charges of these SCFTs are related to a\n$SL(2)$ Chern-Simons (CS) invariant on the 3-manifolds. We give a rigorous\ndefinition of the invariant in terms of resurgence theory and a state-integral\nmodel for the complex CS theory. We numerically evaluate the central charges\nfor several closed 3-manifolds with small hyperbolic volume. The computation\nsuggests that the wrapped M5-brane systems give infinitely many discrete SCFTs\nwith small central charges. We also analyze these `minimal' SCFTs in the eye of\n3d $\\mathcal{N}=2$ superconformal bootstrap.", "category": "hep-th" }, { "text": "Superconformal Quantum Mechanics and the Discrete Light-Cone\n Quantisation of N=4 SUSY Yang-Mills: We study the quantum mechanical sigma model arising in the discrete\nlight-cone quantisation of N=4 supersymmetric Yang-Mills theory. The target\nspace is a certain torus fibration over a scale-invariant special Kahler\nmanifold. We show that the expected SU(1,1|4) light-cone superconformal\ninvariance of the N=4 theory emerges in a limit where the volume of the fibre\ngoes to zero and give an explicit construction of the generators. The\nconstruction given here yields a large new family of superconformal quantum\nmechanical models with SU(1,1|4) invariance.", "category": "hep-th" }, { "text": "Geometric Transitions, Flops and Non-Kahler Manifolds: I: We construct a duality cycle which provides a complete supergravity\ndescription of geometric transitions in type II theories via a flop in\nM-theory. This cycle connects the different supergravity descriptions before\nand after the geometric transitions. Our construction reproduces many of the\nknown phenomena studied earlier in the literature and allows us to describe\nsome new and interesting aspects in a simple and elegant fashion. A precise\nsupergravity description of new torsional manifolds that appear on the type IIA\nside with branes and fluxes and the corresponding geometric transition are\nobtained. A local description of new G_2 manifolds that are circle fibrations\nover non-Kahler manifolds is presented.", "category": "hep-th" }, { "text": "Possible Effects of Spacetime Foam in Particle Physics: We present an extension of quantum field theory to the case when the\nspacetime topology fluctuates (spacetime foam). In this extension the number of\nbosonic fields becomes a variable and the ground state is characterized by a\nfinite particle number density. It is shown that when the number of fields\nremains a constant, the standard field theory is restored. However, in the\ncomplete theory the ground state has a nontrivial properties. In particular, it\nproduces an increase in the level of quantum fluctuations in the field\npotentials and an additional renormalization of masses of particles. We examine\nfluctuations of massless fields and show that in the presence of a temperature\n(thermal state) these fluctuations has 1/f spectrum. Thus, the main prediction\nof the theory is that our universe should be filled with a random\nelectromagnetic field which should produce an additional 1/f - noise in\nelectric circuits.", "category": "hep-th" }, { "text": "Color Current Induced by Gluon in Background Field Method of QCD: By using the background field method of QCD in a path integral approach, we\nderive the equation of motion for the classical chromofield and for the gluon\nin a system containing the gluon and the classical chromofield simultaneously.\nThis inhomogeneous field equation contains a current term, which is the\nexpectation value of a composite operator including linear, square and cubic\nterms of the gluon field. We also derive identities which the current should\nobey from the gauge invariance. We calculate the current at the leading order\nwhere the current induced by the gluon is opposite in sign to that induced by\nthe quark. This is just the feature of the non-Abelian gauge field theory which\nhas asymptotic freedom. Physically, the induced current can be treated as the\n'displacement' current in the polarized vacuum, and its effect is equivalent to\nredefining the field and the coupling constant.", "category": "hep-th" }, { "text": "Shear viscosity of the $\u03a6^4$ theory from classical simulation: Shear viscosity of the classical $\\Phi^4$ theory is measured using classical\nmicrocanonical simulation. To calculate the Kubo formula, we measure the\nenergy-momentum tensor correlation function, and apply the Green-Kubo relation.\nBeing a classical theory, the results depend on the cutoff which should be\nchosen in the range of the temperature. Comparison with experimentally\naccessible systems is also performed.", "category": "hep-th" }, { "text": "Emergent gravity from off-shell energy fixing: Off-shell processes do not preserve the Energy Momentum Tensor (EMT) in QFT.\nFixing the EMT throughout off-shell processes, implies a graviton-like quantum\nfield to emerge without dynamics. Its dynamics are generated through quantum\ncorrections. This Fixed Off-Shell Energy Condition (FOSEC) implies the\nexistence of a linear gravity-like theory, and in special cases the full\nPoincar\\`e gauge theory. In this work it is shown that imposing the FOSEC in\nQFT implies the emergence of a viable quantum theory of gravity.", "category": "hep-th" }, { "text": "Non-Minimal Warm Inflation and Perturbations on the Warped DGP Brane\n with Modified Induced Gravity: We construct a warm inflation model with inflaton field non-minimally coupled\nto induced gravity on a warped DGP brane. We incorporate possible modification\nof the induced gravity on the brane in the spirit of $f(R)$-gravity. We study\ncosmological perturbations in this setup. In the case of two field inflation\nsuch as warm inflation, usually entropy perturbations are generated. While it\nis expected that in the case of one field inflation these perturbations to be\nremoved, we show that even in the absence of the radiation field, entropy\nperturbations are generated in our setup due to non-minimal coupling and\nmodification of the induced gravity.", "category": "hep-th" }, { "text": "Tachyons and the preferred frames: Quantum field theory of space-like particles is investigated in the framework\nof absolute causality scheme preserving Lorentz symmetry. It is related to an\nappropriate choice of the synchronization procedure (definition of time). In\nthis formulation existence of field excitations (tachyons) distinguishes an\ninertial frame (privileged frame of reference) via spontaneous breaking of the\nso called synchronization group. In this scheme relativity principle is broken\nbut Lorentz symmetry is exactly preserved in agreement with local properties of\nthe observed world. It is shown that tachyons are associated with unitary\norbits of Poincar\\'e mappings induced from $SO(2)$ little group instead of\n$SO(2,1)$ one. Therefore the corresponding elementary states are labelled by\nhelicity. The cases of the helicity $\\lambda = 0$ and $\\lambda =\n\\pm\\frac{1}{2}$ are investigated in detail and a corresponding consistent field\ntheory is proposed. In particular, it is shown that the Dirac-like equation\nproposed by Chodos et al., inconsistent in the standard formulation of QFT, can\nbe consistently quantized in the presented framework. This allows us to treat\nmore seriously possibility that neutrinos might be fermionic tachyons as it is\nsuggested by experimental data about neutrino masses.", "category": "hep-th" }, { "text": "Light-Cone Quantization a of Scalar Field on Time-Dependent Backgrounds: We discuss what is light-cone quantization on a curved spacetime also without\na null Killing vector. Then we consider as an example the light-cone\nquantization of a scalar field on a background with a Killing vector and the\nconnection with the second quantization of the particle in the same background.\nIt turns out that the proper way to define the light-cone quantization is to\nrequire that the constant light-cone time hypersurface is null or,\nequivalently, that the particle Hamiltonian is free of square roots. Moreover,\nin order to quantize the scalar theory it is necessary to use not the original\nscalar rather a scalar field density, i.e. the Schr\\\"odinger wave functional\ndepends on a scalar density and not on the original field. Finally we recover\nthis result as the second quantization of a particle on the same background,\nwhere it is necessary to add as input the fact that we are dealing with a\nscalar density.", "category": "hep-th" }, { "text": "Non-BPS D8-branes and Dynamic Domain Walls in Massive IIA Supergravities: We study the D8-branes of the Romans massive IIA supergravity theory using\nthe coupled supergravity and worldvolume actions. D8 branes can be regarded as\ndomain walls with the jump in the extrinsic curvature at the brane given by the\nIsrael matching conditions. We examine the restrictions that these conditions\nplace on extreme and non-extreme solutions and find that they rule out some of\nthe supersymmetric solutions given by Bergshoeff {\\em et al}. We consider what\nhappens when the dilaton varies on the worldvolume of the brane, which implies\nthat the brane is no longer static. We obtain a family of D8-brane solutions\nparametrized by a non-extremality term on each side of the brane and the\nasymptotic values of the 10-form field. The non-extremality parameters can be\nrelated to the velocity of the brane. We also study 8-brane solutions of a\nmassive IIA supergravity theory introduced by Howe, Lambert and West. This\ntheory also admits a 10-form formulation, but the 10-form is not a R-R sector\nfield and so these 8-branes are not D-branes.", "category": "hep-th" }, { "text": "On the Duffin-Kemmer-Petiau Formulation of the Covariant Hamiltonian\n Dynamics in Field Theory: We show that the De Donder-Weyl (DW) covariant Hamiltonian field equations of\nany field can be written in Duffin-Kemmer-Petiau (DKP) matrix form. As a\nconsequence, the (modified) DKP beta-matrices (5 X 5 in four space-time\ndimensions) are of universal significance for all fields admitting the DW\nHamiltonian formulation, not only for a scalar field, and can be viewed as\nfield theoretic analogues of the symplectic matrix, leading to the so-called\n``k-symplectic'' (k=4) structure. We also briefly discuss what could be viewed\nas the covariant Poisson bracket given by beta-matrices and the corresponding\nPoisson bracket formulation of DW Hamiltonian field equations.", "category": "hep-th" }, { "text": "Black branes on the linear dilaton background: We show that the complete static black p-brane supergravity solution with a\nsingle charge contains two and only two branches with respect to behavior at\ninfinity in the transverse space. One branch is the standard family of\nasymptotically flat black branes, and another is the family of black branes\nwhich asymptotically approach the linear dilaton background with antisymmetric\nform flux (LDB). Such configurations were previously obtained in the\nnear-horizon near-extreme limit of the dilatonic asymptotically flat p-branes,\nand used to describe the thermal phase of field theories involved in the DW/QFT\ndualities and the thermodynamics of little string theory in the case of the\nNS5-brane. Here we show by direct integration of the Einstein equations that\nthe asymptotically LDB p-branes are indeed exact supergravity solutions, and we\nprove a new uniqueness theorem for static p-brane solutions satisfying cosmic\ncensorship. In the non-dilatonic case, our general non-asymptotically flat\np-branes are uncharged black branes on the background $AdS_{p+2}\\times\nS^{D-p-2}$ supported by the form flux. We develop the general formalism of\nquasilocal quantities for non-asymptotically flat supergravity solutions with\nantisymmetric form fields, and show that our solutions satisfy the first law of\ntheormodynamics. We also suggest a constructive procedure to derive rotating\nasymptotically LDB brane solutions.", "category": "hep-th" }, { "text": "Born sigma model for branes in exceptional geometry: In double field theory, the physical space has been understood as a subspace\nof the doubled space. Recently, the doubled space is defined as the\npara-Hermitian manifold and the physical space is realized as a leaf of a\nfoliation of the doubled space. This construction naturally introduces the\nfundamental 2-form, which plays an important role in a reformulation of string\ntheory known as the Born sigma model. In this paper, we present the Born sigma\nmodel for $p$-branes in M-theory and type IIB theory by extending the\nfundamental 2-form into U-duality-covariant $(p+1)$-forms.", "category": "hep-th" }, { "text": "Noncommuting Electric Fields and Algebraic Consistency in Noncommutative\n Gauge theories: We show that noncommuting electric fields occur naturally in\n$\\theta$-expanded noncommutative gauge theories. Using this noncommutativity,\nwhich is field dependent, and a hamiltonian generalisation of the\nSeiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian\nformulations of these theories, is established. A comparison of results in\ndifferent descriptions shows that this generalised map acts as canonical\ntransformation in the physical subspace only. Finally, we apply the hamiltonian\nformulation to derive the gauge symmetries of the action.", "category": "hep-th" }, { "text": "On the holographic width of flux tubes: We investigate the width of the flux tube between heavy static quark charges.\nUsing the gauge/gravity duality, we find the properties of the minimal\nconnected surface related to the width of the bound state. We show that in the\nconfining phase, the logarithmic broadening predicted by the effective string\ndescription and observed in lattice simulations is a generic property of all\nconfining backgrounds. We also study the transverse fluctuations of the string\nconnecting two static quarks in curved backgrounds. Our formalism is applied to\nAdS space where we compute the expectation value of the square of transverse\ndeviations of the string, a quantity related to the width.", "category": "hep-th" }, { "text": "Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4: We show that a scalar field conformally coupled to AdS gravity in four\ndimensions with a quartic self-interaction can be embedded into M-theory. The\nholographic effective potential is exactly calculated, allowing us to study\nnon-perturbatively the stability of AdS_4 in the presence of the conformally\ncoupled scalar. It is shown that there exists a one-parameter family of\nconformal scalar boundary conditions for which the boundary theory has an\nunstable vacuum. In this case, the bulk theory has instanton solutions that\nmediate the decay of the AdS_4 space. These results match nicely with the\nvacuum structure and the existence of instantons in an effective\nthree-dimensional boundary model.", "category": "hep-th" }, { "text": "D-branes and Discrete Torsion: We show that discrete torsion is implemented in a D-brane world-volume theory\nby using a projective representation of the orbifold point group. We study the\nexample of C^3/Z_2 x Z_2 and show that the resolution of singularities agrees\nwith that proposed by Vafa and Witten. A new type of fractional brane appears.", "category": "hep-th" }, { "text": "On String Junctions in Supersymmetric Gauge Theories: We study junctions consisting of confining strings in N=1 supersymmetric\nlarge N gauge theories by means of the gauge/gravity correspondence. We realize\nthese junctions as D-brane configurations in infrared geometries of the\nKlebanov-Strassler (KS) and the Maldacena-Nunez (MN) solutions. After\ndiscussing kinematics associated with the balance of tensions, we compute the\nenergies of baryon vertices numerically. In the KS background, baryon vertices\ngive negative contributions to the energies. The results for the MN background\nstrongly suggest that the energies of baryon vertices exactly vanish, as in the\ncase of supersymmetric (p,q)-string junctions. We find that brane\nconfigurations in the MN background have a property similar to the holomorphy\nof the M-theory realization of (p,q)-string junctions. With the help of this\nproperty, we analytically prove the vanishing of the energies of baryon\nvertices in the MN background.", "category": "hep-th" }, { "text": "Fluid-gravity correspondence in the scalar-tensor theory of gravity:\n (in)equivalence of Einstein and Jordan frames: The duality of gravitational dynamics (projected on a null hypersurface) and\nof fluid dynamics is investigated for the scalar tensor (ST) theory of gravity.\nThe description of ST gravity, in both Einstein and Jordan frames, is analyzed\nfrom fluid-gravity viewpoint. In the Einstein frame the dynamical equation for\nthe metric leads to the Damour-Navier-Stokes (DNS) equation with an external\nforcing term, coming from the scalar field in ST gravity. In the Jordan frame\nthe situation is more subtle. We observe that finding the DNS equation in this\nframe can lead to two pictures. In one picture, the usual DNS equation is\nmodified by a Coriolis-like force term, which originates completely from the\npresence of a non-minimally coupled scalar field ($\\phi$) on the gravity side.\nMoreover, the identified fluid variables are no longer conformally equivalent\nwith those in the Einstein frame. However, this picture is consistent with the\nsaturation of Kovtun-Son-Starinets (KSS) bound. In the other picture, we find\nthe standard DNS equation (i.e. without the Coriolis-like force), with the\nfluid variables conformally equivalent with those in Einstein frame. But, the\nsecond picture, may not agree with the KSS bound for some values of $\\phi$. We\nconclude by rewriting the Raychaudhuri equation and the tidal force equation in\nterms of the relevant parameters to demonstrate how the expansion scalar and\nthe shear-tensor evolve in the spacetime. Although, the area law of entropy is\nbroken in ST gravity, we show that the rewritten form of Raychaudhuri's\nequation correctly results in the generalized second law of black hole\nthermodynamics.", "category": "hep-th" }, { "text": "Novel algebraic structures from the polysymplectic form in field theory: The polysymplectic $(n+1)$-form is introduced as an analogue of the\nsymplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of\nfield theory. The corresponding Poisson brackets on differential forms are\nconstructed. The analogues of the Poisson algebra are shown to be generalized\n(non-commutative and higher-order) Gerstenhaber algebras defined in the text.", "category": "hep-th" }, { "text": "Universal Terms of Entanglement Entropy for 6d CFTs: We derive the universal terms of entanglement entropy for 6d CFTs by applying\nthe holographic and the field theoretical approaches, respectively. Our\nformulas are conformal invariant and agree with the results of [34,35].\nRemarkably, we find that the holographic and the field theoretical results\nmatch exactly for the $C^2$ and $Ck^2$ terms. Here $C$ and $k$ denote the Weyl\ntensor and the extrinsic curvature, respectively. As for the $k^4$ terms, we\nmeet the splitting problem of the conical metrics. The splitting problem in the\nbulk can be fixed by equations of motion. As for the splitting on the boundary,\nwe assume the general forms and find that there indeed exists suitable\nsplitting which can make the holographic and the field theoretical $k^4$ terms\nmatch. Since we have much more equations than the free parameters, the match\nfor $k^4$ terms is non-trivial.", "category": "hep-th" }, { "text": "Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with\n Matter: Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in\n4-dimensions with massless matter multiplets in the fundamental representation\nof the gauge group. The beta-functions represent the flow of the couplings as\nthe VEV of the Higgs field is lowered and are modular forms of weight -2. They\nhave the correct asymptotic behaviour at both the strong and weak coupling\nfixed points. Corrections to the massless beta-functions when masses are turned\non are discussed.", "category": "hep-th" }, { "text": "$T{\\overline T}$ deformations and the width of fundamental particles: We provide a simple geometric meaning for deformations of so-called\n$T{\\overline T}$ type in relativistic and non-relativistic systems.\nDeformations by the cross products of energy and momentum currents in\nintegrable quantum field theories are known to modify the thermodynamic Bethe\nansatz equations by a \"CDD factor\". In turn, CDD factors may be interpreted as\nadditional, fixed shifts incurred in scattering processes: a finite width added\nto the fundamental particles (or, if negative, to the free space between them).\nWe suggest that this physical effect is a universal way of understanding\n$T{\\overline T}$ deformations, both in classical and quantum systems. We first\nshow this in non-relativistic systems, with particle conservation and\ntranslation invariance, using the deformation formed out of the densities and\ncurrents of particles and momentum. This holds at the level of the equations of\nmotion, and for any interaction potential, integrable or not. We then argue,\nand show by similar techniques in free relativistic particle systems, that\n$T\\overline T$ deformations of relativistic systems produce the equivalent\nphenomenon, accounting for length contractions. We also show that, in both the\nrelativistic and non-relativistic cases, the width of particles is equivalent\nto a state-dependent change of metric, where the distance function discounts\nthe particles' widths, or counts the additional free space. This generalises\nand explains the known field-dependent coordinate change describing $T\\overline\nT$ deformations. The results connect such deformations with generalised\nhydrodynamics, where the relations between scattering shifts, widths of\nparticles and state-dependent changes of metric have been established.", "category": "hep-th" }, { "text": "Towards AdS Distances in String Theory: The AdS Distance Conjecture proposes to assign a notion of distance between\nAdS vacua in quantum gravity. We perform some initial developments of this\nidea. We first propose more sharply how to define a metric on conformal\nvariations of AdS through the action. This metric is negative, making the\ndistance ill-defined, a property relating to the famous conformal factor\nproblem of quantum gravity. However, in string theory, variations of the AdS\nconformal factor are accompanied by variations of the internal dimensions and\nof the background flux. We propose an $\\textit{action metric}$, which accounts\nfor all of these variations simultaneously. Accounting for the variations of\nthe overall volume of the internal dimensions can flip the sign of the action\nmetric making it positive. This positivity is related to the absence of scale\nseparation between the internal and external dimensions: the negative external\nconformal contribution must be sub-dominant to the positive internal\ncontribution. We then focus specifically on the families of solutions of\neleven-dimensional supergravity on AdS$_4 \\times S^7$ and AdS$_7 \\times S^4$.\nFor these, there is only a single further additional contribution to the action\nmetric coming from variations of the Freund-Rubin flux. This contribution is\nsubtle to implement, and the unique prescription we find requires singling out\nthe radial direction of AdS as special. Adding the flux contribution yields an\noverall total action metric which becomes positive for both the AdS$_4$ and\nAdS$_7$ families of solutions. The final result is therefore a procedure which\nyields a well-defined distance for these families of solutions.", "category": "hep-th" }, { "text": "Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills: We conjecture that every rational Yangian invariant in N=4 SYM theory\nsatisfies a recently introduced notion of cluster adjacency. We provide\nevidence for this conjecture by using the Sklyanin Poisson bracket on Gr(4,n)\nto check numerous examples.", "category": "hep-th" }, { "text": "The black hole/string transition in AdS$_3$ and confining backgrounds: String stars, or Horowitz-Polchinski solutions, are Euclidean string theory\nsaddles with a normalizable condensate of thermal winding strings. String stars\nwere suggested as a possible description of stringy (Euclidean) black holes\nclose to the Hagedorn temperature. In this work, we continue the study\ninitiated in arXiv:2202.06966 by investigating the thermodynamic properties of\nstring stars in asymptotically (thermal) anti-de Sitter backgrounds. First, we\ndiscuss the case of AdS$_3$ with mixed RR and NS-NS fluxes (including the pure\nNS-NS system) and comment on a possible BTZ/string transition unique to\nAdS$_3$. Second, we present new ``winding-string gas'' saddles for confining\nholographic backgrounds such as the Witten model, and determine the subleading\ncorrection to their Hagedorn temperature. We speculate a black brane/string\ntransition in these models and argue for a possible relation to the deconfined\nphase of 3+1 dimensional pure Yang-Mills.", "category": "hep-th" }, { "text": "Holographic torus correlators in $\\text{AdS}_3$ gravity coupled to\n scalar field: This paper investigates holographic torus correlators of generic operators at\nconformal infinity and a finite cutoff within AdS$_3$ gravity coupled with a\nfree scalar field. Using a near-boundary analysis and solving the gravitational\nboundary value problem, we solve Einstein's equation and calculate mixed\ncorrelators for massless and massive coupled scalar fields. The conformal ward\nidentity on the torus has been reproduced holographically, which can be\nregarded as a consistency check. Further, recurrence relations for a specific\nclass of higher-point correlators are derived, validating AdS$_3$/CFT$_2$ with\nnon-trivial boundary topology. While the two-point scalar correlator is\naccurately computed on the thermal AdS$_3$ saddle, the higher-point correlators\nassociated with scalar and stress tensor operators are explored.", "category": "hep-th" }, { "text": "Trialities and Exceptional Lie Algebras: DECONSTRUCTING the Magic Square: A construction of the magic square, and hence of exceptional Lie algebras, is\ncarried out using trialities rather than division algebras. By way of\npreparation, a comprehensive discussion of trialities is given, incorporating a\nnumber of novel results and proofs. Many of the techniques are closely related\nto, or derived from, ideas which are commonplace in theoretical physics. The\nimportance of symmetric spaces in the magic square construction is clarified,\nallowing the Jacobi property to be verified for each algebra in a uniform and\ntransparent way, with no detailed calculations required. A variation on the\nconstruction, corresponding to other symmetric spaces, is also given.", "category": "hep-th" }, { "text": "Third Order Tree Contributions in the Causal Approach: We consider the general framework of perturbative quantum field theory for\nthe pure Yang-Mills model developed in [9] and prove that the tree\ncontributions do not give anomalies. We will provide a more general form of\nthis gauge invariance property.", "category": "hep-th" }, { "text": "W Algebras, W Gravities and their Moduli Spaces: By generalizing the Drinfel'd--Sokolov reduction we construct a large class\nof W algebras as reductions of Kac--Moody algebras. Furthermore we construct\nactions, invariant under local left and right W transformations, which are the\nclassical covariant induced actions for W gravity. Talk presented by T. Tjin at\nthe Trieste Summerschool on strings and related topics.", "category": "hep-th" }, { "text": "Lax Operator and superspin chains from 4D CS gauge theory: We study the properties of interacting line defects in the four-dimensional\nChern Simons (CS) gauge theory with invariance given by the $SL\\left(\nm|n\\right) $ super-group family. From this theory, we derive the oscillator\nrealisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry.\nTo this end, we investigate the holomorphic property of the bosonic Lax\noperator $\\mathcal{L}$ and build a differential equation $%\n\\mathfrak{D}\\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of\n$\\mathcal{L}$ in the framework of\\ the CS theory. We generalize this\nconstruction to the case of gauge super-groups, and develop a Dynkin\nsuper-diagram algorithm to\\ deal with the decomposition of the Lie\nsuperalgebras. We obtain the generalisation of the Lax operator describing the\ninteraction between the electric Wilson super-lines and the magnetic 't Hooft\nsuper-defects. This coupling is given in terms of a mixture of bosonic and\nfermionic oscillator degrees of freedom in the phase space of magnetically\ncharged 't Hooft super-lines. The purely fermionic realisation of the superspin\nchain Lax operator is also investigated and it is found to coincide exactly\nwith the $\\mathbb{Z}_{2}$- gradation of Lie superalgebras.\\ \\newline Keywords:\n4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin\nsuper-diagrams, Superspin chains and integrability, Super- Lax operator.", "category": "hep-th" }, { "text": "Is quantum teleportation beyond horizon possible?: We ask whether quantum teleportation from the outside to the inside of a\nhorizon is possible, using entanglement extracted from a vacuum. We first\ncalculate analytically, within the perturbation theory, entanglement extracted\nfrom the Minkowski vacuum into a pair of an inertial and an accelerated\nUnruh-DeWitt detectors, which are initially in the ground states and interact\nwith a neutral massless scalar field for an infinitely long time. We find that\nentanglement can be extracted, but is \"fragile\", depending on adiabaticity of\nswitching of the detectors at the infinite past and future. We then consider\nthe standard scheme of quantum teleportation utilizing the extracted\nentanglement, and find that the standard teleportation is not superior to\nchannels without entanglement.", "category": "hep-th" }, { "text": "Non-local self-healing of Higgs inflation: Higgs inflation is known to be a minimal extension of the Standard Model\nallowing for the description of the early Universe inflation. This model is\nconsidered as an effective field theory since it has a relatively low cutoff\nscale, thus requiring further extensions to be a valid description of the\nreheating phase. We present a novel unified approach to the problem of\nunitarization and UV completion of the Higgs inflation model without\nintroducing new massive degrees of freedom. This approach is based on an\nanalytic infinite derivative modification of the Higgs field kinetic term. We\nconstruct a unitary non-local UV completion of the original Higgs inflation\nmodel while the inflationary stage is kept stable with respect to quantum\ncorrections.", "category": "hep-th" }, { "text": "Remarks on the thermofield double state in 4D black hole background: Recently it was shown that there is an anomalous singularity of propagators\nin spacetimes with horizons for thermal states with non--canonical\ntemperatures. In this paper we extend these observations to the situation when\nthe background geometry is given by the four--dimensional Schwarzschild and\nReissner-Nordstr\\\"om black holes. Namely, we demonstrate that the two-point\nfunction in the free scalar field theory acquires anomalous singularity when\nthe two points are located on the horizon. This singularity is anomalous in the\nsense that the coefficient before the divergent term in the two-point function\ndiffers from the canonical one and depends explicitly on the temperature of the\nstate. As it was previously shown, it leads to the explosive behavior of the\nregularised stress-energy tensor on the horizon when the temperature of the\nstate does not coincide with the canonical temperature of the horizon.", "category": "hep-th" }, { "text": "A selection rule for transitions in PT-symmetric quantum theory: Carl Bender and collaborators have developed a quantum theory governed by\nHamiltonians that are PT-symmetric rather than Hermitian. To implement this\ntheory, the inner product was redefined to guarantee positive norms of\neigenstates of the Hamiltonian. In the general case, which includes arbitrary\ntime-dependence in the Hamiltonian, a modification of the Schrodinger equation\nis necessary as shown by Gong and Wang to conserve probability. In this paper,\nwe derive the following selection rule: transitions induced by time dependence\nin a PT-symmetric Hamiltonian cannot occur between normalized states of\ndiffering PT-norm. We show three examples of this selection rule in action: two\nmatrix models and one in the continuum.", "category": "hep-th" }, { "text": "Extraction of shear viscosity in stationary states of relativistic\n particle systems: Starting from a classical picture of shear viscosity we construct a\nstationary velocity gradient in a microscopic parton cascade. Employing the\nNavier-Stokes ansatz we extract the shear viscosity coefficient $\\eta$. For\nelastic isotropic scatterings we find an excellent agreement with the analytic\nvalues. This confirms the applicability of this method. Furthermore for both\nelastic and inelastic scatterings with pQCD based cross sections we extract the\nshear viscosity coefficient $\\eta$ for a pure gluonic system and find a good\nagreement with already published calculations.", "category": "hep-th" }, { "text": "Spectral properties of the 2D magnetic Weyl-Dirac operator with a\n short-range potential: This paper is devoted to the study of the spectral properties of the\nWeyl-Dirac or massless Dirac operators, describing the behavior of quantum\nquasi-particles in dimension 2 in a homogeneous magnetic field, $B^{\\rm ext}$,\nperturbed by a chiral-magnetic field, $b^{\\rm ind}$, with decay at infinity and\na short-range scalar electric potential, $V$, of the Bessel-Macdonald type.\nThese operators emerge from the action of a pristine graphene-like QED$_3$\nmodel recently proposed in Eur. Phys. J. B93} (2020) 187. First, we establish\nthe existence of states in the discrete spectrum of the Weyl-Dirac operators\nbetween the zeroth and the first (degenerate) Landau level assuming that $V=0$.\nIn sequence, with $V_s \\not= 0$, where $V_s$ is an attractive potential\nassociated with the $s$-wave, which emerges when analyzing the $s$- and\n$p$-wave M{\\o}ller scattering potentials among the charge carriers in the\npristine graphene-like QED$_3$ model, we provide lower bounds for the sum of\nthe negative eigenvalues of the operators $|\\boldsymbol{\\sigma} \\cdot\n\\boldsymbol{p}_{\\boldsymbol{A}_\\pm}|+ V_s$. Here, $\\boldsymbol{\\sigma}$ is the\nvector of Pauli matrices,\n$\\boldsymbol{p}_{\\boldsymbol{A}_\\pm}=\\boldsymbol{p}-\\boldsymbol{A}_\\pm$, with\n$\\boldsymbol{p}=-i\\boldsymbol{\\nabla}$ the two-dimensional momentum operator\nand $\\boldsymbol{A}_\\pm$ certain magnetic vector potentials. As a by-product of\nthis, we have the stability of bipolarons in graphene in the presence of\nmagnetic fields.", "category": "hep-th" }, { "text": "Two Dimensional Horava-Lifshitz Black Hole Solutions: In this paper we address the issue of black hole solutions in\n(1+1)-dimensional non-projectable Horava-Lifshitz gravity. We consider several\nmodels by considering different potentials in the scalar matter sector. We also\nconsider the gravitational collapse of a distribution of pressureless dust\nfilling a region in one-dimensional space. The time of the collapse can be\nfaster or slower depending on the parameter $\\lambda$ of the theory.", "category": "hep-th" }, { "text": "The Black Ring is Unstable: We study non-axisymmetric linearised gravitational perturbations of the\nEmparan-Reall black ring using numerical methods. We find an unstable mode\nwhose onset lies within the \"fat\" branch of the black ring and continues into\nthe \"thin\" branch. Together with previous results using Penrose inequalities\nthat fat black rings are unstable, this provides numerical evidence that the\nentire black ring family is unstable.", "category": "hep-th" }, { "text": "Intersecting S-Brane Solutions of D=11 Supergravity: We construct all possible orthogonally intersecting S-brane solutions in\n11-dimensions corresponding to standard supersymmetric M-brane intersections.\nIt is found that the solutions can be obtained by multiplying the brane and the\ntransverse directions with appropriate powers of two hyperbolic functions of\ntime. This is the S-brane analog of the ``harmonic function rule''. The\ntransverse directions can be hyperbolic, flat or spherical. We also discuss\nsome properties of these solutions.", "category": "hep-th" }, { "text": "Confinement interaction in nonlinear generalizations of the\n Wick-Cutkosky model: We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky\nmodel. Using an iterative approach and eliminating the mediating field by means\nof the covariant Green function we arrive at a Lagrangian density containing\nmany-point time-nonlocal interaction terms. In low-order approximations of\n$\\phi^3{+}\\phi^4$ theory we obtain the usual two-current interaction as well as\na three-current interaction of a confining type. The same result is obtained\nwithout approximation for a version of the dipole model. The transition to the\nHamiltonian formalism and subsequent canonical quantization is performed with\ntime non-locality taken into account approximately.\n A relativistic three-particle wave equation is derived variationally by using\na three-particle Fock space trial state. The non-relativistic limit of this\nequation is obtained and its properties are analyzed and discussed.", "category": "hep-th" }, { "text": "One-loop effective potential on hyperbolic manifolds: The one-loop effective potential for a scalar field defined on an ultrastatic\nspace-time whose spatial part is a compact hyperbolic manifold, is studied\nusing zeta-function regularization for the one-loop effective action. Other\npossible regularizations are discussed in detail. The renormalization group\nequations are derived and their connection with the conformal anomaly is\npointed out. The symmetry breaking and the topological mass generation are also\ndiscussed.", "category": "hep-th" }, { "text": "Corfu 05 lectures - part I: Strings on curved backgrounds: In these introductory lectures we summarize some basic facts and techniques\nabout perturbative string theory (sections 1 to 6). These are further developed\n(sections 7 and 8) for describing string propagation in the presence of\ngravitational or gauge fields. We also remind some solutions of the string\nequations of motion, which correspond to remarkable (NS or D) brane\nconfigurations.\n A part II by Emilian Dudas will be devoted to orientifold constructions and\napplications to string model building.", "category": "hep-th" }, { "text": "Deviations from Fermi-Liquid behaviour in (2+1)-dimensional Quantum\n Electrodynamics and the normal phase of high-$T_c$ Superconductors: We argue that the gauge-fermion interaction in multiflavour quantum\nelectrodynamics in $(2 + 1)$-dimensions is responsible for non-fermi liquid\nbehaviour in the infrared, in the sense of leading to the existence of a\nnon-trivial (quasi) fixed point that lies between the trivial fixed point (at\ninfinite momenta) and the region where dynamical symmetry breaking and mass\ngeneration occurs. This quasi-fixed point structure implies slowly varying,\nrather than fixed, couplings in the intermediate regime of momenta, a situation\nwhich resembles that of (four-dimensional) `walking technicolour' models of\nparticle physics. The inclusion of wave-function renormalization yields\nmarginal $O(1/N)$-corrections to the `bulk' non-fermi liquid behaviour caused\nby the gauge interaction in the limit of infinite flavour number. Such\ncorrections lead to the appearance of modified critical exponents. In\nparticular, at low temperatures there appear to be logarithmic scaling\nviolations of the linear resistivity of the system of order $O(1/N)$.\nConnection with the anomalous normal-state properties of certain condensed\nmatter systems relevant for high-temperature superconductivity is briefly\ndiscussed. The relevance of the large (flavour) $N$ expansion to the\nfermi-liquid problem is emphasized. As a partial result of our analysis, we\npoint out the absence of Charge-Density-Wave Instabilities from the effective\nlow-energy theory, as a consequence of gauge invariance.", "category": "hep-th" }, { "text": "Black holes without firewalls: The postulates of black hole complementarity do not imply a firewall for\ninfalling observers at a black hole horizon. The dynamics of the stretched\nhorizon, that scrambles and re-emits information, determines whether infalling\nobservers experience anything out of the ordinary when entering a large black\nhole. In particular, there is no firewall if the stretched horizon degrees of\nfreedom retain information for a time of order the black hole scrambling time.", "category": "hep-th" }, { "text": "N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect: It is argued that there are strong similarities between the infra-red physics\nof N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both\nsystems exhibit a hierarchy of vacua with a sub-group of the modular group\nmapping between them. The scaling flow for pure SU(2) N=2 supersymmetric\nYang-Mills in 4-dimensions is re-examined and an earlier suggestion in the\nliterature, that was singular at strong coupling, is modified to a form that is\nwell behaved at both weak and strong coupling and describes the crossover in an\nanalytic fashion. Similarities between the phase diagram and the flow of SUSY\nYang-Mills and that of the quantum Hall effect are then described, with the\nHall conductivity in the latter playing the role of the theta-parameter in the\nformer. Hall plateaux, with odd denominator filling fractions, are analogous to\nfixed points at strong coupling in N=2 SUSY Yang-Mills, where the massless\ndegrees of freedom carry an odd monopole charge.", "category": "hep-th" }, { "text": "Anti-de Sitter space, branes, singletons, superconformal field theories\n and all that: There has recently been a revival of interest in anti de-Sitter space (AdS)\nbrought about by the conjectured duality beteeen physics in the bulk of AdS and\na conformal field theory on the boundary. Since the whole subject of branes,\nsingletons and superconformal field theories on the AdS boundary was an active\narea of research about ten years ago, I begin with a historical review,\nincluding the ``Membrane at the end of the universe'' idea. Next I discuss two\nrecent papers with Lu and Pope on on $AdS_{5} \\times S^{5}$ and on $AdS_{3}\n\\times S^{3}$, respectively. In each case we note that odd-dimensional spheres\n$S^{{2n+1}}$ may be regarded as U(1) bundles over $CP^{n}$ and that this\npermits an unconventional ``Hopf''duality along the U(1) fibre. This leads in\nparticular to the phenomenon of BPS without BPS whereby states which appear to\nbe non-BPS in one picture are seen to be BPS in the dual picture.", "category": "hep-th" }, { "text": "Critical Composite Superconformal String: In the paper the nilpotent conditions of BRST operator for new superconformal\nstring model were found. This string includes anticommutation $2-d$ fields\nadditional to the standard Neveu-Schwarz superconformal set which carry quark\nquantum numbers. In this case the superconformal symmetry is realized by a\nnon-linear way. In the superconformal composite string new constraints for 1\nand 1/2 conformal dimension should be added to the standard system of Virasoro\nsuperalgebra constraints for 2 and 3/2 conformal dimensions. The number $N$ of\nthe constraints and numbers $D$ and $D'$ of bosonic and fermionic $2-d$ fields\nare connected by a simple relationship $D'/2+D-3N-15=0.$ Also perspectives of\nthe critical composite superconformal string are discussed.", "category": "hep-th" }, { "text": "Heisenberg Groups and Noncommutative Fluxes: We develop a group-theoretical approach to the formulation of generalized\nabelian gauge theories, such as those appearing in string theory and M-theory.\nWe explore several applications of this approach. First, we show that there is\nan uncertainty relation which obstructs simultaneous measurement of electric\nand magnetic flux when torsion fluxes are included. Next we show how to define\nthe Hilbert space of a self-dual field. The Hilbert space is Z2-graded and we\nshow that, in general, self-dual theories (including the RR fields of string\ntheory) have fermionic sectors. We indicate how rational conformal field\ntheories associated to the two-dimensional Gaussian model generalize to\n(4k+2)-dimensional conformal field theories. When our ideas are applied to the\nRR fields of string theory we learn that it is impossible to measure the\nK-theory class of a RR field. Only the reduction modulo torsion can be\nmeasured.", "category": "hep-th" }, { "text": "The holographic Weyl semi-metal: We present a holographic model of a Weyl semi-metal. We show that upon\nvarying a mass parameter the model undergoes a quantum phase transition from a\ntopologically non-trivial state to a trivial one. The order parameter for this\nphase transition is the anomalous Hall effect (AHE). We give an interpretation\nof the results in terms of a holographic RG flow and compare to a weakly\ncoupled field theoretical model. Since there are no quasiparticle excitations\nin the strongly coupled holographic model the topological phase can not be\nbound to notions of topology in momentum space.", "category": "hep-th" }, { "text": "On the Topology of the Reduced Classical Configuration Space of Lattice\n QCD: We study the topological structure of the quotient of $SU(3)\\times SU(3)$ by\ndiagonal conjugation. This is the simplest nontrivial example for the classical\nreduced configuration space of chromodynamics on a spatial lattice in the\nHamiltonian approach. We construct a cell complex structure of the quotient in\nsuch a way that the closures of strata are subcomplexes and we compute the\nhomology and cohomology groups of the strata and their closures.", "category": "hep-th" }, { "text": "Topological Field Theories associated with Three Dimensional\n Seiberg-Witten monopoles: Three dimensional topological field theories associated with the three\ndimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are\npresented. These three dimensional monopole equations are obtained by a\ndimensional reduction of the four dimensional ones. The starting actions to be\nconsidered are Gaussian types with random auxiliary fields. As the local gauge\nsymmetries with topological shifts are found to be first stage reducible,\nBatalin-Vilkovisky algorithm is suitable for quantization. Then BRST\ntransformation rules are automatically obtained. Non-trivial observables\nassociated with Chern classes are obtained from geometric sector and are found\nto correspond to those of the topological field theory of Bogomol'nyi\nmonopoles.", "category": "hep-th" }, { "text": "Quantization of the Riemann Zeta-Function and Cosmology: Quantization of the Riemann zeta-function is proposed. We treat the Riemann\nzeta-function as a symbol of a pseudodifferential operator and study the\ncorresponding classical and quantum field theories. This approach is motivated\nby the theory of p-adic strings and by recent works on stringy cosmological\nmodels. We show that the Lagrangian for the zeta-function field is equivalent\nto the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of\nthe Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and\nthe Langlands program is indicated. The Beilinson conjectures on the values of\nL-functions of motives are interpreted as dealing with the cosmological\nconstant problem. Possible cosmological applications of the zeta-function field\ntheory are discussed.", "category": "hep-th" }, { "text": "Narain to Narnia: We generalize the holographic correspondence between topological gravity\ncoupled to an abelian Chern-Simons theory in three dimensions and an ensemble\naverage of Narain's family of massless free bosons in two dimensions,\ndiscovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the\ncorrespondence also works for toroidal orbifolds but not for K3 or Calabi-Yau\nsigma-models and not always for the minimal models. We conjecture that the\ncorrespondence requires that the central charge is equal to the critical\ncentral charge defined by the asymptotic density of states of the chiral\nalgebra. For toroidal orbifolds, we extend the holographic correspondence to\ncorrelation functions of twist operators by using topological properties of\nrational tangles in the three-dimensional ball, which represent configurations\nof vortices associated to a discrete gauge symmetry.", "category": "hep-th" }, { "text": "Functional Schroedinger and BRST Quantization of (1+1)--Dimensional\n Gravity: We discuss the quantization of pure string--inspired dilaton--gravity in\n$(1+1)$--dimensions, and of the same theory coupled to scalar matter. We\nperform the quantization using the functional Schroedinger and BRST formalisms.\nWe find, both for pure gravity and the matter--coupled theory, that the two\nquantization procedures give inequivalent ``physical'' results.", "category": "hep-th" }, { "text": "Non-Gaussianity in String Cosmology: A Case Study: We study non-gaussianity effects, using the $\\delta N$ formalism, in a\nmulti-field inflationary model consisting of K\\\"ahler moduli derived from type\nIIB string compactification in the large volume limit. The analytical work in\nthis paper mostly follows the separable potential method developed by Vernizzi\nand Wands. The numerical analysis is then used in computing non-gaussianity\nbeyond slow-roll regime. The possibility of the curvaton scenario is also\ndiscussed. We give the condition for the existence of the curvaton and\ncalculate the non-guassianity generated by the curvaton decay in the large\nvolume limit.", "category": "hep-th" }, { "text": "Entropy and replica geometry in generic two-dimensional dilaton gravity\n theories: We set up a new version of black hole information paradox in an eternal\nNarayan black hole, a generic two-dimensional dilaton gravity theory with\nnon-trivial on-shell bulk action and a product of dimensional reduction from\nhigher-dimensional AdS black brane, joined to Minkowski bath on both sides. We\nalso report both similarities as well as important differences between our\nmodel and the famous model of JT gravity coupled with baths. The contradiction\nof Hawking's result of entanglement entropy with unitarity is resolved by\nincluding a new saddle in the Euclidean gravitational path integral. As part of\nongoing and developing research, we attempt, and have had partial success, to\nexplicitly construct the replica wormhole geometry for our model to fully\njustify the quantum extremal surface calculations with Euclidean gravitational\npath integral, without using holography.", "category": "hep-th" }, { "text": "Integrable open-boundary conditions for the supersymmetric t-J model.\n The quantum group invariant case: We consider integrable open--boundary conditions for the supersymmetric t--J\nmodel commuting with the number operator $n$ and $S^{z}$. Four families, each\none depending on two arbitrary parameters, are found. We find the relation\nbetween Sklyanin's method of constructing open boundary conditions and the one\nfor the quantum group invariant case based on Markov traces. The eigenvalue\nproblem is solved for the new cases by generalizing the Nested Algebraic Bethe\nansatz of the quantum group invariant case (which is obtained as a special\nlimit). For the quantum group invariant case the Bethe ansatz states are shown\nto be highest weights of $spl_{q}(2,1)$.", "category": "hep-th" }, { "text": "Distributions of nonsupersymmetric flux vacua: We continue the study of the distribution of nonsupersymmetric flux vacua in\nIIb string theory compactified on Calabi-Yau manifolds, as in hep-th/0404116.\nWe show that the basic structure of this problem is that of finding\neigenvectors of the matrix of second derivatives of the superpotential, and\nthat many features of the results are determined by features of the generic\nensemble of such matrices, the CI ensemble of Altland and Zirnbauer originating\nin mesoscopic physics. We study some simple examples in detail, exhibiting\nvarious factors which can favor low or high scale supersymmetry breaking.", "category": "hep-th" }, { "text": "Aspects of holography and rotating AdS black holes: A comparison is made between the thermodynamics of weakly and strongly\ncoupled Yang-Mills with fixed angular momentum. The free energy of the strongly\ncoupled Yang-Mills is calculated by using a dual supergravity description\ncorresponding to a rotating black hole in an Anti de Sitter (AdS) background.\nAll thermodynamic quantities are shown have the same ratio of 3/4 (independent\nof angular momentum) between strong and weak coupling.", "category": "hep-th" }, { "text": "Wormhole interaction in 2d Horava-Lifshitz quantum gravity: A lattice regularization for the $2$d projectable Horava-Lifshitz (HL)\nquantum gravity is known to be the $2$d causal dynamical triangulations (CDT),\nand the $2$d CDT can be generalized so as to include all possible genus\ncontributions non-perturbatively. We show that in the context of HL gravity,\neffects coming from such a non-perturbative sum over topologies can be\nsuccessfully taken into account, if we quantize the $2$d projectable HL gravity\nwith a simple bi-local wormhole interaction. This conference paper is based on\nthe article, Phys. Lett. B 816 (2021), 136205.", "category": "hep-th" }, { "text": "The partition function versus boundary conditions and confinement in the\n Yang-Mills theory: We analyse dependence of the partition function on the boundary condition for\nthe longitudinal component of the electric field strength in gauge field\ntheories. In a physical gauge the Gauss law constraint may be resolved\nexplicitly expressing this component via an integral of the physical\ntransversal variables. In particular, we study quantum electrodynamics with an\nexternal charge and SU(2) gluodynamics. We find that only a charge distribution\nslowly decreasing at spatial infinity can produce a nontrivial dependence in\nthe Abelian theory. However, in gluodynamics for temperatures below some\ncritical value the partition function acquires a delta-function like dependence\non the boundary condition, which leads to colour confinement.", "category": "hep-th" }, { "text": "Code Properties of the Holographic Sierpinski Triangle: We study the holographic quantum error correcting code properties of a\nSierpinski Triangle-shaped boundary subregion in $AdS_4/CFT_3$. Due to existing\nno-go theorems in topological quantum error correction regarding fractal noise,\nthis gives holographic codes a specific advantage over topological codes. We\nthen further argue that a boundary subregion in the shape of the Sierpinski\ngasket in $AdS_5/CFT_4$ does not possess these holographic quantum error\ncorrection properties.", "category": "hep-th" }, { "text": "Categorical Pentagon Relations and Koszul Duality: The Kontsevich-Soibelman wall-crossing formula is known to control the\njumping behavior of BPS state counting indices in four-dimensional theories\nwith $\\mathcal{N}=2$ supersymmetry. The formula can take two equivalent forms:\na ``fermionic'' form with nice positivity properties and a ``bosonic'' form\nwith a clear physical interpretation. In an important class of examples, the\nfermionic form of the formula has a mathematical categorification involving PBW\nbases for a Cohomological Hall Algebra. The bosonic form lacks an analogous\ncategorification. We construct an equivalence of chain complexes which\ncategorifies the simplest example of the bosonic wall-crossing formula: the\nbosonic pentagon identity for the quantum dilogarithm. The chain complexes can\nbe promoted to differential graded algebras which we relate to the PBW bases of\nthe relevant CoHA by a certain quadratic duality. The equivalence of complexes\nthen follows from the relation between quadratic duality and Koszul duality. We\nargue that this is a special case of a general phenomenon: the bosonic\nwall-crossing formulae are categorified to equivalences of $A_\\infty$ algebras\nwhich are quadratic dual to PBW presentations of algebras which underlie the\nfermionic wall-crossing formulae. We give a partial interpretation of our\ndifferential graded algebras in terms of a holomorphic-topological version of\nBPS webs.", "category": "hep-th" }, { "text": "Two-dimensional topological field theories as taffy: In this paper we use trivial defects to define global taffy-like operations\non string worldsheets, which preserve the field theory. We fold open and closed\nstrings on a space X into open strings on products of multiple copies of X, and\nperform checks that the \"taffy-folded\" worldsheets have the same massless\nspectra and other properties as the original worldsheets. Such folding tricks\nare a standard method in the defects community; the novelty of this paper lies\nin deriving mathematical identities to check that e.g. massless spectra are\ninvariant in topological field theories. We discuss the case of the B model\nextensively, and also derive the same identities for string topology, where\nthey become statements of homotopy invariance. We outline analogous results in\nthe A model, B-twisted Landau-Ginzburg models, and physical strings. We also\ndiscuss the understanding of the closed string states as the Hochschild\nhomology of the open string algebra, and outline possible applications to\nelliptic genera.", "category": "hep-th" }, { "text": "Baby Skyrme model and fermionic zero modes: In this work we investigate some features of the fermionic sector of the\nsupersymmetric version of the baby Skyrme model. We find that, in the\nbackground of BPS compact Skyrmions, fermionic zero modes are confined to the\ndefect core. Further, we show that, while three SUSY generators are broken in\nthe defect core, SUSY is completely restored outside. We study also the effect\nof a D-term deformation of the model. Such a deformation allows for the\nexistence of fermionic zero modes and broken SUSY outside the compact defect.", "category": "hep-th" }, { "text": "Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits: We approach the topic of Classical group nilpotent orbits from the\nperspective of their moduli spaces, described in terms of Hilbert series and\ngenerating functions. We review the established Higgs and Coulomb branch quiver\ntheory constructions for A series nilpotent orbits. We present systematic\nconstructions for BCD series nilpotent orbits on the Higgs branches of quiver\ntheories defined by canonical partitions; this paper collects earlier work into\na systematic framework, filling in gaps and providing a complete treatment. We\nfind new Coulomb branch constructions for above minimal nilpotent orbits,\nincluding some based upon twisted affine Dynkin diagrams. We also discuss\naspects of 3d mirror symmetry between these Higgs and Coulomb branch\nconstructions and explore dualities and other relationships, such as\nHyperKahler quotients, between quivers. We analyse all Classical group\nnilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert\nseries and the Highest Weight Generating functions for their decompositions\ninto characters of irreducible representations and/or Hall Littlewood\npolynomials.", "category": "hep-th" }, { "text": "Renormalisation of \u03c6^4-theory on noncommutative R^4 to all orders: We present the main ideas and techniques of the proof that the\nduality-covariant four-dimensional noncommutative \\phi^4-model is\nrenormalisable to all orders. This includes the reformulation as a dynamical\nmatrix model, the solution of the free theory by orthogonal polynomials as well\nas the renormalisation by flow equations involving power-counting theorems for\nribbon graphs drawn on Riemann surfaces.", "category": "hep-th" }, { "text": "Anisotropic homogeneous string cosmology with two-loop corrections: The two-loop (order $\\alpha'$) $\\beta$-function equations, which are\nequivalent to the equations of motion of $\\alpha'$-corrected string effective\naction, are considered for anisotropic homogeneous space-times. These equations\nare solved for all Bianchi-type models in two schemes of effective action,\nnamely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then\nthe metric, dilaton and $B$-field are found at $\\alpha'$ perturbative\ncorrections.", "category": "hep-th" }, { "text": "Nuttier Bubbles: We construct new explicit solutions of general relativity from double\nanalytic continuations of Taub-NUT spacetimes. This generalizes previous\nstudies of 4-dimensional nutty bubbles. One 5-dimensional locally\nasymptotically AdS solution in particular has a special conformal boundary\nstructure of $AdS_3\\times S^1$. We compute its boundary stress tensor and\nrelate it to the properties of the dual field theory. Interestingly enough, we\nalso find consistent 6-dimensional bubble solutions that have only one timelike\ndirection. The existence of such spacetimes with non-trivial topology is\nclosely related to the existence of the Taub-NUT(-AdS) solutions with more than\none NUT charge. Finally, we begin an investigation of generating new solutions\nfrom Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality,\nwe provide new explicit time-dependent backgrounds in six dimensions.", "category": "hep-th" }, { "text": "Quantum Field Theory on Fock Projective Space: It is shown that some analog of the ``second quantization'' exists in the\nframework of CP(N) theory. I analyse conditions under that ``geometrical\nbosons'' may be identified with real physical fields. The compact character of\na state manifold should preserve the quantities of dynamical variables from\ndivergences.", "category": "hep-th" }, { "text": "Classification of N=6 superconformal theories of ABJM type: Studying the supersymmetry enhancement mechanism of Aharony, Bergman,\nJafferis and Maldacena, we find a simple condition on the gauge group\ngenerators for the matter fields. We analyze all possible compact Lie groups\nand their representations. The only allowed gauge groups leading to the\nmanifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x\nU(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s.\nMatter representations are restricted to be the (bi)fundamentals. As a\nbyproduct we obtain another proof of the complete classification of the three\nalgebras considered by Bagger and Lambert.", "category": "hep-th" }, { "text": "Hidden Symmetries of M Theory: A worldvolume action for membrane is considered to study the target space\nlocal symmetries. We introduce a set of generators of canonical transformations\nto exhibit the target space symmetries such as the general coordinate\ntransformation and the gauge transformation of antisymmetric tensor field.\nSimilar results are derived for type IIB string with manifestly\nS-duality-invariant worldsheet action.", "category": "hep-th" }, { "text": "Loop Transfer Matrix and Loop Quantum Mechanics: We extend the previous construction of loop transfer matrix to the case of\nnonzero self-intersection coupling constant $\\kappa$. The loop generalization\nof Fourier transformation allows to diagonalize transfer matrices depending on\nsymmetric difference of loops and express all eigenvalues of $3d$ loop transfer\nmatrix through the correlation functions of the corresponding 2d statistical\nsystem. The loop Fourier transformation allows to carry out analogy with\nquantum mechanics of point particles, to introduce conjugate loop momentum P\nand to define loop quantum mechanics. We also consider transfer matrix on $4d$\nlattice which describes propagation of memebranes. This transfer matrix can\nalso be diagonalized by using generalized Fourier transformation, and all its\neigenvalues are equal to the correlation functions of the corresponding $3d$\nstatistical system.", "category": "hep-th" }, { "text": "IIB matrix model and regularized big bang: The large-$N$ master field of the Lorentzian IIB matrix model can, in\nprinciple, give rise to a particular degenerate metric relevant to a\nregularized big bang. The length parameter of this degenerate metric is then\ncalculated in terms of the IIB-matrix-model length scale.", "category": "hep-th" }, { "text": "Footballs, Conical Singularities and the Liouville Equation: We generalize the football shaped extra dimensions scenario to an arbitrary\nnumber of branes. The problem is related to the solution of the Liouville\nequation with singularities and explicit solutions are presented for the case\nof three branes. The tensions of the branes do not need to be tuned with each\nother but only satisfy mild global constraints.", "category": "hep-th" }, { "text": "Emergence in Holographic Scenarios for Gravity: 'Holographic' relations between theories have become an important theme in\nquantum gravity research. These relations entail that a theory without gravity\nis equivalent to a gravitational theory with an extra spatial dimension. The\nidea of holography was first proposed in 1993 by Gerard 't Hooft on the basis\nof his studies of evaporating black holes. Soon afterwards the holographic\n'AdS/CFT' duality was introduced, which since has been intensively studied in\nthe string theory community and beyond. Recently, Erik Verlinde has proposed\nthat even Newton's law of gravitation can be related holographically to the\n`thermodynamics of information' on screens. We discuss these scenarios, with\nspecial attention to the status of the holographic relation in them and to the\nquestion of whether they make gravity and spacetime emergent. We conclude that\nonly Verlinde's scheme straightfowardly instantiates emergence. However,\nassuming a non-standard interpretation of AdS/CFT may create room for the\nemergence of spacetime and gravity there as well.", "category": "hep-th" }, { "text": "Unitary Minimal Liouville Gravity and Frobenius Manifolds: We study unitary minimal models coupled to Liouville gravity using Douglas\nstring equation. Our approach is based on the assumption that there exist an\nappropriate solution of the Douglas string equation and some special choice of\nthe resonance transformation such that necessary selection rules of the minimal\nLiouville gravity are satisfied. We use the connection with the Frobenius\nmanifold structure. We argue that the flat coordinates on the Frobenius\nmanifold are the most appropriate choice for calculating correlation functions.\nWe find the appropriate solution of the Douglas string equation and show that\nit has simple form in the flat coordinates. Important information is encoded in\nthe structure constants of the Frobenius algebra. We derive these structure\nconstants in the canonical coordinates and in the physically relevant domain in\nthe flat coordinates. We find the leading terms of the resonance transformation\nand express the coefficients of the resonance transformation in terms of Jacobi\npolynomials.", "category": "hep-th" }, { "text": "Iterative Non-iterative Integrals in Quantum Field Theory: Single scale Feynman integrals in quantum field theories obey difference or\ndifferential equations with respect to their discrete parameter $N$ or\ncontinuous parameter $x$. The analysis of these equations reveals to which\norder they factorize, which can be different in both cases. The simplest\nsystems are the ones which factorize to first order. For them complete solution\nalgorithms exist. The next interesting level is formed by those cases in which\nalso irreducible second order systems emerge. We give a survey on the latter\ncase. The solutions can be obtained as general $_2F_1$ solutions. The\ncorresponding solutions of the associated inhomogeneous differential equations\nform so-called iterative non-iterative integrals. There are known conditions\nunder which one may represent the solutions by complete elliptic integrals. In\nthis case one may find representations in terms of meromorphic modular\nfunctions, out of which special cases allow representations in the framework of\nelliptic polylogarithms with generalized parameters. These are in general\nweighted by a power of $1/\\eta(\\tau)$, where $\\eta(\\tau)$ is Dedekind's\n$\\eta$-function. Single scale elliptic solutions emerge in the\n$\\rho$-parameter, which we use as an illustrative example. They also occur in\nthe 3-loop QCD corrections to massive operator matrix elements and the massive\n3-loop form factors.", "category": "hep-th" }, { "text": "Black Hole Condensation and Duality in String Theory: This is a non-technical version of a talk presented at the conference,\n\"S-Duality and Mirror Symmetry in String Theory\" Trieste, June, 1996 which will\nappear in the proceedings.", "category": "hep-th" }, { "text": "Non-gravitational exceptional supermultiplets: We examine non-gravitational minimal supermultiplets which are based on the\ntensor gauge fields appearing as matter fields in exceptional generalised\ngeometry. When possible, off-shell multiplets are given. The fields in the\nmultiplets describe non-gravitational parts of the internal dynamics of\ncompactifications of M-theory. In flat backgrounds, they enjoy a global\nU-duality symmetry, but also provide multiplets with a possibility of coupling\nto a generalised exceptional geometry.", "category": "hep-th" }, { "text": "Spin-Statistics Correlations in Various Noncommutative Field Theories: In this thesis we study field theories written on a particular model of\nnoncommutative spacetime, the Groenewold-Moyal (GM) plane. We start with\nbriefly reviewing the novel features of field theories on GM plane e.g. the\n$\\ast$-product, restoration of Poincar\\'e-Hopf symmetry and twisted commutation\nrelations. We then discuss our work on renormalization of field theories on GM\nplane. We show that any generic noncommutative theory involving pure matter\nfields with polynomial interactions, is a renormalizable theory if the\nanalogous commutative theory is renormalizable. We further show that all such\nnoncommutative theories will have same fixed points and $\\beta$-functions for\nthe couplings, as that of the analogous commutative theory. The unique feature\nof these field theories is the twisted statistics obeyed by the particles.\nMotivated by it, we look at the possibility of twisted statistics by deforming\ninternal symmetries instead of spacetime symmetries. We construct two different\ntwisted theories which can be viewed as internal symmetry analogue of the GM\nplane and dipole field theories which arise in the low energy limit of certain\nstring configurations. We further study their various properties like the issue\nof causality and the scattering formalism. Having studied the mathematical\nproperties of noncommutative and twisted internal symmetries we move on to\ndiscuss their potential phenomenological signatures. We first discuss the\nnoncommutative thermal correlation functions and show that because of the\ntwisted statistics, all correlation functions except two-point function get\nmodified. Finally we discuss the modifications in Hanbury-Brown Twiss (HBT)\ncorrelation functions due to twisted statistics on GM plane and the potential\nof observing signatures of noncommutativity by doing a HBT correlation\nexperiment with Ultra High Energy Cosmic Rays (UHECRs).", "category": "hep-th" }, { "text": "Thermodynamics of Rotating Black Branes in Gauss-Bonnet-nonlinear\n Maxwell Gravity: We consider the Gauss-Bonnet gravity in the presence of a new class of\nnonlinear electromagnetic field, namely, power Maxwell invariant. By use of a\nsuitable transformation, we obtain a class of real rotating solutions with $k$\nrotation parameters and investigate some properties of the solutions such as\nexistence of singularity(ies) and asymptotic behavior of them. Also, we\ncalculate the finite action, thermodynamic and conserved quantities of the\nsolutions and using the the Smarr-type formula to check the first law of\nthermodynamics.", "category": "hep-th" }, { "text": "Reply to `Can infrared gravitons screen $\u039b$?': We reply to the recent criticism by Garriga and Tanaka of our proposal that\nquantum gravitational loop corrections may lead to a secular screening of the\neffective cosmological constant. Their argument rests upon a renormalization\nscheme in which the composite operator $(R \\sqrt{-g} - 4 \\Lambda \\sqrt{-g}\n)_{\\rm ren}$ is defined to be the trace of the renormalized field equations.\nAlthough this is a peculiar prescription, we show that it {\\it does not\npreclude secular screening}. Moreover, we show that a constant Ricci scalar\n{\\it does not even classically} imply a constant expansion rate. Other\nimportant points are: (1) the quantity $R_{\\rm ren}$ of Garriga and Tanaka is\nneither a properly defined composite operator, nor is it constant; (2) gauge\ndependence does not render a Green's function devoid of physical content; (3)\nscalar models on a non-dynamical de Sitter background (for which there is no\ngauge issue) can induce arbitrarily large secular contributions to the stress\ntensor; (4) the same secular corrections appear in observable quantities in\nquantum gravity; and (5) the prospects seem good for deriving a simple\nstochastic formulation of quantum gravity in which the leading secular effects\ncan be summed and for which the expectation values of even complicated, gauge\ninvariant operators can be computed at leading order.", "category": "hep-th" }, { "text": "Topological Sigma Models with H-Flux: We investigate the topological theory obtained by twisting the N=(2,2)\nsupersymmetric nonlinear sigma model with target a bihermitian space with\ntorsion. For the special case in which the two complex structures commute, we\nshow that the action is a Q-exact term plus a quasi-topological term. The\nquasi-topological term is locally given by a closed two-form which corresponds\nto a flat gerbe-connection and generalises the usual topological term of the\nA-model. Exponentiating it gives a Wilson surface, which can be regarded as a\ngeneralization of a Wilson line. This makes the quantum theory globally\nwell-defined.", "category": "hep-th" }, { "text": "Supertwistor formulation for higher dimensional superstrings: Considered is the formulation for the superstring action in 6 and 10\ndimensions involving supertwistor variables that appropriately generalize\n4-dimensional Ferber supertwistors. Equations of motion and kappa-symmetry\ntransformations in terms of the supertwistors are derived. It is shown that\ncovariant kappa-symmetry gauge fixing reduces superstring action to the\nquadratic one with respect to supertwistors. Upon gauge fixing remaining\nsymmetries it can be cast into the form of the light-cone gauge Green-Schwarz\nsuperstring action.", "category": "hep-th" }, { "text": "Supersymmetric gauge theory and the Yangian: This paper develops a new connection between supersymmetric gauge theories\nand the Yangian. I show that a twisted, deformed version of the pure N=1\nsupersymmetric gauge theory is controlled by the Yangian, in the same way that\nChern-Simons theory is controlled by the quantum group. This result is used to\ngive an exact calculation, in perturbation theory, of the expectation value of\na certain net of n+m Wilson operators in the deformed N=1 gauge theory. This\nexpectation value coincides with the partition function of a spin-chain\nintegrable lattice model on an n-by-m doubly-periodic lattice.", "category": "hep-th" }, { "text": "Perturbations of General Relativity to All Orders and the General\n $n^{\\rm th}$ Order Terms: We derive all-order expressions for perturbations of the Einstein-Hilbert\naction and the Einstein equation with the general $n$-th order terms. To this\nend, we employ Cheung and Remmen's perturbation conventions both in tensor\ndensity and the usual metric tensor formalisms, including the Einstein-dilaton\ntheory. Remarkably, we find minimal building blocks that generate the entire\nperturbations for each of our formulations. We show that the number of terms of\nperturbations grows linearly as the order of perturbations increases. We regard\nour results as the reference and discuss how to derive perturbations in other\nconventions from the reference. As a consistency check, we compute graviton\nscattering amplitudes using the perturbiner method based on the perturbative\nEinstein equation. Finally we discuss how to generalise the results to curved\nbackgrounds and incorporate additional matter.", "category": "hep-th" }, { "text": "A New Perspective on DGP Gravity: We examine brane induced gravity on codimension-1 branes, a.k.a DGP gravity,\nas a theory of five-dimensional gravity containing a certain class\nfour-dimensional branes. From this perspective, the model suffers from a number\nof pathologies which went unnoticed before. By generalizing the 5D geometry\nfrom Minkowski to Schwarzschild, we find that when the bulk mass is large\nenough, the brane hits a pressure singularity at finite radius. Further, on the\nself-accelerating branch, the five-dimensional energy is unbounded from below,\nimplying that the self-accelerating backgrounds are unstable. Even in an empty\nMinkowski bulk, standard Euclidean techniques suggest that the spontaneous\nnucleation of self-accelerating branes is unsuppressed. If so, quantum effects\nwill strongly modify any classical intuition about the theory. We also note\nthat unless considered as Z_2-orbifold boundaries, self-accelerating branes\ncorrespond to `wormhole' configurations, which introduces the usual problematic\nissues associated with wormholes. Altogether these pathologies present a\nserious challenge that any proposed UV completion of the DGP model must\novercome.", "category": "hep-th" }, { "text": "Instantons, Monopoles and Toric HyperKaehler Manifolds: In this paper, the metric on the moduli space of the k=1 SU(n) periodic\ninstanton -or caloron- with arbitrary gauge holonomy at spatial infinity is\nexplicitly constructed. The metric is toric hyperKaehler and of the form\nconjectured by Lee and Yi. The torus coordinates describe the residual\nU(1)^{n-1} gauge invariance and the temporal position of the caloron and can\nalso be viewed as the phases of n monopoles that constitute the caloron. The\n(1,1,..,1) monopole is obtained as a limit of the caloron. The calculation is\nperformed on the space of Nahm data, which is justified by proving the\nisometric property of the Nahm construction for the cases considered. An\nalternative construction using the hyperKaehler quotient is also presented. The\neffect of massless monopoles is briefly discussed.", "category": "hep-th" }, { "text": "Energy-momentum tensor of bouncing gravitons: In models of the Universe with extra dimensions gravity propagates in the\nwhole space-time. Graviton production by matter on the brane is significant in\nthe early hot Universe. In a model of 3-brane with matter embedded in 5D\nspace-time conditions for gravitons emitted from the brane to the bulk to\nreturn back to the brane are found. For a given 5-momentum of graviton falling\nback to the brane the interval between the times of emission and return to the\nbrane is calculated. A method to calculate contribution to the energy-momentum\ntensor from multiple graviton bouncings is developed. Explicit expressions for\ncontributions to the energy-momentum tensor of gravitons which have made one,\ntwo and three bounces are obtained and their magnitudes are numerically\ncalculated. These expressions are used to solve the evolution equation for dark\nradiation. A relation connecting reheating temperature and the scale of extra\ndimension is obtained. For the reheating temperature $T_R\\sim 10^6 GeV$ we\nestimate the scale of extra dimension $\\m$ to be of order $10^{-9} GeV\\,\\,\\,\n(\\m^{-1}\\sim 10^{-5} cm )$.", "category": "hep-th" }, { "text": "Quantization of the anisotropic conformal Horava theory: We perform the Batalin-Fradkin-Vilkovisky quantization of the anisotropic\nconformal Horava theory in d spatial dimensions. We introduce a model with a\nconformal potential suitable for any dimension. We define an anisotropic and\nlocal gauge-fixing condition that accounts for the spatial diffeomorphisms and\nthe anisotropic Weyl transformations. We show that the BRST transformations can\nbe expressed mainly in terms of a spatial diffeomorphism along a ghost field\nplus a conformal transformation with another ghost field as argument. We study\nthe quantum Lagrangian in the d=2 case, obtaining that all propagators are\nregular, except for the fields associated with the measure of the second-class\nconstraints. This behavior is qualitatively equal to the nonconformal case.", "category": "hep-th" }, { "text": "Finite Tensor Deformations of Supergravity Solitons: We consider brane solutions where the tensor degrees of freedom are excited.\nExplicit solutions to the full non-linear supergravity equations of motion are\ngiven for the M5 and D3 branes, corresponding to finite selfdual tensor or\nBorn-Infeld field strengths. The solutions are BPS-saturated and\nhalf-supersymmetric. The resulting metric space-times are analysed.", "category": "hep-th" }, { "text": "Nonperturbative black hole entropy and Kloosterman sums: Non-perturbative quantum corrections to supersymmetric black hole entropy\noften involve nontrivial number-theoretic phases called Kloosterman sums. We\nshow how these sums can be obtained naturally from the functional integral of\nsupergravity in asymptotically AdS_2 space for a class of black holes. They are\nessentially topological in origin and correspond to charge-dependent phases\narising from the various gauge and gravitational Chern-Simons terms and\nboundary Wilson lines evaluated on Dehn-filled solid 2-torus. These corrections\nare essential to obtain an integer from supergravity in agreement with the\nquantum degeneracies, and reveal an intriguing connection between topology,\nnumber theory, and quantum gravity. We give an assessment of the current\nunderstanding of quantum entropy of black holes.", "category": "hep-th" }, { "text": "Sommerfeld effect as the vertex correction in three-dimensional space: It is shown that the correction to the vertex for fermion pair annihilation\nand production in the low-energy region is equal to the value of the wave\nfunction for the two-body system at the origin. The procedure also shows\ndirectly that the emergence of the Sommerfeld effect in quantum mechanics is\nthe product of the reduction of the vertex correction from four spacetime\ndimensions to three-dimensional space. Meanwhile, the reciprocal wave function\nis introduced into quantum mechanics.", "category": "hep-th" }, { "text": "Matching the circular Wilson loop with dual open string solution at\n 1-loop in strong coupling: We compute the 1-loop correction to the effective action for the string\nsolution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, the\nmethod we use can be applied whenever the two dimensional spectral problem\nfactorizes, to regularize and define the fluctuation determinants in terms of\nsolutions of one-dimensional differential equations. A such it can be applied\nto non-homogeneous solutions both for open and closed strings and to various\nboundary conditions. In the case of the circular Wilson loop, we obtain, for\nthe 1-loop partition function a result which up to a factor of two matches the\nexpectation from the exact gauge theory computation. The discrepancy can be\nattributed to an overall constant in the string partition function coming from\nthe normalization of zero modes, which we have not fixed.", "category": "hep-th" }, { "text": "Boundary Effects in Quantum Physics: We analyze the role of boundaries in the infrared behavior of quantum field\ntheories. By means of a novel method we calculate the vacuum energy for a\nmassless scalar field confined between two homogeneous parallel plates with the\nmost general type of boundary properties. This allows the discrimination\nbetween boundary conditions which generate attractive or repulsive Casimir\nforces between the plates. In the interface between both regimes we find a very\ninteresting family of boundary conditions which do not induce any type of\nCasimir force. We analyze the effect of the renormalization group flow on these\nboundary conditions. Even if the Casimirless conformal invariant conditions are\nphysically unstable under renormalization group flow they emerge as a new set\nof conformally invariant boundary conditions which are anomaly free.", "category": "hep-th" }, { "text": "Vibrational modes of Q-balls: We study linear perturbations of classically stable Q-balls in theories\nadmitting analytic solutions. Although the corresponding boundary value problem\nis non-Hermitian, the analysis of perturbations can also be performed\nanalytically in certain regimes. We show that in theories with the flat\npotential, large Q-balls possess soft excitations. We also find a specific\nvibrational mode for Q-balls with a near-critical charge, where the\nperturbation theory for excitations can be developed. Comparing with the\nresults on stability of Q-balls provides additional checks of our analysis.", "category": "hep-th" }, { "text": "Exploring the Abelian 4D, $\\mathcal{N}$ = 4 Vector-Tensor Supermultiplet\n and Its Off-Shell Central Charge Structure: An abelian 4D, $\\mathcal{N}$ = 4 vector supermultiplet allows for a duality\ntransformation to be applied to one of its spin-0 states. The resulting theory\ncan be described as an abelian 4D, $\\mathcal{N}$ = 4 vector-tensor\nsupermultiplet. It is seen to decompose into a direct sum of an off-shell 4D,\n$\\mathcal{N}$ = 2 vector supermultiplet and an off-shell 4D, $\\mathcal{N}$ = 2\ntensor supermultiplet. The commutator algebra of the other two supersymmetries\nare still found to be on-shell. However, the central charge structure in the\nresulting 4D, $\\mathcal{N}$ = 4 vector-tensor supermultiplet is considerably\nsimpler that that of the parent abelian 4D, $\\mathcal{N}$ = 4 vector\nsupermultiplet. This appears to be due to the replacement of the usual SO(4)\nsymmetry associated with the abelian 4D, $\\mathcal{N}$ = 4 vector\nsupermultiplet being replaced by a\nGL(2,$\\mathbb{R}$)$\\otimes$GL(2,$\\mathbb{R}$) symmetry in the 4D, $\\mathcal{N}$\n= 4 vector-tensor supermultiplet. The $Mathematica$ code detailing the\ncalculations is available open-source at the HEPTHools Data Repository on\nGitHub.", "category": "hep-th" }, { "text": "One-Loop N-Point Superstring Amplitudes with Manifest d=4 Supersymmetry: The hybrid formalism for the superstring is used to compute one-loop\namplitudes with an arbitrary number of external d=4 supergravity states. These\none-loop N-point amplitudes are expressed as Koba-Nielsen-like formulas with\nmanifest d=4 supersymmetry.", "category": "hep-th" }, { "text": "Symmetries of post-Galilean expansions: In this letter we study an infinite extension of the Galilei symmetry group\nin any dimension that can be thought of as a non-relativistic or post-Galilean\nexpansion of the Poincare symmetry. We find an infinite-dimensional vector\nspace on which this generalized Galilei group acts and usual Minkowski space\ncan be modeled by our construction. We also construct particle and string\nactions that are invariant under these transformations.", "category": "hep-th" }, { "text": "On quantum corrections to geodesics in de-Sitter spacetime: We find a coordinate-independent wave-packet solution of the massive\nKlein-Gordon equation with the conformal coupling to gravity in the de-Sitter\nuniverse. This solution can locally be represented through the superposition of\npositive-frequency plane waves at any space-time point, assuming that the\nscalar-field mass $M$ is much bigger than the de-Sitter Hubble constant $H$.\nThe solution is also shown to be related to the two-point function in the\nde-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over\ncosmological times, depending on the ratio of $M$ and $H$. In doing so, we find\nthat this wave packet propagates like a point-like particle of the same mass if\n$M \\ggg H$, but, if otherwise, the wave packet behaves highly non-classically.", "category": "hep-th" }, { "text": "Trouble Finding the Optimal AdS/QCD: In the bottom-up approach to AdS/QCD based on a five-dimensional gravity\ndilaton action the exponential of the dilaton field is usually identified as\nthe strong or 't Hooft coupling. There is currently no model known which fits\nthe measurements of the running coupling and lattice results for pressure at\nthe same time. With a one parametric toy model we demonstrate the effect of\nfitting the pressure on the coupling and vice versa.", "category": "hep-th" }, { "text": "Chiral Symmetry Breaking in the $d=3$ Nambu-Jona-Lasinio Model in Curved\n Spacetime: The phase structure of the $d=3$ Nambu-Jona-Lasinio model in curved spacetime\nis considered to leading order in the $1/N$--expansion and in the linear\ncurvature approximation. The possibility of a curvature-induced first-order\nphase transition is investigated numerically. The dynamically generated\nfermionic mass is calculated for some values of the curvature.", "category": "hep-th" }, { "text": "Symplectic Fermions: We study two-dimensional conformal field theories generated from a\n``symplectic fermion'' - a free two-component fermion field of spin one - and\nconstruct the maximal local supersymmetric conformal field theory generated\nfrom it. This theory has central charge c=-2 and provides the simplest example\nof a theory with logarithmic operators.\n Twisted states with respect to the global SL(2,C)-symmetry of the symplectic\nfermions are introduced and we describe in detail how one obtains a consistent\nset of twisted amplitudes. We study orbifold models with respect to finite\nsubgroups of SL(2,C) and obtain their modular invariant partition functions. In\nthe case of the cyclic orbifolds explicit expressions are given for all two-,\nthree- and four-point functions of the fundamental fields. The C_2-orbifold is\nshown to be isomorphic to the bosonic local logarithmic conformal field theory\nof the triplet algebra encountered previously. We discuss the relation of the\nC_4-orbifold to critical dense polymers.", "category": "hep-th" }, { "text": "Dual gravity and E11: We consider the equation of motion in the gravity sector that arises from the\nnon-linear realisation of the semi-direct product of E11 and its first\nfundamental representation, denoted by l1, in four dimensions. This equation is\nfirst order in derivatives and at low levels relates the usual field of gravity\nto a dual gravity field. When the generalised space-time is restricted to be\nthe usual four dimensional space-time we show that this equation does correctly\ndescribe Einstein's theory at the linearised level. We also comment on previous\ndiscussions of dual gravity.", "category": "hep-th" }, { "text": "Anomaly inflow and RR anomalous couplings: We review the anomaly inflow mechanism on D-branes and O-planes. In\nparticular, we compute the one-loop world-volume anomalies and derive the RR\nanomalous couplings required for their cancellation.", "category": "hep-th" }, { "text": "A general holographic insulator/superconductor model away from the probe\n limit: We investigate holographic phase transitions affected by dark matter sector\nin the AdS soliton background away from the probe limit. When neglecting\nbackreaction, the scalar charge q can be scaled unity without loss of\ngenerality. While considering backreaction in this work, we obtain much more\nricher physics by choosing various scalar charge q. Firstly, we observe\nunstable retrograde condensation appears due to the dark matter sector and also\nderive stable conditions. For stable solutions, we find that the larger\ncoupling parameter $\\alpha$ makes the gap of condensation shallower and the\ncritical chemical potential keeps as a constant with a large scalar charge q,\nwhich is similar to cases in the probe limit. In contrast, the dark matter\nsector could affect the critical chemical potential and the order of phase\ntransitions for very small charge q. We also arrive at the same conclusion from\nthe holographic topological entanglement entropy approach. Moreover, we state\nthat the entanglement entropy approach is especially powerful in studying the\neffects of the dark matter sector in this general insulator/superconductor\nsystem.", "category": "hep-th" }, { "text": "Black hole entropy and the renormalization group: Four decades after its first postulation by Bekenstein, black hole entropy\nremains mysterious. It has long been suggested that the entanglement entropy of\nquantum fields on the black hole gravitational background should represent at\nleast an important contribution to the total Bekenstein-Hawking entropy, and\nthat the divergences in the entanglement entropy should be absorbed in the\nrenormalization of the gravitational couplings. In this talk, we describe how\nan improved understanding of black hole entropy is obtained by combining these\nnotions with the renormalization group. By introducing an RG flow scale, we\ninvestigate whether the total entropy of the black hole can be partitioned in a\n\"gravitational\" part related to the flowing gravitational action, and a\n\"quantum\" part related to the unintegrated degrees of freedom. We describe the\nrealization of this idea for free fields, and the complications and\nqualifications arising for interacting fields.", "category": "hep-th" }, { "text": "Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic\n Classes: We investigate the generic 3D topological field theory within AKSZ-BV\nframework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly\ncocycles of the Lie algebra of formal Hamiltonian vector fields and we argue\nthat the perturbative partition function gives rise to secondary characteristic\nclasses. We investigate a toy model which is an odd analogue of Chern-Simons\ntheory, and we give some explicit computation of two point functions and show\nthat its perturbation theory is identical to the Chern-Simons theory. We give\nconcrete example of the homomorphism taking Lie algebra cocycles to\nQ-characteristic classes, and we reinterpreted the Rozansky-Witten model in\nthis light.", "category": "hep-th" }, { "text": "On algebraic structures in supersymmetric principal chiral model: Using the Poisson current algebra of the supersymmetric principal chiral\nmodel, we develop the algebraic canonical structure of the model by evaluating\nthe fundamental Poisson bracket of the Lax matrices that fits into the rs\nmatrix formalism of non-ultralocal integrable models. The fundamental Poisson\nbracket has been used to compute the Poisson bracket algebra of the monodromy\nmatrix that gives the conserved quantities in involution.", "category": "hep-th" }, { "text": "The simplest non-associative generalization of supersymmetry: Nonassociative generalization of supersymmetry is suggested. 3- and 4-point\nassociators for supersymmetric generators are considered. On the basis of zero\nJacobiators for three supersymmetric generators, we have obtained the simplest\nform of 3-point associators. The connection between 3- and 4-point associators\nis considered. On the basis of this connection, 4-point associators are\nobtained. The Jacobiators for the product of four supersymmetric generators are\ncalculated. We discuss the possible physical meaning of numerical coefficients\npresented on the right-hand sides of associators. The possible connection\nbetween supersymmetry, hidden variables, and nonassociativity is discussed.", "category": "hep-th" }, { "text": "Probing the Constituent Structure of Black Holes: Based on recent ideas, we propose a framework for the description of black\nholes in terms of constituent graviton degrees of freedom. Within this\nformalism a large black hole can be understood as a bound state of N\nlongitudinal gravitons. In this context black holes are similar to baryonic\nbound states in quantum chromodynamics which are described by fundamental quark\ndegrees of freedom. As a quantitative tool we employ a quantum bound state\ndescription originally developed in QCD that allows to consider black holes in\na relativistic Hartree like framework. As an application of our framework we\ncalculate the cross section for scattering processes between graviton emitters\noutside of a Schwarzschild black hole and absorbers in its interior, that is\ngravitons. We show that these scatterings allow to directly extract structural\nobservables such as the momentum distribution of black hole constituents.", "category": "hep-th" }, { "text": "Universality of anomalous conductivities in theories with\n higher-derivative holographic duals: Anomalous chiral conductivities in theories with global anomalies are\nindependent of whether they are computed in a weakly coupled quantum (or\nthermal) field theory, hydrodynamics, or at infinite coupling from holography.\nWhile the presence of dynamical gauge fields and mixed, gauge-global anomalies\ncan destroy this universality, in their absence, the non-renormalisation of\nanomalous Ward identities is expected to be obeyed at all intermediate coupling\nstrengths. In holography, bulk theories with higher-derivative corrections\nincorporate coupling constant corrections to the boundary theory observables in\nan expansion around infinite coupling. In this work, we investigate the\ncoupling constant dependence and universality of anomalous conductivities (and\nthus of the anomalous Ward identities) in general, four-dimensional systems\nthat possess asymptotically anti-de Sitter holographic duals with a\nnon-extremal black brane in five dimensions, and anomalous transport introduced\ninto the boundary theory via the bulk Chern-Simons action. We show that in bulk\ntheories with arbitrary gauge- and diffeomorphism-invariant higher-derivative\nactions, anomalous conductivities, which can incorporate an infinite series of\n(inverse) coupling constant corrections, remain universal. Owing to the\nexistence of the membrane paradigm, the proof reduces to a construction of bulk\neffective theories at the horizon and the boundary. It only requires us to\nimpose the condition of horizon regularity and correct boundary conditions on\nthe fields. We also discuss ways to violate the universality by violating\nconditions for the validity of the membrane paradigm, in particular, by adding\nmass to the vector fields (a case with a mixed, gauge-global anomaly) and in\nbulk geometries with a naked singularity.", "category": "hep-th" }, { "text": "Maximally Supersymmetric Yang-Mills in five dimensions in light-cone\n superspace: We formulate maximally supersymmetric Yang-Mills theory in five dimensions in\nlight-cone superspace. The light-cone Hamiltonian is of the quadratic form and\nthe theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory\nin four dimensions. We specifically study three-point counterterms and show how\nthese counterterms vanish on-shell. This study is a preliminary to set up the\ntechnique in order to study possible four-point counterterms.", "category": "hep-th" }, { "text": "Weyl Card Diagrams: To capture important physical properties of a spacetime we construct a new\ndiagram, the card diagram, which accurately draws generalized Weyl spacetimes\nin arbitrary dimensions by encoding their global spacetime structure,\nsingularities, horizons, and some aspects of causal structure including null\ninfinity. Card diagrams draw only non-trivial directions providing a clearer\npicture of the geometric features of spacetimes as compared to Penrose\ndiagrams, and can change continuously as a function of the geometric\nparameters. One of our main results is to describe how Weyl rods are\ntraversable horizons and the entirety of the spacetime can be mapped out. We\nreview Weyl techniques and as examples we systematically discuss properties of\na variety of solutions including Kerr-Newman black holes, black rings,\nexpanding bubbles, and recent spacelike-brane solutions. Families of solutions\nwill share qualitatively similar cards. In addition we show how card diagrams\nnot only capture information about a geometry but also its analytic\ncontinuations by providing a geometric picture of analytic continuation. Weyl\ntechniques are generalized to higher dimensional charged solutions and applied\nto generate perturbations of bubble and S-brane solutions by Israel-Khan rods.\nThis paper is a condensed and simplified presentation of the card diagrams in\nhep-th/0409070.", "category": "hep-th" }, { "text": "Universal horizons in maximally symmetric spaces: Universal horizons in Ho\\v{r}ava-Lifshitz gravity and Einstein-{\\ae}ther\ntheory are the equivalent of causal horizons in general relativity and appear\nto have many of the same properties, including a first law of horizon\nthermodynamics and thermal radiation. Since universal horizons are infrared\nsolutions of a putative power counting renormalizable quantum gravitational\ntheory, fully understanding their thermodynamics will shed light on the\ninterplay between black hole thermodynamics and quantum gravity. In this paper,\nwe provide a complete classification, including asymptotic charges, of all four\ndimensional static and spherically symmetric universal horizon solutions with\nmaximally symmetric asymptotics -- the equivalents of the Schwarzschild,\nSchwarzschild de Sitter or Schwarzschild anti-de Sitter spacetimes.\nAdditionally we derive the associated first laws for the universal horizon\nsolutions. Finally we prove that independent of asymptotic boundary conditions,\nany spherically symmetric solution in Ho\\v{r}ava-Lifshitz gravity with a\nuniversal horizon is also a solution of Einstein-{\\ae}ther theory, thereby\nbroadening and complementing the known equivalence region of the solution\nspaces.", "category": "hep-th" }, { "text": "On the Natural Gauge Fields of Manifolds: The gauge symmetry inherent in the concept of manifold has been discussed.\nWithin the scope of this symmetry the linear connection or displacement field\ncan be considered as a natural gauge field on the manifold. The gauge invariant\nequations for the displacement field have been derived. It has been shown that\nthe energy-momentum tensor of this field conserves and hence the displacement\nfield can be treated as one that transports energy and gravitates. To show the\nexistence of the solutions of the field equations we have derived the general\nform of the displacement field in Minkowski space-time which is invariant under\nrotation and space and time inversion. With this anzats we found\nspherically-symmetric solutions of the equations in question.", "category": "hep-th" }, { "text": "Twisted topological structures related to M-branes II: Twisted Wu and\n Wu^c structures: Studying the topological aspects of M-branes in M-theory leads to various\nstructures related to Wu classes. First we interpret Wu classes themselves as\ntwisted classes and then define twisted notions of Wu structures. These\ngeneralize many known structures, including Pin^- structures, twisted Spin\nstructures in the sense of Distler-Freed-Moore, Wu-twisted differential\ncocycles appearing in the work of Belov-Moore, as well as ones introduced by\nthe author, such as twisted Membrane and twisted String^c structures. In\naddition, we introduce Wu^c structures, which generalize Pin^c structures, as\nwell as their twisted versions. We show how these structures generalize and\nencode the usual structures defined via Stiefel-Whitney classes.", "category": "hep-th" }, { "text": "The complete one-loop spin chain for N=2 Super-Yang-Mills: We show that the complete planar one-loop mixing matrix of the N=2 Super\nYang--Mills theory can be obtained from a reduction of that of the N=4 theory.\nFor composite operators of scalar fields, this yields an anisotropic XXZ spin\nchain, whose spectrum of excitations displays a mass gap.", "category": "hep-th" }, { "text": "The Family Problem: Hints from Heterotic Line Bundle Models: Within the class of heterotic line bundle models, we argue that N=1 vacua\nwhich lead to a small number of low-energy chiral families are preferred. By\nimposing an upper limit on the volume of the internal manifold, as required in\norder to obtain finite values of the four-dimensional gauge couplings, and\nvalidity of the supergravity approximation we show that, for a given manifold,\nonly a finite number of line bundle sums are consistent with supersymmetry. By\nexplicitly scanning over this finite set of line bundle models on certain\nmanifolds we show that, for a sufficiently small volume of the internal\nmanifold, the family number distribution peaks at small values, consistent with\nthree chiral families. The relation between the maximal number of families and\nthe gauge coupling is discussed, which hints towards a possible explanation of\nthe family problem.", "category": "hep-th" }, { "text": "From Fusion Hierarchy to Excited State TBA: Functional relations among the fusion hierarchy of quantum transfer matrices\ngive a novel derivation of the TBA equations, namely without string hypothesis.\nThis is demonstrated for two important models of 1D highly correlated electron\nsystems, the supersymmetric $t-J$ model and the supersymmetric extended Hubbard\nmodel. As a consequence, \"the excited state TBA\" equations, which characterize\ncorrelation lengths, are explicitly derived for the $t-J$ model. To the\nauthors' knowledge, this is the first explicit derivation of excited state TBA\nequations for 1D lattice electron systems.", "category": "hep-th" }, { "text": "Hemisphere Partition Function and Analytic Continuation to the Conifold\n Point: We show that the hemisphere partition function for certain U(1) gauged linear\nsigma models (GLSMs) with D-branes is related to a particular set of\nMellin-Barnes integrals which can be used for analytic continuation to the\nsingular point in the K\\\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY)\nprojective hypersurface. We directly compute the analytic continuation of the\nfull quantum corrected central charge of a basis of geometric D-branes from the\nlarge volume to the singular point. In the mirror language this amounts to\ncompute the analytic continuation of a basis of periods on the mirror CY to the\nconifold point. However, all calculations are done in the GLSM and we do not\nhave to refer to the mirror CY. We apply our methods explicitly to the cubic,\nquartic and quintic CY hypersurfaces.", "category": "hep-th" }, { "text": "A solution of 2D QCD at Finite $N$ using a conformal basis: We study 2D QCD with a fundamental fermion at small-$N$ using the recently\nproposed conformal basis approach. We find that effective conformal dominance\nstill holds, namely that the spectrum converges efficiently, with high\nscaling-dimension operators decoupling exponentially quickly from the stable\nsingle-particle states. Consequently, for these stable bound states, accurate,\nanalytic expressions for wavefunctions and parton distribution functions can be\ngiven, even for $N=3$.", "category": "hep-th" }, { "text": "Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional\n Toroidal Manifolds: We discuss heterotic strings on Z_2 x Z_2 orbifolds of non factorisable\nsix-tori. Although the number of fixed tori is reduced as compared to the\nfactorisable case, Wilson lines are still needed for the construction of three\ngeneration models. An essential new feature is the straightforward appearance\nof three generation models with one generation per twisted sector. We\nillustrate our general arguments for the occurrence of that property by an\nexplicit example. Our findings give further support for the conjecture that\nfour dimensional heterotic strings formulated at the free fermionic point are\nrelated to Z_2 x Z_2 orbifolds.", "category": "hep-th" }, { "text": "The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and\n Celestial Amplitudes: The soft limits of scattering amplitudes have been extensively studied due to\ntheir essential role in the computation of physical observables in collider\nphysics. The universal factorisation that occurs in these kinematic limits has\nbeen shown to be related to conservation laws associated with asymptotic, or\nlarge, gauge symmetries. This connection has led to a deeper understanding of\nthe symmetries of gauge and gravitational theories and to a reformulation of\nscattering amplitudes in a basis of boost eigenstates which makes manifest the\ntwo-dimensional global conformal symmetry of the celestial sphere. The recast,\nor celestial, amplitudes possess many of the properties of conformal field\ntheory correlation functions which has suggested a path towards a holographic\ndescription of asymptotically flat spacetimes. In this review we consider these\ninterconnected developments in our understanding of soft theorems, asymptotic\nsymmetries and conformal field theory with a focus on the structure and\nsymmetries of the celestial amplitudes and their holographic interpretation.", "category": "hep-th" }, { "text": "Feynman rules for Coulomb gauge QCD: The Coulomb gauge in nonabelian gauge theories is attractive in principle,\nbut beset with technical difficulties in perturbation theory. In addition to\nordinary Feynman integrals, there are, at 2-loop order, Christ-Lee (CL) terms,\nderived either by correctly ordering the operators in the Hamiltonian, or by\nresolving ambiguous Feynman integrals. Renormalization theory depends on the\nsubgraph structure of ordinary Feynamn graphs. The CL terms do not have\nsubgraph structure. We show how to carry out enormalization in the presene of\nCL terms, by re-expressing these as `pseudo-Feynman' inegrals. We also explain\nhow energy divergences cancel.", "category": "hep-th" }, { "text": "The evolution of the universe from noncompact Kaluza-Klein theory: We develope a 5D mechanism inspired in the Campbell's theorem, to explain the\n(neutral scalar field governed) evolution of the universe from a initially\ninflationary expansion that has a change of phase towards a decelerated\nexpansion and thereinafter evolves towards the present day observed celerated\n(quintessential) expansion.", "category": "hep-th" }, { "text": "Magnetic-field-driven topological phase transition in the holograpic\n Weyl semimetal: We study the magnetic field effects on the quantum critical point (QCP) in\nthe holographic Weyl semimetal model. We show that it increases quadratically\nwith the magnetic field for weak field and linear with the magnetic field for\nstrong field. Our findings are compatible with previous results in the\nliterature from other approaches.", "category": "hep-th" }, { "text": "Runaway directions in O'Raifeartaigh models: R-symmetries, which are needed for supersymmetry (SUSY) breaking in\nO'Raifeartaigh models, often lead to SUSY runaway directions trough a\ncomplexified R-transformation. Non-R symmetries also lead to runaway directions\nin a similar way. This work investigates the occurrence of runaway directions\nof both SUSY and SUSY breaking types. We clarify previous issues on fractional\ncharges and genericness, and make a refined statement on conditions for runaway\ndirections related to either R-symmetries or non-R symmetries. We present a\ngeneric and anomaly-free model to show the existence of runaway directions\nrelated to non-R symmetries. We also comment on the possibility to combine the\nnon-R symmetry case to the R-symmetry case by an R-charge redefinition.", "category": "hep-th" }, { "text": "The Static Gauge Potential with a Cutoff: The static potential, corresponding to the interaction of two heavy sources\nis computed for $\\mathcal{N}=4$ Super Yang Mills in the strong 't Hooft\ncoupling regime by using the AdS/CFT conjecture and performing a computation of\na rectangular Wilson loop at a finite distance of the boundary.", "category": "hep-th" }, { "text": "RG limit cycles: In this review we consider the concept of limit cycles in the renormalization\ngroup flows. The examples of this phenomena in the quantum mechanics and field\ntheory will be presented.", "category": "hep-th" }, { "text": "Operator Product Expansion in Logarithmic Conformal Field Theory: In logarithmic conformal field theory, primary fields come together with\nlogarithmic partner fields on which the stress-energy tensor acts\nnon-diagonally. Exploiting this fact and global conformal invariance of two-\nand three-point functions, operator product expansions of logarithmic operators\nin arbitrary rank logarithmic conformal field theory are investigated. Since\nthe precise relationship between logarithmic operators and their primary\npartners is not yet sufficiently understood in all cases, the derivation of\noperator product expansion formulae is only possible under certain assumptions.\nThe easiest cases are studied in this paper: firstly, where operator product\nexpansions of two primaries only contain primary fields, secondly, where the\nprimary fields are pre-logarithmic operators. Some comments on generalization\ntowards more relaxed assumptions are made, in particular towards the case where\nlogarithmic fields are not quasi-primary. We identify an algebraic structure\ngenerated by the zero modes of the fields, which proves useful in determining\nsettings in which our approach can be successfully applied.", "category": "hep-th" }, { "text": "Singularities and Gauge Theory Phases: Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we\npresent a correspondence between networks of small resolutions for singular\nelliptic fibrations and Coulomb branches of five-dimensional N=1 gauge\ntheories. While resolutions correspond to subchambers of the Coulomb branch,\npartial resolutions correspond to higher codimension loci at which the Coulomb\nbranch intersects the Coulomb-Higgs branches. Flops between different\nresolutions are identified with reflections on the Coulomb branch. Physics\naside, this correspondence provides an interesting link between elliptic\nfibrations and representation theory.", "category": "hep-th" }, { "text": "Toward the End of Time: The null-brane space-time provides a simple model of a big crunch/big bang\nsingularity. A non-perturbative definition of M-theory on this space-time was\nrecently provided using matrix theory. We derive the fermion couplings for this\nmatrix model and study the leading quantum effects. These effects include\nparticle production and a time-dependent potential. Our results suggest that as\nthe null-brane develops a big crunch singularity, the usual notion of\nspace-time is replaced by an interacting gluon phase. This gluon phase appears\nto constitute the end of our conventional picture of space and time.", "category": "hep-th" }, { "text": "Decoupling of High Dimension Operators from the Low Energy Sector in\n Holographic Models: We study the decoupling of high dimension operators from the the description\nof the low-energy spectrum in theories where conformal symmetry is broken by a\nsingle scale, which we refer to as `broken CFTs'. Holographic duality suggests\nthat this decoupling occurs in generic backgrounds. We show how the decoupling\nof high mass states in the (d+1)-dimensional bulk relates to the decoupling of\nhigh energy states in the d-dimensional broken CFT. In other words, we explain\nwhy both high dimension operators and high mass states in the CFT decouple from\nthe low-energy physics of the mesons and glueballs. In many cases, the\ndecoupling can occur exponentially fast in the dimension of the operator.\nHolography motivates a new kind of form factor proportional to the two point\nfunction between broken CFT operators with very different scaling dimensions.\nThis new notion of decoupling can provide a systematic justification for\nholographic descriptions of QCD and condensed matter systems with only light\ndegrees of freedom in the bulk.", "category": "hep-th" }, { "text": "Nonlocal vertices and analyticity: Landau equations and general Cutkosky\n rule: We study the analyticity properties of amplitudes in theories with nonlocal\nvertices of the type occurring in string field theory and a wide class of\nnonlocal field theory models. Such vertices are given in momentum space by\nentire functions of rapid decay in certain (including Euclidean) directions\nensuring UV finiteness but are necessarily of rapid increase in others. A\nparametric representation is obtained by integrating out the loop (Euclidean)\nmomenta after the introduction of generalized Schwinger parameters. Either in\nthe original or parametric representation, the well-defined resulting\namplitudes are then continued in the complex space of the external momenta\ninvariants. We obtain the alternative forms of the Landau equations determining\nthe singularity surfaces showing that the nonlocal vertices serve as UV\nregulators but do not affect the local singularity structure. As a result the\nfull set of singularities known to occur in local field theory also occurs\nhere: normal and anomalous thresholds as well as acnodes, crunodes, and cusps\nthat may under certain circumstances appear even on the physical sheet.\nSingularities of the second type also appear as shown from the parametric\nrepresentation. We obtain the general Cutkosky discontinuity rule for\nencircling a singularity by employing contour deformations only in the finite\nplane. The unitarity condition (optical theorem) is then discussed as a special\napplication of the rule across normal thresholds and the hermitian analyticity\nproperty of amplitudes.", "category": "hep-th" }, { "text": "Quantum Cauchy problem in cosmology: We develop a general framework for effective equations of expectation values\nin quantum cosmology and pose for them the quantum Cauchy problem with\nno-boundary and tunneling wavefunctions. We apply this framework in the model\nwith a big negative non-minimal coupling, which incorporates a recently\nproposed low energy (GUT scale) mechanism of the quantum origin of the\ninflationary Universe and study the effects of the quantum inflaton mode.", "category": "hep-th" }, { "text": "Infrared Modification of Gravity: In this lecture I address the issue of possible large distance modification\nof gravity and its observational consequences. Although, for the illustrative\npurposes we focus on a particular simple generally-covariant example, our\nconclusions are rather general and apply to large class of theories in which,\nalready at the Newtonian level, gravity changes the regime at a certain very\nlarge crossover distance $r_c$. In such theories the cosmological evolution\ngets dramatically modified at the crossover scale, usually exhibiting a\n\"self-accelerated\" expansion, which can be differentiated from more\nconventional \"dark energy\" scenarios by precision cosmology. However, unlike\nthe latter scenarios, theories of modified-gravity are extremely constrained\n(and potentially testable) by the precision gravitational measurements at much\nshorter scales. Despite the presence of extra polarizations of graviton, the\ntheory is compatible with observations, since the naive perturbative expansion\nin Newton's constant breaks down at a certain intermediate scale. This happens\nbecause the extra polarizations have couplings singular in $1/r_c$. However,\nthe correctly resummed non-linear solutions are regular and exhibit continuous\nEinsteinian limit. Contrary to the naive expectation, explicit examples\nindicate that the resummed solutions remain valid after the ultraviolet\ncompletion of the theory, with the loop corrections taken into account.", "category": "hep-th" }, { "text": "Double Field Theory at SL(2) angles: An extended field theory is presented that captures the full SL(2) x O(6,6+n)\nduality group of four-dimensional half-maximal supergravities. The theory has\nsection constraints whose two inequivalent solutions correspond to minimal D=10\nsupergravity and chiral half-maximal D=6 supergravity, respectively coupled to\nvector and tensor multiplets. The relation with O(6,6+n) (heterotic) double\nfield theory is thoroughly discussed. Non-Abelian interactions as well as\nbackground fluxes are captured by a deformation of the generalised\ndiffeomorphisms. Finally, making use of the SL(2) duality structure, it is\nshown how to generate gaugings with non-trivial de Roo-Wagemans angles via\ngeneralised Scherk-Schwarz ansaetze. Such gaugings allow for moduli\nstabilisation including the SL(2) dilaton.", "category": "hep-th" }, { "text": "Functional quantization of Generalized Scalar Duffin-Kemmer-Petiau\n Electrodynamics: The main goal of this work is to study systematically the quantum aspects of\nthe interaction between scalar particles in the framework of Generalized Scalar\nDuffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is\nquantized after a constraint analysis following Dirac's methodology by\ndetermining the Hamiltonian transition amplitude. In particular, the covariant\ntransition amplitude is established in the generalized non-mixing Lorenz gauge.\nThe complete Green's functions are obtained through functional methods and the\ntheory's renormalizability is also detailed presented. Next, the radiative\ncorrections for the Green's functions at $\\alpha $-order are computed; and, as\nit turns out, an unexpected $m_{P}$-dependent divergence on the DKP sector of\nthe theory is found. Furthermore, in order to show the effectiveness of the\nrenormalization procedure on the present theory, a diagrammatic discussion on\nthe photon self-energy and vertex part at $\\alpha ^{2}$-order are presented,\nwhere it is possible to observe contributions from the DKP self-energy\nfunction, and then analyse whether or not this novel divergence propagates to\nhigher-order contributions. Lastly, an energy range where the theory is well\ndefined: $m^{2}\\ll k^{2}=6, which are orientifold p-planes of negative charge with stuck\nDp-branes. We study the consistency of configurations with various orientifold\nplanes and propose a resolution to this puzzle. It is argued that O6~-planes\nare possible in massive IIA theory with odd cosmological constant, while\nO7~-planes and O8~-planes are not allowed. Various relations between\norientifold planes and non-BPS D-branes are also addressed.", "category": "hep-th" }, { "text": "2d (0,2) Quiver Gauge Theories and D-Branes: We initiate a systematic study of 2d (0,2) quiver gauge theories on the\nworldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present\nan algorithm for efficiently calculating the classical mesonic moduli spaces of\nthese theories, which correspond to the probed geometries. We also introduce a\nsystematic procedure for constructing the gauge theories for arbitrary toric\nsingularities by means of partial resolution, which translates to higgsing in\nthe field theory. Finally, we introduce Brane Brick Models, a novel class of\nbrane configurations that consist of D4-branes suspended from an NS5-brane\nwrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are\nthe 2d analogues of Brane Tilings and allow a direct connection between\ngeometry and gauge theory.", "category": "hep-th" }, { "text": "Scale Vs. Conformal Invariance in the AdS/CFT Correspondence: We present two examples of non-trivial field theories which are scale\ninvariant, but not conformally invariant. This is done by placing certain field\ntheories, which are conformally invariant in flat space, onto curved\nbackgrounds of a specific type. We define this using the AdS/CFT\ncorrespondence, which relates the physics of gravity in asymptotically Anti-de\nSitter (AdS) spacetimes to that of a conformal field theory (CFT) in one\ndimension fewer. The AdS rotating (Kerr) black holes in five and seven\ndimensions provide us with the examples, since by the correspondence we are\nable to define and compute the action and stress tensor of four and six\ndimensional field theories residing on rotating Einstein universes, using the\n``boundary counterterm'' method. The rotation breaks conformal but not scale\ninvariance. The AdS/CFT framework is therefore a natural arena for generating\nsuch examples of non-trivial scale invariant theories which are not conformally\ninvariant.", "category": "hep-th" }, { "text": "New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to\n Separation of Variables: The supersymmetric intertwining relations with second order supercharges\nallow to investigate new two-dimensional model which is not amenable to\nstandard separation of variables. The corresponding potential being the\ntwo-dimensional generalization of well known one-dimensional P\\\"oschl-Teller\nmodel is proven to be exactly solvable for arbitrary integer value of parameter\n$p:$ all its bound state energy eigenvalues are found analytically, and the\nalgorithm for analytical calculation of all wave functions is given. The shape\ninvariance of the model and its integrability are of essential importance to\nobtain these results.", "category": "hep-th" }, { "text": "Possible Lorentz symmetry violation from broken Weyl invariance: In this work, we investigate a theory of linear Weyl gravity coupled to a\nscalar field and study the scenario in which Lorentz symmetry is broken by a\nnon-vanishing vacuum expectation value of the Weyl field in the flat space\nlimit after Weyl symmetry breaking. We show that a $CPT$-odd Lorentz-violating\ninteraction is generated after symmetry breaking. Features of different\nsymmetry-broken phases and their dependence on the spacetime character of the\ngenerated Lorentz-violating background are discussed. Also, we analyze the\nnaturalness of the theory by showing that the light mass scale is protected\nfrom large radiative corrections due to an enhanced spacetime symmetry.", "category": "hep-th" }, { "text": "Soldering Chiralities II: Non-Abelian Case: We study the non-abelian extension of the soldering process of two chiral WZW\nmodels of opposite chiralities, resulting in a (non-chiral) WZW model living in\na 2D space-time with non trivial Riemanian curvature.", "category": "hep-th" }, { "text": "Bootstrapping 2D CFTs in the Semiclassical Limit: We study two dimensional conformal field theories in the semiclassical limit.\nIn this limit, the four-point function is dominated by intermediate primaries\nof particular weights along with their descendants, and the crossing equations\nsimplify drastically. For a four-point function receiving sufficiently small\ncontributions from the light primaries, the structure constants involving heavy\nprimaries follow a universal formula. Applying our results to the four-point\nfunction of the $\\mathbb Z_2$ twist field in the symmetric product orbifold, we\nproduce the Hellerman bound and the logarithmically corrected Cardy formula\nthat is valid for $h \\geq c/12$.", "category": "hep-th" }, { "text": "Geometric Aspects of the `Deformation Method': At the classical level, redefinitions of the field content of a Lagrangian\nallow to rewrite an interacting model on a flat target space, in the form of a\nfree field model (no potential term) on a curved target space. In the present\nwork we extend the idea of the `deformation method' introduced in\n\\cite{defmet}, to show that it is possible to write an explicit correspondence\nbetween the metrics of the curved target spaces that arise in the free versions\nof distinct scalar field models. This is accomplished by obtaining an explicit\nrelation between the map function linking the fields and the free models'\nmetrics. By considering complex and even quaternionic field models, we extend\nthe procedure --initially proposed for models of a single scalar field-- to\nsystems with a content of two and four (despite constrained) real fields,\nrespectively, widening the range of applicability. We also analyze\nsupersymmetric models to illustrate more possibilities. In particular, we show\nhow to relate a flat Minkowskian metric to a Fubini-Study space.", "category": "hep-th" }, { "text": "Quantized Einstein-Rosen waves, AdS_2, and spontaneous symmetry breaking: 4D cylindrical gravitational waves with aligned polarizations (Einstein-Rosen\nwaves) are shown to be described by a weight 1/2 massive free field on the\ndouble cover of AdS_2. Thorn's C-energy is one of the sl(2,R) generators, the\nreconstruction from the (timelike) symmetry axis is the CFT_1 holography.\nClassically the phase space is also invariant under a O(1,1) group action on\nthe metric coefficients that is a remnant of the original 4D diffeomorphism\ninvariance. In the quantum theory this symmetry is found to be spontaneously\nbroken while the AdS_2 conformal invariance remains intact.", "category": "hep-th" }, { "text": "Excitations in Hot Non-Commutative Theories: We study the dispersion relation for scalar excitations in supersymmetric,\nnon-commutative theories at finite temperature. In N=4 Yang-Mills the low\nmomenta modes have superluminous group velocity. In the massless Wess-Zumino\nmodel the minimum of the dispersion relation is at non zero momentum for\ntemperatures above T_0 ~ (g \\theta)^(-1\\2). We briefly comment on N=2\nYang-Mills at finite density.", "category": "hep-th" }, { "text": "Primordial Black Hole Pair Creation Probability in Modified\n Gravitational Theory: The probability for quantum creation of an inflationary universe with a pair\nof black holes is computed in a modified gravitational theory. Considering a\ngravitational action which includes a cosmological constant ($\\Lambda$) in\naddition to $ \\alpha R^{2} $ and $ \\delta R^{-1}$ terms, the probabilities have\nbeen evaluated for two different kinds of spatial sections, one accommodating a\npair of black holes and the other without black hole. We adopt a technique\nprescribed by Bousso and Hawking to calculate the above creation probability in\na semiclassical approximation with Hartle-Hawking boundary condition. Depending\non the parameters in the action some new and physically interesting instanton\nsolutions are presented here which may play an important role in the creation\nof the early universe. We note that the probability of creation of a universe\nwith a pair of black holes is strongly suppressed with a positive cosmological\nconstant when $\\delta = \\frac{4 \\Lambda^{2}}{3}$ for $\\alpha > 0$ but it is\nmore probable for $\\alpha < - \\frac{1}{6 \\Lambda}$. It is also found that\ninstanton solutions are allowed without a cosmological constant in the theory\nprovided $\\delta < 0$.", "category": "hep-th" }, { "text": "Exactly solvable potentials of Calogero type for q-deformed Coxeter\n groups: We establish that by parameterizing the configuration space of a\none-dimensional quantum system by polynomial invariants of q-deformed Coxeter\ngroups it is possible to construct exactly solvable models of Calogero type. We\nadopt the previously introduced notion of solvability which consists of\nrelating the Hamiltonian to finite dimensional representation spaces of a Lie\nalgebra. We present explicitly the $G_2^q $-case for which we construct the\npotentials by means of suitable gauge transformations.", "category": "hep-th" }, { "text": "Closed-form expression for cross-channel conformal blocks near the\n lightcone: In the study of conformal field theories, conformal blocks in the lightcone\nlimit are fundamental to the analytic conformal bootstrap method. Here we\nconsider the lightcone limit of 4-point functions of generic scalar primaries.\nBased on the nonperturbative pole structure in spin of Lorentzian inversion, we\npropose the natural basis functions for cross-channel conformal blocks. In this\nnew basis, we find a closed-form expression for crossed conformal blocks in\nterms of the Kamp\\'e de F\\'eriet function, which applies to intermediate\noperators of arbitrary spin in general dimensions. We derive the general\nLorentzian inversion for the case of identical external scaling dimensions. Our\nresults for the lightcone limit also shed light on the complete analytic\nstructure of conformal blocks in the lightcone expansion.", "category": "hep-th" }, { "text": "Master Ward Identity for Nonlocal Symmetries in D=2 Principal Chiral\n Models: We derive, in path integral approach, the (anomalous) master Ward identity\nassociated with an infinite set of nonlocal conservation laws in\ntwo-dimensional principal chiral models", "category": "hep-th" }, { "text": "Gauging spacetime inversions in quantum gravity: Spacetime inversion symmetries such as parity and time reversal play a\ncentral role in physics, but they are usually treated as global symmetries. In\nquantum gravity there are no global symmetries, so any spacetime inversion\nsymmetries must be gauge symmetries. In particular this includes\n$\\mathcal{CRT}$ symmetry (in even dimensions usually combined with a rotation\nto become $\\mathcal{CPT}$), which in quantum field theory is always a symmetry\nand seems likely to be a symmetry of quantum gravity as well. In this article\nwe discuss what it means to gauge a spacetime inversion symmetry, and we\nexplain some of the more unusual consequences of doing this. In particular we\nargue that the gauging of $\\mathcal{CRT}$ is automatically implemented by the\nsum over topologies in the Euclidean gravity path integral, that in a closed\nuniverse the Hilbert space of quantum gravity must be a real vector space, and\nthat in Lorentzian signature manifolds which are not time-orientable must be\nincluded as valid configurations of the theory. In particular we give an\nexample of an asymptotically-AdS time-unorientable geometry which must be\nincluded to reproduce computable results in the dual CFT.", "category": "hep-th" }, { "text": "Semiclassical partition function for strings dual to Wilson loops with\n small cusps in ABJM: We compute the 1-loop partition function for strings in\n$AdS_4\\times\\mathbb{CP}^3$, whose worldsheets end along a line with small cusp\nangles in the boundary of AdS. We obtain these 1-loop results in terms of the\nvacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz\nand Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to\nthe next to leading order in the strong coupling expansion. The agreement is\nobserved for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.", "category": "hep-th" }, { "text": "Abrikosov String in N=2 Supersymmetric QED: We study the Abrikosov-Nielsen-Olesen string in N=2 supersymmetric QED with\nN=2-preserving superpotential, in which case the Abrikosov string is found to\nbe 1/2-BPS saturated. Adding a quadratic small perturbation in the\nsuperpotential breaks N=2 supersymmetry to N=1 supersymmetry. Then the\nAbrikosov string is no longer BPS saturated. The difference between the string\ntensions for the non-BPS and BPS saturated situation is found to be negative to\nthe first order of the perturbation parameter.", "category": "hep-th" }, { "text": "Quasimodular instanton partition function and the elliptic solution of\n Korteweg-de Vries equations: The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric\ngauge theories to some quantum integrable models, in simple cases the\nintegrable models can be treated as solvable quantum mechanics models. For\nSU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the\npotential of corresponding quantum model is the elliptic function. If the mass\nof matter takes special value then the potential is an elliptic solution of KdV\nhierarchy. We show that the deformed prepotential of gauge theory can be\nobtained from the average densities of conserved charges of the classical KdV\nsolution, the UV gauge coupling dependence is assembled into the Eisenstein\nseries. The gauge theory with adjoint mass is taken as the example.", "category": "hep-th" }, { "text": "Erasure of Strings and Vortexes: The interaction of defects can lead to a phenomenon of erasure. During this\nprocess, a lower-dimensional object gets absorbed and dissolved by a\nhigher-dimensional one. The phenomenon is very general and has a wide range of\nimplications, both cosmological and fundamental. In particular, all types of\nstrings, such as cosmic strings, QCD flux tubes, or fundamental strings, get\nerased when encountering a defect, either solitonic or a $D$-brane that\ndeconfines their fluxes. This leads to a novel mechanism of cosmic string\nbreak-up, accompanied by gravitational and electromagnetic radiations. The\narguments based on loss of coherence and the entropy count suggest that the\nerasure probability is very close to one, and strings never make it through the\ndeconfining layer. We confirm this by a numerical simulation of the system,\nwhich effectively captures the essence of the phenomenon: a $2+1$-dimensional\nproblem of interaction between a Nielsen-Olesen vortex of a $U(1)$ Higgs model\nand a domain wall inside which the $U(1)$ gauge group is unHiggsed and the\nmagnetic flux is deconfined. In accordance with the entropy argument, in our\nsimulation, the vortex never makes it across the wall.", "category": "hep-th" }, { "text": "Subleading-color contributions to gluon-gluon scattering in N=4 SYM\n theory and relations to N=8 supergravity: We study the subleading-color (nonplanar) contributions to the four-gluon\nscattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory. Using the\nformalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit\nexpressions for the infrared-divergent contributions of all the\nsubleading-color L-loop amplitudes up to three loops, and make some conjectures\nfor the IR behavior for arbitrary L. We also derive several intriguing\nrelations between the subleading-color one- and two-loop four-gluon amplitudes\nand the four-graviton amplitudes of N=8 supergravity. The exact one- and\ntwo-loop N=8 supergravity amplitudes can be expressed in terms of the one- and\ntwo-loop N-independent N=4 SYM amplitudes respectively, but the natural\ngeneralization to higher loops fails, despite having a simple interpretation in\nterms of the 't Hooft picture. We also find that, at least through two loops,\nthe subleading-color amplitudes of N=4 SYM theory have uniform\ntranscendentality (as do the leading-color amplitudes). Moreover, the N=4 SYM\nCatani operators, which express the IR-divergent contributions of loop\namplitudes in terms of lower-loop amplitudes, are also shown to have uniform\ntranscendentality, and to be the maximum transcendentality piece of the QCD\nCatani operators.", "category": "hep-th" }, { "text": "Lorentz-violating Chern-Simons action under high temperature in massless\n QED: Lorentz and CPT violating QED with massless fermions at finite temperature is\nstudied. We show that there is no ambiguity in the induced coefficient of the\nChern-Simons-like term that defines the so-called Carroll-Field-Jackiw model at\nhigh temperature. We also show that this system constitutes an example where\nthe breaking of CPT and Lorentz symmetries is more severe at high temperature\nthan in the zero temperature case thus precluding any naive expectations of\nLorentz symmetry restoration.", "category": "hep-th" }, { "text": "Null Vectors in Logarithmic Conformal Field Theory: The representation theory of the Virasoro algebra in the case of a\nlogarithmic conformal field theory is considered. Here, indecomposable\nrepresentations have to be taken into account, which has many interesting\nconsequences. We study the generalization of null vectors towards the case of\nindecomposable representation modules and, in particular, how such logarithmic\nnull vectors can be used to derive differential equations for correlation\nfunctions. We show that differential equations for correlation functions with\nlogarithmic fields become inhomogeneous.", "category": "hep-th" }, { "text": "Patterns of gauge symmetry in the background field method: The correlation functions of Yang-Mills theories formulated in the background\nfield method satisfy linear Slavnov-Taylor identities, which are naive\ngeneralizations of simple tree level relations, with no deformations\noriginating from the ghost sector of the theory. In recent years, a stronger\nversion of these identities has been found to hold at the level of the\nbackground gluon self-energy, whose transversality is enforced separately for\neach special block of diagrams contributing to the gluon Schwinger-Dyson\nequation. In the present work we demonstrate by means of explicit calculations\nthat the same distinct realization of the Slavnov-Taylor identity persists in\nthe case of the background three-gluon vertex. The analysis is carried out at\nthe level of the exact Schwinger-Dyson equation for this vertex, with no\ntruncations or simplifying assumptions. The demonstration entails the\ncontraction of individual vertex diagrams by the relevant momentum, which\nactivates Slavnov-Taylor identities of vertices and multi-particle kernels\nnested inside these graphs; the final result emerges by virtue of a multitude\nof extensive cancellations, without the need of performing explicit\nintegrations. In addition, we point out that background Ward identities amount\nto replacing derivatives of propagators by zero-momentum background-gluon\ninsertions, in exact analogy to standard properties of Abelian gauge theories.\nFinally, certain potential applications of these results are briefly discussed.", "category": "hep-th" }, { "text": "Dynamical realizations of l-conformal Newton-Hooke group: The method of nonlinear realizations and the technique previously developed\nin arXiv:1208.1403 are used to construct a dynamical system without higher\nderivative terms, which holds invariant under the l-conformal Newton-Hooke\ngroup. A configuration space of the model involves coordinates, which\nparametrize a particle moving in d spatial dimensions and a conformal mode,\nwhich gives rise to an effective external field.The dynamical system describes\na generalized multi-dimensional oscillator, which undergoes\naccelerated/decelerated motion in an ellipse in accord with evolution of the\nconformal mode. Higher derivative formulations are discussed as well. It is\ndemonstrated that the multi-dimensional Pais-Uhlenbeck oscillator enjoys the\nl=3/2-conformal Newton-Hooke symmetry for a particular choice of its\nfrequencies.", "category": "hep-th" }, { "text": "Yang-Mills and Born-Infeld actions on finite group spaces: Discretized nonabelian gauge theories living on finite group spaces G are\ndefined by means of a geometric action \\int Tr F\\wedge *F . This technique is\nextended to obtain a discrete version of the Born-Infeld action.", "category": "hep-th" }, { "text": "Quasi-normal modes of dyonic black holes and magneto-hydrodynamics: We revisit the magneto-hydrodynamics in (2+1) dimensions and confirm that it\nis consistent with the quasi-normal modes of the (3+1) dimensional dyonic black\nholes in the most general set-up with finite density, magnetic field and wave\nvector. We investigate all possible modes (sound, shear, diffusion, cyclotron\netc.) and their interplay. For the magneto-hydrodynamics we perform a complete\nand detailed analysis correcting some prefactors in the literature, which is\nimportant for the comparison with quasi-normal modes. For the quasi-normal mode\ncomputations in holography we identify the independent fluctuation variables of\nthe dyonic black holes, which is nontrivial at finite density and magnetic\nfield. As an application of the quasi-normal modes of the dyonic black holes we\ninvestigate a transport property, the diffusion constant. We find that the\ndiffusion constant at finite density and magnetic field saturates the lower\nbound at low temperature. We show that this bound can be understood from the\npole-skipping point.", "category": "hep-th" }, { "text": "Statical Structures of the BCS-like Holographic Superfluid in AdS4\n Spacetime: We investigate in detail the m^{2}=0 Abelian Higgs model in AdS4, which is\nconsidered as the holographic dual of the most BCS-like superfluid. In\nhomogeneous and isotropic superfluid solutions, we calculate the sound speeds,\nsquare of which approaches to 1/2 with increasing chemical potential (lowering\ntemperature). Then we present the single dark soliton solutions, which becomes\nthinner with increasing chemical potential. For the first time, we also find\nthe interesting double and triple dark soliton solutions, which is unexpected\nand shows the possibility of more complicated static configurations. Finally,\nwe investigate vortex solutions. For winding number n=1, the vortex becomes\nthinner with increasing chemical potential. At a given chemical potential, with\nincreasing winding number, firstly the vortex becomes bigger and the charge\ndensity depletion becomes larger, then the charge density depletion settles\ndown at a certain value and the growth of the vortex size is found to obey a\nscaling symmetry.", "category": "hep-th" }, { "text": "A paucity of bulk entangling surfaces: AdS wormholes with de Sitter\n interiors: We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying\nthe null energy condition and having two asymptotically AdS boundaries\nconnected through a (non-traversable) inflating wormhole. As for other\nwormholes, it is natural to expect dual descriptions in terms of two\ndisconnected CFTs in appropriate entangled states. But for our cases certain\nexpected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT)\nprescription to compute CFT entropy do not exist. In particular, no real\ncodimension-2 extremal surface can run from one end of the wormhole to the\nother. According to HRT, the mutual information between any two finite-sized\nsubregions (one in each CFT) must then vanish at leading order in large $N$ --\nthough the leading-order mutual information per unit area between the two CFTs\ntaken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have\nplane-symmetric surfaces that would compute the total entropy of either CFT. We\nsuggest this to remain true of less-symmetric surfaces so that the HRT entropy\nis ill-defined and some modified prescription is required. It may be possible\nto simply extend HRT or the closely-related maximin construction by a limiting\nprocedure, though complex extremal surfaces could also play an important role.", "category": "hep-th" }, { "text": "Cosmological String Backgrounds from Gauged WZW Models: We discuss the four-dimensional target-space interpretation of bosonic\nstrings based on gauged WZW models, in particular of those based on the\nnon-compact coset space $SL(2,{\\bf R})\\times SO(1,1)^2 /SO(1,1)$. We show that\nthese theories lead, apart from the recently broadly discussed black-hole type\nof backgrounds, to cosmological string backgrounds, such as an expanding\nUniverse. Which of the two cases is realized depends on the sign of the level\nof the corresponding Kac-Moody algebra. We discuss various aspects of these new\ncosmological string backgrounds.", "category": "hep-th" }, { "text": "Renormalization Group Flows on D3 branes at an Orbifolded Conifold: We consider D3-branes at an orbifolded conifold whose horizon ${X_5}$\nresolves into a smooth Einstein manifold which joins several copies of ${\\bf\nT}^{1,1}$. We describe in details the resolution of the singular horizon\n${X_5}$ and describe different types of two-cycles appearing in the resolution.\nFor a large number of D3 branes, the AdS/CFT conjecture becomes a duality\nbetween type IIB string theory on $AdS_5 \\times {X_5} $ and the ${\\cal N} = 1$\nfield theory living on the D3 branes. We study the fractional branes as small\nperturbations of the string background and we reproduce the logarithmic flow of\nfield theory couplings by studying fluxes of NS-NS and R-R two forms through\ndifferent 2-cycles of the resolved horizon.", "category": "hep-th" }, { "text": "An upper bound on transport: The linear growth of operators in local quantum systems leads to an effective\nlightcone even if the system is non-relativistic. We show that consistency of\ndiffusive transport with this lightcone places an upper bound on the\ndiffusivity: $D \\lesssim v^2 \\tau_\\text{eq}$. The operator growth velocity $v$\ndefines the lightcone and $\\tau_\\text{eq}$ is the local equilibration\ntimescale, beyond which the dynamics of conserved densities is diffusive. We\nverify that the bound is obeyed in various weakly and strongly interacting\ntheories. In holographic models this bound establishes a relation between the\nhydrodynamic and leading non-hydrodynamic quasinormal modes of planar black\nholes. Our bound relates transport data --- including the electrical\nresistivity and the shear viscosity --- to the local equilibration time, even\nin the absence of a quasiparticle description. In this way, the bound sheds\nlight on the observed $T$-linear resistivity of many unconventional metals, the\nshear viscosity of the quark-gluon plasma and the spin transport of unitary\nfermions.", "category": "hep-th" }, { "text": "EFT and the SUSY Index on the 2nd Sheet: The counting of BPS states in four-dimensional ${\\cal N}=1$ theories has\nattracted a lot of attention in recent years. For superconformal theories,\nthese states are in one-to-one correspondence with local operators in various\nshort representations. The generating function for this counting problem has\nbranch cuts and hence several Cardy-like limits, which are analogous to\nhigh-temperature limits. Particularly interesting is the second sheet, which\nhas been shown to capture the microstates and phases of supersymmetric black\nholes in AdS$_5$. Here we present a 3d Effective Field Theory (EFT) approach to\nthe high-temperature limit on the second sheet. We use the EFT to derive the\nbehavior of the index at orders $\\beta^{-2},\\beta^{-1},\\beta^0$. We also make a\nconjecture for $O(\\beta)$, where we argue that the expansion truncates up to\nexponentially small corrections. An important point is the existence of vector\nmultiplet zero modes, unaccompanied by massless matter fields. The runaway of\nAffleck-Harvey-Witten is however avoided by a non-perturbative confinement\nmechanism. This confinement mechanism guarantees that our results are robust.", "category": "hep-th" }, { "text": "TCFHs, IIB warped AdS backgrounds and hidden symmetries: We present the twisted covariant form hierarchies (TCFHs) on the internal\nspaces of all type IIB warped AdS backgrounds. As a result we demonstrate that\nthe form bilinears on the internal spaces satisfy a generalisation of the\nconformal Killing-Yano equation. We also explore some of the properties of the\nTCFHs, like for example the holonomy of the TCFH connections. In addition, we\npresent examples where the form bilinears generate hidden symmetries for\nparticle probes propagating on the internal spaces of some AdS backgrounds.\nThese include the maximally supersymmetric AdS$_5$ solution as well as some of\nthe near horizon geometries of intersecting IIB branes.", "category": "hep-th" }, { "text": "Quantizations of D=3 Lorentz symmetry: Using the isomorphism\n$\\mathfrak{o}(3;\\mathbb{C})\\simeq\\mathfrak{sl}(2;\\mathbb{C})$ we develop a new\nsimple algebraic technique for complete classification of quantum deformations\n(the classical $r$-matrices) for real forms $\\mathfrak{o}(3)$ and\n$\\mathfrak{o}(2,1)$ of the complex Lie algebra $\\mathfrak{o}(3;\\mathbb{C})$ in\nterms of real forms of $\\mathfrak{sl}(2;\\mathbb{C})$: $\\mathfrak{su}(2)$,\n$\\mathfrak{su}(1,1)$ and $\\mathfrak{sl}(2;\\mathbb{R})$. We prove that the $D=3$\nLorentz symmetry\n$\\mathfrak{o}(2,1)\\simeq\\mathfrak{su}(1,1)\\simeq\\mathfrak{sl}(2;\\mathbb{R})$\nhas three different Hopf-algebraic quantum deformations which are expressed in\nthe simplest way by two standard $\\mathfrak{su}(1,1)$ and\n$\\mathfrak{sl}(2;\\mathbb{R})$ $q$-analogs and by simple Jordanian\n$\\mathfrak{sl}(2;\\mathbb{R})$ twist deformations. These quantizations are\npresented in terms of the quantum Cartan-Weyl generators for the quantized\nalgebras $\\mathfrak{su}(1,1)$ and $\\mathfrak{sl}(2;\\mathbb{R})$ as well as in\nterms of quantum Cartesian generators for the quantized algebra\n$\\mathfrak{o}(2,1)$. Finaly, some applications of the deformed $D=3$ Lorentz\nsymmetry are mentioned.", "category": "hep-th" }, { "text": "Is dark energy from cosmic Hawking radiation?: It is suggested that dark energy is the energy of the Hawking radiation from\na cosmic horizon. Despite of its extremely low Gibbons-Hawking temperature,\nthis radiation could have the appropriate magnitude $O(M_P^2 H^2)$ and the\nequation of state to explain the observed cosmological data if there is a\nPlanck scale UV-cutoff, where $H$ is the Hubble parameter.", "category": "hep-th" }, { "text": "Excitation Spectra of Spin Models constructed from Quantized Affine\n Algebras of type $B_n^{(1)}$, $D_n^{(1)}$: The energy and momentum spectrum of the spin models constructed from the\nvector representation of the quantized affine algebras of type $\\B$ and $\\D$\nare computed using the approach of Davies et al. \\cite{DFJMN92}. The results\nare for the anti-ferromagnetic (massive) regime, and they agree with the mass\nspectrum found from the factorized S--matrix theory by Ogievetsky et al.\n\\cite{ORW87}. The other new result is the explicit realization of the fusion\nconstruction for the quantized affine algebras of type $\\B$ and $\\D$.}", "category": "hep-th" }, { "text": "Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets,\n Green's Functions, and a Supersymmetric Proof of the Index Theorem: The Peierls bracket quantization scheme is applied to the supersymmetric\nsystem corresponding to the twisted spin index theorem. A detailed study of the\nquantum system is presented, and the Feynman propagator is exactly computed.\nThe Green's function methods provide a direct derivation of the index formula.\nNote: This is essentially a new SUSY proof of the index theorem.", "category": "hep-th" }, { "text": "Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in\n Arbitrary Higher-Spin Background: Analysis of the first-order corrections to higher-spin equations is extended\nto homotopy operators involving shift parameters with respect to the spinor $Y$\nvariables, the argument of the higher-spin connection $\\omega(Y)$ and the\nargument of the higher-spin zero-form $C(Y)$. It is shown that a relaxed\nuniform $(y+p)$-shift and a shift by the argument of $\\omega(Y)$ respect the\nproper form of the free higher-spin equations and constitute a one-parametric\nclass of vertices that contains those resulting from the conventional (no\nshift) homotopy. A pure shift by the argument of $\\omega(Y)$ is shown not to\naffect the one-form higher-spin field $W$ in the first order and, hence, the\nform of the respective vertices.", "category": "hep-th" }, { "text": "Nilpotent Spinor Symmetry with Interacting Spin 3/2 Field: Consistent interactions of spin 3/2 field that realize a nilpotent spinorial\nsymmetry are presented. Based on our previous results on purely bosonic\nnon-Abelian tensor with consistent interactions, we present a new system for\ninteracting spin 3/2 field that realizes the nilpotent fermionic symmetry.", "category": "hep-th" }, { "text": "Positivity bounds on effective field theories with spontaneously broken\n Lorentz invariance: We derive positivity bounds on EFT coefficients in theories where boosts are\nspontaneously broken. We employ the analytic properties of the retarded Green's\nfunction of conserved currents (or of the stress-energy tensor) and assume the\ntheory becomes conformal in the UV. The method is general and applicable to\nboth cosmology and condensed matter systems. As a concrete example, we look at\nthe EFT of conformal superfluids which describes the universal low-energy\ndynamics of CFT's at large chemical potential and we derive inequalities on the\ncoefficients of the operators, in three dimensions, at NLO and NNLO.", "category": "hep-th" }, { "text": "Derivation of theories: structures of the derived system in terms of\n those of the original system in classical mechanics: We present the technique of derivation of a theory to obtain an\n$(n+1)f$-degrees-of-freedom theory from an $f$-degrees-of-freedom theory and\nshow that one can calculate all of the quantities of the derived theory from\nthose of the original one. Specifically, we show that one can use this\ntechnique to construct, from an integrable system, other integrable systems\nwith more degrees of freedom.", "category": "hep-th" }, { "text": "Revisiting toric SU(3) structures: Three-dimensional smooth compact toric varieties (SCTV) admit SU(3)\nstructures, and may thus be relevant for string compactifications, if they have\neven first Chern class (c1). This condition can be fulfilled by infinitely many\nSCTVs, including CP3 and CP1 bundles over all two-dimensional SCTVs. We show\nthat as long as c1 is even, toric SU(3) structures can be constructed using a\nmethod proposed in arXiv:1005.2194. We perform a systematic study of the\nparametric freedom of the resulting SU(3) structures, with a particular focus\non the metric and the torsion classes. Although metric positivity constrains\nthe SU(3) parameters, we find that every SCTV admits several toric SU(3)\nstructures and that parametric choices can sometimes be made to match\nrequirements of string vacua. We also provide a short review on the constraints\nthat an SU(3) structure must meet to be relevant for four-dimensional,\nmaximally symmetric N=1 or N=0 string vacua.", "category": "hep-th" }, { "text": "UV-finite scalar field theory with unitarity: In this paper we show how to define the UV completion of a scalar field\ntheory such that it is both UV-finite and perturbatively unitary. In the UV\ncompleted theory, the propagator is an infinite sum of ordinary propagators. To\neliminate the UV divergences, we choose the coefficients and masses in the\npropagator to satisfy certain algebraic relations, and define the infinite sums\ninvolved in Feynman diagram calculation by analytic continuation. Unitarity can\nbe proved relatively easily by Cutkosky's rules. The theory is equivalent to\ninfinitely many particles with specific masses and interactions. We take the\n$\\phi^4$ theory as an example and demonstrate our idea through explicit Feynman\ndiagram computation.", "category": "hep-th" }, { "text": "2-Group Symmetries and their Classification in 6d: We uncover 2-group symmetries in 6d superconformal field theories. These\nsymmetries arise when the discrete 1-form symmetry and continuous flavor\nsymmetry group of a theory mix with each other. We classify all 6d\nsuperconformal field theories with such 2-group symmetries. The approach taken\nin 6d is applicable more generally, with minor modifications to include\ndimension specific operators (such as instantons in 5d and monopoles in 3d),\nand we provide a discussion of the dimension-independent aspects of the\nanalysis. We include an ancillary mathematica code for computing 2-group\nsymmetries, once the dimension specific input is provided. We also discuss a\nmixed 't Hooft anomaly between discrete 0-form and 1-form symmetries in 6d.", "category": "hep-th" }, { "text": "The spectral problem of the ABJ Fermi gas: The partition function on the three-sphere of ABJ theory can be rewritten\ninto a partition function of a non-interacting Fermi gas, with an accompanying\none-particle Hamiltonian. We study the spectral problem defined by this\nHamiltonian. We determine the exact WKB quantization condition, which involves\nquantities from refined topological string theory, and test it successfully\nagainst numerical calculations of the spectrum.", "category": "hep-th" }, { "text": "Partial duality in SU(N) Yang-Mills theory: Recently we have proposed a set of variables for describing the infrared\nlimit of four dimensional SU(2) Yang-Mills theory. here we extend these\nvariables to the general case of four dimensional SU(N) Yang-Mills theory. We\nfind that the SU(N) connection A decomposes according to irreducible\nrepresentations of SO(N-1) and the curvature two-form F is related to the\nsymplectic Kirillov two forms that characterize irreducible representations of\nSU(N). We propose a general class of nonlinear chiral models that may describe\nstable, soliton-like configurations with nontrivial topological numbers.", "category": "hep-th" }, { "text": "Regge trajectories of the charged string in a magnetic background: The set of Casimir operators associated with the global symmetries of a\ncharged string in a constant magnetic background are found. It is shown that\nthe string rest energy can be expressed as a combination of these invariants.\nUsing this result, the Regge trajectories of the system are derived. The first\nRegge trajectory is given by a family of infinitely many parallel\nstraight-lines, one for each spin projection along the magnetic field.", "category": "hep-th" }, { "text": "Nonlinear ${\\cal N}=2$ Supersymmetry and 3D Supersymmetric Born-Infeld\n Theory: D$p$-branes acquire effective nonlinear descriptions whose bosonic part is\nrelated to the Born-Infeld action. This nonlinearity has been proven to be a\nconsequence of the partial ${\\cal N}=2\\to{\\cal N}=1$ supersymmetry breaking,\noriginating from the solitonic nature of the branes. In this work, we focus on\nthe effective descriptions of D2-branes. Using the Goldstone multiplet\ninterpretation of the action and the method of nilpotent ${\\cal N}=2$\nsuperfields, we construct the 3D, ${\\cal N}=1$ superspace effective action\nwhich makes the first supersymmetry manifest and realizes the second,\nspontaneously broken, supersymmetry nonlinearly. We show that there are two\nsuch supersymmetric extensions of the 3D Born-Infeld action which correspond to\nthe dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the\nTensor-Goldstone multiplet respectively. Moreover, we demonstrate that these\nresults are derived by applying the constrained superfield approach on the\n${\\cal N}=2, D=3$ vector and chiral multiplets after expanding them around a\nnontrivial vacuum. We find that these two descriptions are related by a duality\ntransformation which results in the inversion of a dimensionless parameter. For\nboth descriptions we derive the explicit bosonic and fermionic parts of the 3D\nsuper Born-Infeld action. Finally, consider the deformation of the\nMaxwell-Goldstone superspace action by the characteristic Chern-Simons-like,\ngauge invariant, mass term.", "category": "hep-th" }, { "text": "Two-charge rotating black holes in four-dimensional gauged supergravity: We obtain an asymptotically AdS, non-extremal, electrically charged and\nrotating black hole solution of 4-dimensional U(1)^4 gauged supergravity with 2\nnon-zero and independent U(1) charges. The thermodynamical quantities are\ncomputed. We find BPS solutions that are nakedly singular. The solution is\ngeneralized to include a NUT parameter and dyonic gauge fields. The string\nframe metric has a rank-2 Killing-Stackel tensor and has completely integrable\ngeodesic motion, and the massless Klein-Gordon equation separates for the\nEinstein frame metric.", "category": "hep-th" }, { "text": "Toroidal Compactification Without Vector Structure: Many important ideas about string duality that appear in conventional $\\T^2$\ncompactification have analogs for $\\T^2$ compactification without vector\nstructure. We analyze some of these issues and show, in particular, how\norientifold planes associated with $Sp(n)$ gauge groups can arise from\nT-duality and how they can be interpreted in F-theory. We also, in an appendix,\nresolve a longstanding puzzle concerning the computation of $\\Tr (-1)^F$ in\nfour-dimensional supersymmetric Yang-Mills theory with gauge group SO(n).", "category": "hep-th" }, { "text": "Boundary K-matrix for the quantum Mikhailov-Shabat model: ( We present complete solutions of $K$-matrix for the quantum\nMikhailov-Shabat model. It has been known that there are three diagonal\nsolutions with no free parameters, one being trivial identity solution, the\nothers non-trivial. The most general solutions which we found consist of three\nfamilies corresponding to each diagonal solutions. One family of solutions\ndepends on two arbitrary parameters. If one of the parameters vanishes, the\nother must also vanish so that the solutions reduces to trivial identity\nsolution. The other two families for each non-trivial diagonal solutions have\nonly one arbitrary parameter.)", "category": "hep-th" }, { "text": "Massive Spin-2 Scattering and Asymptotic Superluminality: We place model-independent constraints on theories of massive spin-2\nparticles by considering the positivity of the phase shift in eikonal\nscattering. The phase shift is an asymptotic $S$-matrix observable, related to\nthe time delay/advance experienced by a particle during scattering. Demanding\nthe absence of a time advance leads to constraints on the cubic vertices\npresent in the theory. We find that, in theories with massive spin-2 particles,\nrequiring no time advance means that either: (i) the cubic vertices must appear\nas a particular linear combination of the Einstein-Hilbert cubic vertex and an\n$h_{\\mu\\nu}^3$ potential term or (ii) new degrees of freedom or strong coupling\nmust enter at parametrically the mass of the massive spin-2 field. These\nconclusions have implications for a variety of situations. Applied to theories\nof large-$N$ QCD, this indicates that any spectrum with an isolated massive\nspin-2 at the bottom must have these particular cubic self-couplings. Applied\nto de Rham-Gabadadze-Tolley massive gravity, the constraint is in accord with\nand generalizes previous results obtained from a shockwave calculation: of the\ntwo free dimensionless parameters in the theory there is a one parameter line\nconsistent with a subluminal phase shift.", "category": "hep-th" }, { "text": "Off-shell unimodular N=1, d=4 supergravity: We formulate a unimodular N=1, d=4 supergravity theory off shell. We see that\nthe infinitesimal Grassmann parameters defining the unimodular supergravity\ntransformations are constrained and show that the conmutator of two\ninfinitesinal unimodular supergravity transformations closes on transverse\ndiffeomorphisms, Lorentz transformations and unimodular supergravity\ntransformations. Along the way, we also show that the linearized theory is a\nsupersymmetric theory of gravitons and gravitinos. We see that de Sitter and\nanti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular\nsupergravity theory.", "category": "hep-th" }, { "text": "The Concept of Particle Weights in Local Quantum Field Theory: The concept of particle weights has been introduced by Buchholz and the\nauthor in order to obtain a unified treatment of particles as well as (charged)\ninfraparticles which do not permit a definition of mass and spin according to\nWigner's theory. Particle weights arise as temporal limits of physical states\nin the vacuum sector and describe the asymptotic particle content. Following a\nthorough analysis of the underlying notion of localizing operators, we give a\nprecise definition of this concept and investigate the characteristic\nproperties. The decomposition of particle weights into pure components which\nare linked to irreducible representations of the quasi-local algebra has been a\nlong-standing desideratum that only recently found its solution. We set out two\napproaches to this problem by way of disintegration theory, making use of a\nphysically motivated assumption concerning the structure of phase space in\nquantum field theory. The significance of the pure particle weights ensuing\nfrom this disintegration is founded on the fact that they exhibit features of\nimproper energy-momentum eigenstates, analogous to Dirac's conception, and\npermit a consistent definition of mass and spin even in an infraparticle\nsituation.", "category": "hep-th" }, { "text": "BV-Structure of the Cohomology of Nilpotent Subalgebras and the Geometry\n of (W-) Strings: Given a simple, simply laced, complex Lie algebra $\\bfg$ corresponding to the\nLie group $G$, let $\\bfnp$ be the subalgebra generated by the positive roots.\nIn this paper we construct a BV-algebra $\\fA[\\bfg]$ whose underlying graded\ncommutative algebra is given by the cohomology, with respect to $\\bfnp$, of the\nalgebra of regular functions on $G$ with values in $\\mywedge\n(\\bfnp\\backslash\\bfg)$. We conjecture that $\\fA[\\bfg]$ describes the algebra of\n{\\it all} physical (i.e., BRST invariant) operators of the noncritical\n$\\cW[\\bfg]$ string. The conjecture is verified in the two explicitly known\ncases, $\\bfg=\\sltw$ (the Virasoro string) and $\\bfg=\\slth$ (the $\\cW_3$\nstring).", "category": "hep-th" }, { "text": "Correlation functions on a curved background: We investigate gravitational correlation functions in a curved background\nwith the help of nonperturbative renormalization group methods. Beta functions\nfor eleven couplings are derived, two of which correspond to running gauge\nparameters. A unique ultraviolet fixed point is found, suitable for a UV\ncompletion in the sense of Asymptotic Safety. To arrive at a well-behaved flow\nin a curved background, the regularization must be chosen carefully. We provide\ntwo admissible choices to solve this issue in the present approximation. We\nfurther demonstrate by an explicit calculation that the Landau limit is a fixed\npoint also for quantum gravity, and additionally show that in this limit, the\ngauge parameter $\\beta$ does not flow.", "category": "hep-th" }, { "text": "Multidimensional Dirac strings and the Witten index of SYMCS theories\n with groups of higher rank: We discuss generalized Dirac strings associated with a given Lie group. They\nlive in r-dimensional complex space (r being the rank of the group). Such\nstrings show up in the effective Born-Oppenheimer Hamiltonian for 3d\nsupersymmetric Yang-Mills-Chern-Simons theories, brought up by the gluon loops.\nWe calculate accurately the number of the vacuum states in the effective\nHamiltonian associated with these strings. We also show that these states are\nirrelevant for the final SYMCS vacuum counting. The Witten index of SYMCS\ntheories depends thus only on the strings generated by fermion loops and\ncarrying fractional generalized fluxes.", "category": "hep-th" }, { "text": "Witten Diagrams for Torus Conformal Blocks: We give a holographic description of global conformal blocks in two\ndimensional conformal field theory on the sphere and on the torus. We show that\nthe conformal blocks for one-point functions on the torus can be written as\nWitten diagrams in thermal AdS. This is accomplished by deriving a general\nconformal Casimir equation for global conformal blocks, and showing that Witten\ndiagrams obey the same equation. We study the semi-classical limit of n-point\nconformal blocks, and show that these equal the action of a network of bulk\nworld-lines obeying appropriate geodesic equations. We give an alternate\ndescription in the Chern-Simons formulation of 3D gravity, where the conformal\nblocks are described by networks of Wilson lines, and argue that these\nformulations are equivalent.", "category": "hep-th" }, { "text": "Solutions of massive gravity theories in constant scalar invariant\n geometries: We solve massive gravity field equations in the framework of locally\nhomogenous and vanishing scalar invariant (VSI) Lorentzian spacetimes, which in\nthree dimensions are the building blocks of constant scalar invariant (CSI)\nspacetimes. At first, we provide an exhaustive list of all Lorentzian\nthree-dimensional homogeneous spaces and then we determine the Petrov type of\nthe relevant curvature tensors. Among these geometries we determine for which\nvalues of their structure constants they are solutions of the field equations\nof massive gravity theories with cosmological constant. The homogeneous\nsolutions founded are of all various Petrov types : I_C, I_R, II, III, D_t,\nD_s, N, O; the VSI geometries which we found are of Petrov type III. The Petrov\ntypes II and III are new explicit CSI spacetimes solutions of these types. We\nalso examine the conditions under which the obtained anti-de Sitter solutions\nare free of tachyonic massive graviton modes.", "category": "hep-th" }, { "text": "Fractional space-like branes: We discuss construction and applications of instanton-like objects which we\ncall fractional space-like branes. These objects are localised at a fixed point\nof a time-like (or more generally space-time) orbifold which is a string\ntheoretical toy model of a cosmological singularity. We formulate them in\nboundary state, adsorption, and fermionisation approaches.", "category": "hep-th" }, { "text": "Fermionic quantization of Hopf solitons: In this paper we show how to quantize Hopf solitons using the\nFinkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if\ntheir Hopf charge is odd. Symmetries of classical minimal energy configurations\ninduce loops in configuration space which give rise to constraints on the wave\nfunction. These constraints depend on whether the given loop is contractible.\nOur method is to exploit the relationship between the configuration spaces of\nthe Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use\nrecent results in the Skyrme model to determine whether loops are contractible.\nWe discuss possible quantum ground states up to Hopf charge Q=7.", "category": "hep-th" }, { "text": "Some aspects of self-duality and generalised BPS theories: If a scalar field theory in (1+1) dimensions possesses soliton solutions\nobeying first order BPS equations, then, in general, it is possible to find an\ninfinite number of related field theories with BPS solitons which obey closely\nrelated BPS equations. We point out that this fact may be understood as a\nsimple consequence of an appropriately generalised notion of self-duality. We\nshow that this self-duality framework enables us to generalize to higher\ndimensions the construction of new solitons from already known solutions. By\nperforming simple field transformations our procedure allows us to relate\nsolitons with different topological properties. We present several interesting\nexamples of such solitons in two and three dimensions.", "category": "hep-th" }, { "text": "Symmetry Breaking in Coupled SYK or Tensor Models: We study a large $N$ tensor model with $O(N)^3$ symmetry containing two\nflavors of Majorana fermions, $\\psi_1^{abc}$ and $\\psi_2^{abc}$. We also study\nits random counterpart consisting of two coupled Sachdev-Ye-Kitaev models, each\none containing $N_{\\rm SYK}$ Majorana fermions. In these models we assume\ntetrahedral quartic Hamiltonians which depend on a real coupling parameter\n$\\alpha$. We find a duality relation between two Hamiltonians with different\nvalues of $\\alpha$, which allows us to restrict the model to the range of\n$-1\\leq \\alpha\\leq 1/3$. The scaling dimension of the fermion number operator\n$Q=i\\psi_1^{abc} \\psi_2^{abc}$ is complex and of the form $1/2 +i f(\\alpha)$ in\nthe range $-1\\leq \\alpha<0$, indicating an instability of the conformal phase.\nUsing Schwinger-Dyson equations to solve for the Green functions, we show that\nin the true low-temperature phase this operator acquires an expectation value.\nThis demonstrates the breaking of an anti-unitary particle-hole symmetry and\nother discrete symmetries. We also calculate spectra of the coupled SYK models\nfor values of $N_{\\rm SYK}$ where exact diagonalizations are possible. For\nnegative $\\alpha$ we find a gap separating the two lowest energy states from\nthe rest of the spectrum; this leads to exponential decay of the\nzero-temperature correlation functions. For $N_{\\rm SYK}$ divisible by $4$, the\ntwo lowest states have a small splitting. They become degenerate in the large\n$N_{\\rm SYK}$ limit, as expected from the spontaneous breaking of a\n$\\mathbb{Z}_2$ symmetry.", "category": "hep-th" }, { "text": "Axion Inflation in Type II String Theory: Inflationary models driven by a large number of axion fields are discussed in\nthe context of type IIB compactifications with N=1 supersymmetry. The inflatons\narise as the scalar modes of the R-R two-forms evaluated on vanishing\ntwo-cycles in the compact geometry. The vanishing cycles are resolved by small\ntwo-volumes or NS-NS B-fields which sit together with the inflatons in the same\nsupermultiplets. String world-sheets wrapping the vanishing cycles correct the\nmetric of the R-R inflatons. They can help to generate kinetic terms close to\nthe Planck scale and a mass hierarchy between the axions and their non-axionic\npartners during inflation. At small string coupling, D-brane corrections are\nsubleading in the metric of the R-R inflatons. However, an axion potential can\nbe generated by D1 instantons or gaugino condensates on D5 branes. Models with\nsufficiently large number of axions admit regions of chaotic inflation which\ncan stretch over the whole axion field range for potentials from gaugino\ncondensates. These models could allow for a possibly detectable amount of\ngravitational waves with tensor to scalar ratio as high as r<0.14.", "category": "hep-th" }, { "text": "Exact partition functions for the $\u03a9$-deformed $\\mathcal N=2^{*}$\n $SU(2)$ gauge theory: We study the low energy effective action of the $\\Omega$-deformed $\\mathcal N\n=2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters\n$\\epsilon_{1},\\epsilon_{2}$, the scalar field expectation value $a$, and the\nhypermultiplet mass $m$. We explore the plane $(\\frac{m}{\\epsilon_{1}},\n\\frac{\\epsilon_{2}}{\\epsilon_{1}})$ looking for special features in the\nmulti-instanton contributions to the prepotential, motivated by what happens in\nthe Nekrasov-Shatashvili limit $\\epsilon_{2}\\to 0$. We propose a simple\ncondition on the structure of poles of the $k$-instanton prepotential and show\nthat it is admissible at a finite set of points in the above plane. At these\nspecial points, the prepotential has poles at fixed positions independent on\nthe instanton number. Besides and remarkably, both the instanton partition\nfunction and the full prepotential, including the perturbative contribution,\nmay be given in closed form as functions of the scalar expectation value $a$\nand the modular parameter $q$ appearing in special combinations of Eisenstein\nseries and Dedekind $\\eta$ function. As a byproduct, the modular anomaly\nequation can be tested at all orders at these points. We discuss these special\nfeatures from the point of view of the AGT correspondence and provide explicit\ntoroidal 1-blocks in non-trivial closed form. The full list of solutions with\n1, 2, 3, and 4 poles is determined and described in details.", "category": "hep-th" }, { "text": "Superstrings on AdS3 at k=1: We study superstring theory in three dimensional Anti-de Sitter spacetime\nwith NS-NS flux, focusing on the case where the radius of curvature is equal to\nthe string length. This corresponds to the critical level k=1 in the\nWess-Zumino-Witten description. Previously, it was argued that a transition\ntakes place at this special radius, from a phase dominated by black holes at\nlarger radius to one dominated by long strings at smaller radius. We argue that\nthe infinite tower of modes that become massless at k=1 is a signal of this\ntransition. We propose a simple two-dimensional conformal field theory as the\nholographic dual to superstring theory at k=1. As evidence for our conjecture,\nwe demonstrate that at large N our putative dual exactly reproduces the full\nspectrum of the long strings of the weakly coupled string theory, including\nstates unprotected by supersymmetry.", "category": "hep-th" }, { "text": "Quantum Wilson surfaces and topological interactions: We introduce the description of a Wilson surface as a 2-dimensional\ntopological quantum field theory with a 1-dimensional Hilbert space. On a\nclosed surface, the Wilson surface theory defines a topological invariant of\nthe principal $G$-bundle $P \\to \\Sigma$. Interestingly, it can interact\ntopologically with 2-dimensional Yang-Mills and BF theories modifying their\npartition functions. We compute explicitly the partition function of the\n2-dimensional Yang-Mills theory with a Wilson surface. The Wilson surface turns\nout to be nontrivial for the gauge group $G$ non-simply connected (and trivial\nfor $G$ simply connected). In particular we study in detail the cases\n$G=SU(N)/\\mathbb{Z}_m$, $G=Spin(4l)/(\\mathbb{Z}_2\\oplus\\mathbb{Z}_2)$ and\nobtain a general formula for any compact connected Lie group.", "category": "hep-th" }, { "text": "Role of Various Entropies in the Black Hole Information Loss Problem: In a recent paper Hawking has argued that there is no information loss in\nblack holes in asymptotically AdS spacetimes. We remind that there are several\ntypes of information (entropy) in statistical physics -- fine grained\n(microscopic) and coarse grained (macroscopic) ones which behave differently\nunder unitary evolution. We suggest that the coarse grained information of the\nrest of the Universe is lost while fine grained information is preserved. A\npossibility to develop in quantum gravity an analogue of the Bogoliubov\nderivation of the irreversible Boltzmann and Navier - Stokes equations from the\nreversible mechanical equations is discussed.", "category": "hep-th" }, { "text": "Computation of D-brane instanton induced superpotential couplings -\n Majorana masses from string theory: We perform a detailed conformal field theory analysis of D2-brane instanton\neffects in four-dimensional type IIA string vacua with intersecting D6-branes.\nIn particular, we explicitly compute instanton induced fermion two-point\ncouplings which play the role of perturbatively forbidden Majorana mass terms\nfor right-handed neutrinos or MSSM mu-terms. These results can readily be\nextended to higher-dimensional operators. In concrete realizations of such\nnon-perturbative effects, the Euclidean D2-brane has to wrap a rigid,\nsupersymmetric cycle with strong constraints on the zero mode structure. Their\nimplications for Type IIA compactifications on the T^6/(Z_2 x Z_2) orientifold\nwith discrete torsion are analyzed. We also construct a local supersymmetric\nGUT-like model allowing for a class of Euclidean D2-branes whose fermionic zero\nmodes meet all the constraints for generating Majorana masses in the\nphenomenologically allowed regime. Together with perturbatively realized Dirac\nmasses, these non-perturbative couplings give rise to the see-saw mechanism.", "category": "hep-th" }, { "text": "Quantum Fluctuations of Effective Fields and the Correspondence\n Principle: The question of Bohr correspondence in quantum field theory is considered\nfrom a dynamical point of view. It is shown that the classical description of\nparticle interactions is inapplicable even in the limit of large particles'\nmasses because of finite quantum fluctuations of the fields produced. In\nparticular, it is found that the relative value of the root mean square\nfluctuation of the Coulomb and Newton potentials of a massive particle is equal\nto 1/sqrt{2}. It is shown also that in the case of a macroscopic body, the\nquantum fluctuations are suppressed by a factor 1/sqrt{N}, where N is the\nnumber of particles in the body. An adequate macroscopic interpretation of the\ncorrespondence principle is given.", "category": "hep-th" }, { "text": "The Role of Conformal Symmetry in Abelian Bosonization of the Massive\n Thirring Model: We show equivalence between the massive Thirring model and the sine-Gordon\ntheory by gauge fixing a wider gauge invariant theory in two different ways.\nThe exact derivation of the equivalence hinges on the existence of an\nunderlying conformal symmetry. Previous derivations were all perturbative in\nmass (althought to all orders).", "category": "hep-th" }, { "text": "The Local Structure of Anomaly Inflow: Anomaly cancellation for M-theory fivebranes requires the introduction of a\n\"bump-form\" which smoothes out the five-brane source. We discuss the physical\norigin of this bump-form in the simpler case of axion strings in 3+1 dimensions\nand construct it in terms of the radial profile of the fermion zero modes. Our\ntreatment allows for a clearer understanding of the role played by covariant\nrather than consistent anomalies when anomalies are canceled by inflow from the\nbulk. We briefly discuss the generalization of these results to fivebrane\nanomalies in M theory.", "category": "hep-th" }, { "text": "Crystal bases and three-dimensional $ \\mathcal{N}=4 $ Coulomb branches: We establish and develop a correspondence between certain crystal bases\n(Kashiwara crystals) and the Coulomb branch of three-dimensional $ \\mathcal{N}\n=4 $ gauge theories. The result holds for simply-laced, non-simply laced and\naffine quivers. Two equivalent derivations are given in the non-simply laced\ncase, either by application of the axiomatic rules or by folding a simply-laced\nquiver. We also study the effect of turning on real masses and the ensuing\nsimplification of the crystal. We present a multitude of explicit examples of\nthe equivalence. Finally, we put forward a correspondence between infinite\ncrystals and Hilbert spaces of theories with isolated vacua.", "category": "hep-th" }, { "text": "Consistent boundary conditions for cosmological topologically massive\n gravity at the chiral point: We show that cosmological topologically massive gravity at the chiral point\nallows not only Brown-Henneaux boundary conditions as consistent boundary\nconditions, but slightly more general ones which encompass the logarithmic\nprimary found in 0805.2610 as well as all its descendants.", "category": "hep-th" }, { "text": "Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy\n and Full Counting Statistics: We consider the symmetry-resolved R\\'{e}nyi and entanglement entropies for\ntwo-dimensional conformal field theories on a circle at nonzero temperature. We\nassume a unique ground state with a nonzero mass gap induced by the system's\nfinite size and then calculate the leading corrections to the contributions of\nindividual charge sectors in a low-temperature expansion. Besides the size of\nthe mass gap and the degeneracy of the first excited state, these universal\ncorrections depend only on the four-point correlation function of the primary\nfields. We also obtain thermal corrections to the full counting statistics of\nthe ground state and define the \\textit{probability fluctuations} function. It\nscales as $e^{-2 \\pi \\Delta_{\\psi} \\beta /L}$, where $\\Delta_{\\psi}$ is the\nscaling dimension of the lowest weight states. As an example, we explicitly\nevaluate the thermal corrections to the symmetry-resolved entanglement entropy\nand FCS for the spinless fermions.", "category": "hep-th" }, { "text": "Nonextremal black holes in gauged supergravity and the real formulation\n of special geometry II: In arXiv:1207.2679 a new prescription for finding nonextremal black hole\nsolutions to N=2, D=4 Fayet-Iliopoulos gauged supergravity was presented, and\nexplicit solutions of various models containing one vector multiplet were\nconstructed. Here we use the same method to find new nonextremal black holes to\nmore complicated models. We also provide a general recipe to construct non-BPS\nextremal solutions for an arbitrary prepotential, as long as an axion-free\ncondition holds. These follow from a set of first-order conditions, and are\nrelated to the corresponding supersymmetric black holes by a multiplication of\nthe charge vector with a constant field rotation matrix S. The fake\nsuperpotential driving this first-order flow is nothing else than Hamilton's\ncharacteristic function in a Hamilton-Jacobi formalism, and coincides in the\nsupersymmetric case (when S is plus or minus the identity) with the\nsuperpotential proposed by Dall'Agata and Gnecchi in arXiv:1012.3756. For the\nnonextremal black holes that asymptote to (magnetic) AdS, we compute both the\nmass coming from holographic renormalization and the one appearing in the\nsuperalgebra. The latter correctly vanishes in the BPS case, but also for\ncertain values of the parameters that do not correspond to any known\nsupersymmetric solution of N=2 gauged supergravity. We finally show that the\nproduct of all horizon areas depends only on the charges and the asymptotic\nvalue of the cosmological constant.", "category": "hep-th" }, { "text": "Domain Walls and Decay Rate of the Excited Vacua in the Large N\n Yang-Mills Theory: In the (non-supersymmetric) Yang-Mills theory in the large N limit there\nexists an infinite set of non-degenerate vacua. The distinct vacua are\nseparated by domain walls whose tension determines the decay rate of the false\nvacua. I discuss the phenomenon from a field-theoretic point of view, starting\nfrom supersymmetric gluodynamics and then breaking supersymmetry, by\nintroducing a gluino mass. By combining previously known results, the decay\nrate of the excited vacua is estimated, \\Gamma \\sim \\exp (-const \\times N^4).\nThe fourth power of N in the exponent is a consequence of the fact that the\nwall tension is proportional to N.", "category": "hep-th" }, { "text": "On the Geometry on Antisymmetric Fields: The geometry of antisymmetric fields with nontrivial transitions over a base\nmanifold is described in terms of exact sequences of cohomology groups. This\nformulation leads naturally to the appearance of nontrivial topological charges\nassociated to the periods of the curvature of the antisymmetric fields. The\nrelation between the partition functions of dual theories is carefully studied\nunder the most general assumptions, and new topological factors related to zero\nmodes and the Ray Singer torsion are found.", "category": "hep-th" }, { "text": "Equivalence of A-Maximization and Volume Minimization: The low energy effective theory on a stack of D3-branes at a Calabi-Yau\nsingularity is an $\\mathcal{N} = 1$ quiver gauge theory. The AdS/CFT\ncorrespondence predicts that the strong coupling dynamics of the gauge theory\nis described by weakly coupled type IIB supergravity on $AdS_5 \\times L^5,$\nwhere $L^5$ is a Sasaki-Einstein manifold. Recent results on Calabi-Yau\nalgebras efficiently determine the Hilbert series of any superconformal quiver\ngauge theory. We use the Hilbert series to determine the volume of the horizon\nmanifold in terms of the fields of the quiver gauge theory. One corollary of\nthe AdS/CFT conjecture is that the volume of the horizon manifold $L^5$ is\ninversely proportional to the a-central charge of the gauge theory. By direct\ncomparison of the volume determined from the Hilbert series and the a-central\ncharge, this prediction is proved independently of the AdS/CFT conjecture.", "category": "hep-th" }, { "text": "AdS twistors for higher spin theory: We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7\nfrom twistors describing massless (super-)particles on AdS spaces. A massless\ntwistor transform is derived in a geometric way from classical kinematics.\nRelaxing the spin-shell constraints on twistor space gives an infinite tower of\nmassless states of a ``higher spin particle'', generalising previous work of\nBandos et al. This can generically be done in a number of ways, each defining\nthe states of a distinct higher spin theory, and the method provides a\nsystematic way of finding these. We reproduce known results in D=4, minimal\nsupersymmetric 5- and 7-dimensional models, as well as supersymmetrisations of\nVasiliev's Sp-models as special cases. In the latter models a dimensional\nenhancement takes place, meaning that the theory lives on a space of higher\ndimension than the original AdS space, and becomes a theory of doubletons. This\ntalk was presented at the XIXth Max Born Symposium ``Fundamental Interactions\nand Twistor-Like Methods'', September 2004, in Wroclaw, Poland.", "category": "hep-th" }, { "text": "Derivative Expansion of the Effective Action for QED in 2+1 and 3+1\n dimensions: The derivative expansion of the one-loop effective action in QED$_3$ and\nQED$_4$ is considered. The first term in such an expansion is the effective\naction for a constant electromagnetic field. An explicit expression for the\nnext term containing two derivatives of the field strength $F_{\\mu\\nu}$, but\nexact in the magnitude of the field strength, is obtained. The general results\nfor fermion and scalar electrodynamics are presented. The cases of pure\nelectric and pure magnetic external fields are considered in details. The\nFeynman rules for the perturbative expansion of the one-loop effective action\nin the number of derivatives is developed.", "category": "hep-th" }, { "text": "On the Mutual Information in Hawking Radiation: We compute the mutual information of two Hawking particles emitted\nconsecutively by an evaporating black hole. Following Page, we find that the\nmutual information is of order exp(-S) where S is the entropy of the black\nhole. We speculate on implications for black hole unitarity, in particular on a\npossible failure of locality at large distances.", "category": "hep-th" }, { "text": "On Classical de Sitter Vacua in String Theory: We review the prospect of obtaining tree-level de Sitter (dS) vacua and\nslow-roll inflation models in string compactifications. Restricting ourselves\nto the closed string sector and assuming the absence of NSNS-sources, we\nclassify the minimal classical ingredients that evade the simplest no-go\ntheorems against dS vacua and inflation. Spaces with negative integrated\ncurvature together with certain combinations of low-dimensional orientifold\nplanes and low-rank RR-fluxes emerge as the most promising setups of this\nanalysis. We focus on two well-controlled classes that lead to an effective 4D,\nN=1 supergravity description: Type IIA theory on group or coset manifolds with\nSU(3)-structure and O6-planes, as well as type IIB compactifications on\nSU(2)-structure manifolds with O5- and O7-planes. While fully stabilized AdS\nvacua are generically possible, a number of problems encountered in the search\nfor dS vacua are discussed.", "category": "hep-th" }, { "text": "A method for solve integrable $A_2$ spin chains combining different\n representations: A non homogeneous spin chain in the representations $ \\{3 \\}$ and $ \\{3^*\\}$\nof $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not\napplicable to this case. A method inspired in the nested Bethe ansatz, that can\nbe applied to more general cases, is developed for that chain. The solution for\nthe eigenvalues of the trace of the monodromy matrix is given as two coupled\nBethe equations different from that for a homogeneous chain. A conjecture about\nthe form of the solutions for more general chains is presented.\n PACS: 75.10.Jm, 05.50+q 02.20 Sv", "category": "hep-th" }, { "text": "Isotropic Lifshitz Scaling in four dimensions: The presence of isotropic Lifshitz points for a O(N)-symmetric scalar theory\nis investigated with the help of the Functional Renormalization Group. In\nparticular, at the supposed lower critical dimension d=4, evidence for a\ncontinuous line of fixed points is found for the O(2) theory, and the observed\nstructure presents clear similarities with the properties observed in the\n2-dimensional Berezinskii-Kosterlitz-Thouless phase.", "category": "hep-th" }, { "text": "Abelian Zero Modes in Odd Dimensions: We show that the Loss-Yau zero modes of the 3d abelian Dirac operator may be\ninterpreted in a simple manner in terms of a stereographic projection from a 4d\nDirac operator with a constant field strength of definite helicity. This is an\nalternative to the conventional viewpoint involving Hopf maps from S^3 to S^2.\nFurthermore, our construction generalizes in a straightforward way to any odd\ndimension. The number of zero modes is related to the Chern-Simons number in a\nnonlinear manner.", "category": "hep-th" }, { "text": "A differential relation between the energy and electric charge of a dyon: The differential relation between the energy and electric charge of a dyon is\nderived. The relation expresses the derivative of the energy with respect to\nthe electric charge in terms of the boundary value for the temporal component\nof the dyon's electromagnetic potential. The use of the Hamiltonian formalism\nand transition to the unitary gauge make it possible to show that this\nderivative is proportional to the phase frequency of the electrically charged\nmassive gauge fields forming the dyon's core. It follows from the differential\nrelation that the energy and electric charge of the non-BPS dyon cannot be\narbitrarily large. Finally, the dyon's properties are investigated numerically\nat different values of the model parameters.", "category": "hep-th" }, { "text": "RR charges of D2-branes in the WZW model: We consider the contribution of the B-field into the RR charge of a spherical\nD2-brane. Extending a recent analysis of Taylor, we show that the boundary and\nbulk contributions do not cancel in general. Instead, they add up to an integer\nas observed by Stanciu. The general formula is applied to compute the RR\ncharges of spherical D-branes of the SU(2) WZW model at level k and it shows\nthat these RR charges are only defined modulo k+2. We support this claim by\nstudying bound state formation of D0-branes using boundary conformal field\ntheory.", "category": "hep-th" }, { "text": "Topology and geometry of elliptic Feynman amplitudes: We report on the analytic computation of the 2-loop amplitude for Bhabha\nscattering in QED. We study the analytic structure of the amplitude, and reveal\nits underlying connections to hyperbolic Coxeter groups and arithmetic\ngeometries of elliptic curves.", "category": "hep-th" }, { "text": "The Geometer's Toolkit to String Compactifications: These lecture notes are meant to serve as an introduction to some geometric\nconstructions and techniques (in particular the ones of toric geometry) often\nemployed by the physicist working on string theory compactifications. The\nemphasis is wholly on the geometry side, not on the physics.\n The treated topics include toroidal orbifolds, methods of toric geometry,\ndesinglularization of toroidal orbifolds and their orientifold quotients.", "category": "hep-th" }, { "text": "Exact late time Hawking radiation and the information loss problem for\n evaporating near-extremal black holes: In this paper we investigate the effects of gravitational backreaction for\nthe late time Hawking radiation of evaporating near-extremal black holes. This\nproblem can be studied within the framework of an effective one-loop solvable\nmodel on AdS_2. We find that the Hawking flux goes down exponentially and it is\nproportional to a parameter which depends on details of the collapsing matter.\nThis result seems to suggest that the information of the initial state is not\nlost and that the boundary of AdS_2 acts, at least at late times, as a sort of\nstretched horizon in the Reissner-Nordstrom spacetime.", "category": "hep-th" }, { "text": "On quantum mechanics as constrained N=2 supersymmetric classical\n mechanics: The Schr\\\"odinger equation is shown to be equivalent to a constrained\nLiouville equation under the assumption that phase space is extended to\nGrassmann algebra valued variables. For onedimensional systems, the underlying\nHamiltonian dynamics has a N=2 supersymmetry. Potential applications to more\nrealistic theories are briefly discussed.", "category": "hep-th" }, { "text": "Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model: We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to\na zero-dimensional 3-Lie algebra model and construct various stable solutions\ncorresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs\nmechanism reduces this model to the IKKT matrix model. We find that in the\nstrong coupling limit, our solutions correspond to ordinary noncommutative\nspaces arising as stable solutions in the IKKT model with D-brane backgrounds.\nIn particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz\nHpp-waves. We expand our model around these backgrounds and find effective\nnoncommutative field theories with complicated interactions involving\nhigher-derivative terms. We also describe the relation of our reduced model to\na cubic supermatrix model based on an osp(1|32) supersymmetry algebra.", "category": "hep-th" }, { "text": "The Lifshitz black branes and DC transport coefficients in massive\n Einstein-Maxwell-dilaton gravity: We construct analytical Lifshitz massive black brane solutions in massive\nEinstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of\nthese black brane solutions and obtain the thermodynamical stability\nconditions. On the dual nonrelativistic boundary field theory with Lifshitz\nsymmetry, we analytically compute the DC transport coefficients, including the\nelectric conductivity, thermoelectric conductivity, and thermal conductivity.\nThe novel property of our model is that the massive term supports the Lifshitz\nblack brane solutions with $z\\neq 1$ in such a way that the DC transport\ncoefficients in the dual field theory are finite. We also find that the\nWiedemann-Franz law in this dual boundary field theory is violated, which\nindicates that it may involve strong interactions.", "category": "hep-th" }, { "text": "S-duality transformation of $\\mathcal{N}$ $=4$ SYM theory at the\n operator level: We consider the S-duality transformation of gauge invariant operators and\nstates in $\\mathcal{N}$ $=4$ SYM theory. The transformation is realized through\nan operator $ S $ which is the $ SL(2,Z) $ canonical transformation in loop\nspace with the gauge invariant electric and the magnetic flux operators\ncomposing the canonical variables. Based on $ S $, S-duals for all of the\nphysical operators and states can be defined. The criterion for the theory to\nbe S-duality invariant is that the superconformal charges and their S-duals\ndiffer by a $ U(1)_{Y} $ phase. The verification can be done by checking the S\ntransformation for supersymmetry and special supersymmetry variations of the\nloop operators. The fact that supercharges preserved by BPS Wilson operators\nand the S-dual BPS 't Hooft operators differ by a $4d $ chiral rotation could\nin some sense serve as a proof.", "category": "hep-th" }, { "text": "A finite model of two-dimensional ideal hydrodynamics: A finite-dimensional su($N$) Lie algebra equation is discussed that in the\ninfinite $N$ limit (giving the area preserving diffeomorphism group) tends to\nthe two-dimensional, inviscid vorticity equation on the torus. The equation is\nnumerically integrated, for various values of $N$, and the time evolution of an\n(interpolated) stream function is compared with that obtained from a simple\nmode truncation of the continuum equation. The time averaged vorticity moments\nand correlation functions are compared with canonical ensemble averages.", "category": "hep-th" }, { "text": "Gauge Theory on Twisted $\u03ba$-Minkowski: Old Problems and Possible\n Solutions: We review the application of twist deformation formalism and the construction\nof noncommutative gauge theory on $\\kappa$-Minkowski space-time. We compare two\ndifferent types of twists: the Abelian and the Jordanian one. In each case we\nprovide the twisted differential calculus and consider ${U}(1)$ gauge theory.\nDifferent methods of obtaining a gauge invariant action and related\nproblems are thoroughly discussed.", "category": "hep-th" }, { "text": "Gauge Symmetry Enhancement by Wilson Lines in Twisted Compactification: We point out a simple realization of gauge symmetry enhancement by Wilson\nlines in QFT with twisted compactification in extra dimensions. We illustrate\nthis in the field contents taken from heterotic supergravity in arbitrary\ndimensions toroidally compactified.", "category": "hep-th" }, { "text": "The Seven-sphere and its Kac-Moody Algebra: We investigate the seven-sphere as a group-like manifold and its extension to\na Kac-Moody-like algebra. Covariance properties and tensorial composition of\nspinors under $S^7$ are defined. The relation to Malcev algebras is\nestablished. The consequences for octonionic projective spaces are examined.\nCurrent algebras are formulated and their anomalies are derived, and shown to\nbe unique (even regarding numerical coefficients) up to redefinitions of the\ncurrents. Nilpotency of the BRST operator is consistent with one particular\nexpression in the class of (field-dependent) anomalies. A Sugawara construction\nis given.", "category": "hep-th" }, { "text": "Holographic Representation of Local Operators In De Sitter Space: Assuming the existence of the dS/CFT correspondence, we construct local\nscalar fields with $m^2>\\left( \\frac{d}{2} \\right)^2$ in de Sitter space by\nsmearing over conformal field theory operators on the future/past boundary. To\nmaintain bulk micro-causality and recover the bulk Wightman function in the\nEuclidean vacuum, the smearing prescription must involve two sets of\nsingle--trace operators with dimensions $\\Delta$ and $d-\\Delta$. Thus the local\noperator prescription in de Sitter space differs from the analytic continuation\nfrom the prescription in anti--de Sitter space. Pushing a local operator in the\nglobal patch to future/past infinity is shown to lead to an operator relation\nbetween single--trace operators in conformal field theories at\n$\\mathcal{I}^\\pm$, which can be interpreted as a basis transformation, also\nidentified as the relation between an operator in CFT and its shadow operator.\nConstruction of spin$-s$ gauge field operators is discussed, it is shown that\nthe construction of higher spin gauge fields in de Sitter space is equivalent\nto constructing scalar fields with specific values of mass parameter\n$m^2<\\left( \\frac{d}{2} \\right)^2$. An acausal higher spin bulk operator which\nmatches onto boundary higher spin current is constructed. Implementation of the\nscalar operator constructions in AdS and dS with embedding formalism is briefly\ndescribed.", "category": "hep-th" }, { "text": "Exploring the Tensor Networks/AdS Correspondence: In this paper we study the recently proposed tensor networks/AdS\ncorrespondence. We found that the Coxeter group is a useful tool to describe\ntensor networks in a negatively curved space. Studying generic tensor network\npopulated by perfect tensors, we find that the physical wave function\ngenerically do not admit any connected correlation functions of local\noperators. To remedy the problem, we assume that wavefunctions admitting such\nsemi-classical gravitational interpretation are composed of tensors close to,\nbut not exactly perfect tensors. Computing corrections to the connected two\npoint correlation functions, we find that the leading contribution is given by\nstructures related to geodesics connecting the operators inserted at the\nboundary physical dofs. Such considerations admit generalizations at least to\nthree point functions. This is highly suggestive of the emergence of the\nanalogues of Witten diagrams in the tensor network. The perturbations alone\nhowever do not give the right entanglement spectrum. Using the Coxeter\nconstruction, we also constructed the tensor network counterpart of the BTZ\nblack hole, by orbifolding the discrete lattice on which the network resides.\nWe found that the construction naturally reproduces some of the salient\nfeatures of the BTZ black hole, such as the appearance of RT surfaces that\ncould wrap the horizon, depending on the size of the entanglement region A.", "category": "hep-th" }, { "text": "Spatial correlations of primordial density fluctuations in the standard\n cosmological model: We revisit the {\\it origin of structures problem} of standard\nFriedmann-Robertson-Walker cosmology to point out an unjustified approximation\nin the prevalent analysis. We follow common procedures in statistical mechanics\nto revise the issue without the disputed approximation. Our conclusions\ncontradict the current wisdom and reveal and unexpected scenario for the origin\nof primordial cosmological structures. We show that standard physics operating\nin the cosmic plasma during the radiation dominated expansion of the universe\nproduce at the time of decoupling scale invariant density anisotropies over\ncosmologically large comoving volumes. Scale invariance is shown to be a direct\nconsequence of the causality constrains imposed by the short FRW comoving\nhorizon at decoupling, which strongly suppress the power spectrum of density\nfluctuations with cosmologically large comoving wavelength. The global\namplitude of these cosmological density anisotropies is fixed by the power\nspectrum in comoving modes whose wavelength is shorter than the causal horizon\nat the time and can be comparable to the amplitude of the primordial\ncosmological inhomogeneities imprinted in the cosmic microwave background\nradiation.", "category": "hep-th" }, { "text": "Faddeev-Jackiw formalism for a topological-like oscillator in planar\n dimensions: The problem of a harmonic oscillator coupling to an electromagnetic potential\nplus a topological-like (Chern-Simons) massive term, in two-dimensional space,\nis studied in the light of the symplectic formalism proposed by Faddeev and\nJackiw for constrained systems.", "category": "hep-th" }, { "text": "Superconformal Sigma Models in Higher Than Two Dimensions: Rigidly superconformal sigma models in higher than two dimensions are\nconstructed. These models rely on the existence of conformal Killing spinors on\nthe $p+1$ dimensional worldvolume $(p\\le 5)$, and homothetic conformal Killing\nvectors in the $d$--dimensional target space. In the bosonic case, substituting\ninto the action a particular form of the target space metric admitting such\nKilling vectors, we obtain an action with manifest worldvolume conformal\nsymmetry, which describes the coupling of $d-1$ scalars to a conformally flat\nmetric on the worldvolume. We also construct gauged sigma models with\nworldvolume conformal supersymmetry. The models considered here are\ngeneralizations of the singleton actions on $S^p\\times S^1$, constructed\nsometime ago by Nicolai and these authors.", "category": "hep-th" }, { "text": "Anisotropic Asymptotics and High Energy Scattering: Recently E.Verlinde and H.Verlinde have suggested an effective\ntwo-dimensional theory describing the high-energy scattering in QCD. In this\nreport we attempt to clarify some issues of this suggestion. We consider {\\it\nanisotropic asymptotics} of correlation functions for scalar and gauge theories\nin four dimensions. Anisotropic asymptotics describe behaviour of correlation\nfunctions when some components of coordinates are large as compare with others\ncomponents. It is occurred that (2+2) anisotropic asymptotics for 4-points\nfunctions are related with the well known Regge regime of scattering\namplitudes. We study an expansion of correlation functions with respect to the\nrescaling parameter $\\lambda$ over a part of variables (anisotropic\n$\\lambda$-expansion). An effective theory describing the anisotropic limit of\nfree scalar field contains two 2 dim conformal theories. One of them is a\nconformal theory in configuration space and another one is a conformal theory\nin momentum space. In some special cases ,in particular for the Wilson line\ncorrelators in gauge theories, the leading term of the anisotropic expansion\ninvolves only one of the conformal theories and it can be described by an\neffective theory with an action being a dimensional reduction of the original\naction.", "category": "hep-th" }, { "text": "Fermions with spin 1/2 as global SO(3) vortices: In this paper we show that the nontrivial fundamental group $\\pi_1 SO(3)\n={\\Bbb Z}_2$ for the group SO(3) of global proper rotations of a\nfour-dimensional Euclidian space (when a spin structure is introduced\npreliminarily in that space) implies always fermions as global SO(3) vortices,\nwhile bosons can be reduced to trivial lines (contracted into a point) in the\nSO(3) group space.", "category": "hep-th" }, { "text": "Dressing Cosets: The account of the Poisson-Lie T-duality is presented for the case when the\naction of the duality group on a target is not free. At the same time a\ngeneralization of the picture is given when the duality group does not even act\non $\\si$-model targets but only on their phase spaces. The outcome is a huge\nclass of dualizable targets generically having no local isometries or\nPoisson-Lie symmetries whatsoever.", "category": "hep-th" }, { "text": "Holographic Interpretation of Relative State Complexity: We investigate a large-$N$ CFT in a high-energy pure state coupled to a small\nauxiliary system of $M$ weakly-interacting degrees of freedom, and argue the\nrelative state complexity of the auxiliary system is holographically dual to an\neffective low-energy notion of computational cost in the bulk, \\textit{i.e.} to\nthe minimal depth of the quantum circuit required to decode its gravitational\ndual. In light of this, using Nielsen's approach, a new measure of quantum\nchaos in terms of the evolution of circuit complexity is proposed. It suggests\nthat studying the evolution of circuit complexity of the auxiliary system can\nteach us about the chaotic properties of the large-$N$ CFT. This new diagnostic\nfor quantum chaos has important implications for the interior dynamics of\nevaporating black holes as it implies the radiated Hawking cloud is\npseudorandom.", "category": "hep-th" }, { "text": "Is N = 8 Supergravity Ultraviolet Finite?: Conventional wisdom holds that no four-dimensional gravity field theory can\nbe ultraviolet finite. This understanding is based mainly on power counting.\nRecent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the\nso-called `no-triangle hypothesis', which states that triangle and bubble\nintegrals cancel from these amplitudes. A consequence of this hypothesis is\nthat for any number of external legs, at one loop N = 8 supergravity and N = 4\nsuper-Yang-Mills have identical superficial degrees of ultraviolet behavior in\nD dimensions. We describe how the unitarity method allows us to promote these\none-loop cancellations to higher loops, suggesting that previous power counts\nwere too conservative. We discuss higher-loop evidence suggesting that N = 8\nsupergravity has the same degree of divergence as N = 4 super-Yang-Mills theory\nand is ultraviolet finite in four dimensions. We comment on calculations needed\nto reinforce this proposal, which are feasible using the unitarity method.", "category": "hep-th" }, { "text": "From 4d Ambitwistor Strings to On Shell Diagrams and Back: We investigate the relation between 4d ambitwistor string theory and on-shell\ndiagrams for planar N=4 super-Yang-Mills and N=8 supergravity, and deduce\nseveral new results about their scattering amplitudes at tree-level and 1-loop.\nIn particular, we derive new Grassmannian integral formulae for tree-level\namplitudes and obtain new worldsheet formulae for 1-loop amplitudes which are\nmanifestly supersymmetric and supported on scattering equations refined by MHV\ndegree.", "category": "hep-th" }, { "text": "Fractional Strings in (p,q) 5-brane and Quiver Matrix String Theory: We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theory\nin the T-dualized ALE background. The most remarkable feature in the\n(p,q)5-brane is the existence of ``fractional string'', which appears as the\ninstanton of 5-brane gauge theory. We approach to the physical aspects of\nfractional string by means of the two types of Matrix string probes: One of\nwhich is that given in hep-th/9710065. As the second probe we present the\nMatrix string theory describing the fractional string itself. We calculate the\nmoduli space metrics in the respective cases and argue on the specific\nbehaviors of fractional string. Especially, we show that the ``joining''\nprocess of fractional strings can be realized as the transition from the\nCoulomb branch to the Higgs branch of the fractional string probe. In this\nargument, we emphasize the importance of some monodromies related with the\ntheta-angle of the 5-brane gauge theory.", "category": "hep-th" }, { "text": "Higher Dimensional Supersymmetry: Higher dimensional super symmetry has been analyzed in terms of quaternion\nvariables and the theory of quaternion harmonic oscillator has been analyzed.\nSupersymmertization of quaternion Dirac equation has been developed for\nmassless,massive and interacting cases including generalized electromagnetic\nfields of dyons. Accordingly higher dimensional super symmetric gauge theories\nof dyons are analyzed.", "category": "hep-th" }, { "text": "Matrix Theory, AdS/CFT and Higgs-Coulomb Equivalence: We discuss the relation between the Matrix theory definitions of a class of\ndecoupled theories and their AdS/CFT description in terms of the corresponding\nnear-horizon geometry. The near horizon geometry, naively part of the Coulomb\nbranch, is embedded in the Higgs branch via a natural change of variables. The\nprinciples of the map apply to all DLCQ descriptions in terms of hyper-K\\\"ahler\nquotients, such as the ADHM quantum mechanics for the D1-D5 system. We then\nfocus the (2,0) field theory, and obtain an explicit mapping from all states in\nthe $N_0=1$ momentum sector of $N_4$ M5-branes to states in (a DLCQ version of)\n$AdS_7\\times S^4$. We show that, even for a single D0-brane, the space-time\ncoordinates become non-commuting variables, suggesting an inherent\nnon-commutativity of space-time in the presence of field strengths even for\ntheories with gravity.", "category": "hep-th" }, { "text": "Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and\n behaviors in IR and UV: We analyze four-dimensional (4d) $N=1$ superconformal field theories (SCFTs)\nobtained as deformations of 4d $N=2$ SCFTs on S-folds by tilting 7-branes.\nGeometric compatibility with the structures of S-folds constrains the forms of\nT-branes. As a result, brane monodromies are constrained. We also discuss two\n4d $N=1$ theories on probe D3-branes, where the two theories behave identically\nin IR, but they originate from different theories in UV. Studying the global\nstructure of their geometry is useful in constructing these two theories.", "category": "hep-th" }, { "text": "Holographic Geometric Entropy at Finite Temperature from Black Holes in\n Global Anti de Sitter Spaces: Using a holographic proposal for the geometric entropy we study its behavior\nin the geometry of Schwarzschild black holes in global $AdS_p$ for $p=3,4,5$.\nHolographically, the entropy is determined by a minimal surface. On the gravity\nside, due to the presence of a horizon on the background, generically there are\ntwo solutions to the surfaces determining the entanglement entropy. In the case\nof $AdS_3$, the calculation reproduces precisely the geometric entropy of an\ninterval of length $l$ in a two dimensional conformal field theory with\nperiodic boundary conditions. We demonstrate that in the cases of $AdS_{4}$ and\n$AdS_{5}$ the sign of the difference of the geometric entropies changes,\nsignaling a transition. Euclideanization implies that various embedding of the\nholographic surface are possible. We study some of them and find that the\ntransitions are ubiquitous. In particular, our analysis renders a very\nintricate phase space, showing, for some ranges of the temperature, up to three\nbranches. We observe a remarkable universality in the type of results we obtain\nfrom $AdS_4$ and $AdS_5$.", "category": "hep-th" }, { "text": "Quantized Noncommutative Geometry from Multitrace Matrix Models: In this article the geometry of quantum gravity is quantized in the sense of\nbeing noncommutative (first quantization) but it is also quantized in the sense\nof being emergent (second quantization). A new mechanism for quantum geometry\nis proposed in which noncommutative geometry can emerge from \"one-matrix\nmultitrace scalar matrix models\" by probing the statistical physics of\ncommutative phases of matter. This is in contrast to the usual mechanism in\nwhich noncommutative geometry emerges from \"many-matrix singletrace Yang-Mills\nmatrix models\" by probing the statistical physics of noncommutative phases of\ngauge theory. In this novel scenario quantized geometry emerges in the form of\na transition between the two phase diagrams of the real quartic matrix model\nand the noncommutative scalar phi-four field theory. More precisely, emergence\nof the geometry is identified here with the emergence of the uniform-ordered\nphase and the corresponding commutative (Ising) and noncommutative (stripe)\ncoexistence lines. The critical exponents and the Wigner's semicircle law are\nused to determine the dimension and the metric respectively. Arguments from the\nsaddle point equation, from Monte Carlo simulation and from the matrix\nrenormalization group equation are provided in support of this scenario.", "category": "hep-th" }, { "text": "Conformal graphs as twisted partition functions: We show that a class of $L$-loop conformal ladder graphs correspond to\ntwisted partition functions of free massive complex scalars in $d=2L+1$\ndimensions. The graphs arise as four-point functions in certain two- and\nfour-dimensional conformal fishnet models. The twisted thermal two-point\nfunction of the scalars is a generator of such conformal graphs for all loops.\nWe argue that this correspondence is seeded by a system of two decoupled\nharmonic oscillators twisted by an imaginary chemical potential. We find a\nnumber of algebraic and differential relations among the conformal graphs which\nmirror the underlying free dynamics.", "category": "hep-th" }, { "text": "A Resummable beta-Function for Massless QED: Within the set of schemes defined by generalized, manifestly gauge invariant\nexact renormalization groups for QED, it is argued that the beta-function in\nthe four dimensional massless theory cannot possess any nonperturbative power\ncorrections. Consequently, the perturbative expression for the beta-function\nmust be resummable. This argument cannot be extended to flows of the other\ncouplings or to the anomalous dimension of the fermions and so perturbation\ntheory does not define a unique trajectory in the critical surface of the\nGaussian fixed point. Thus, resummability of the beta-function is not\ninconsistent with the expectation that a non-trivial fixed point does not\nexist.", "category": "hep-th" }, { "text": "Reflected entropy in Galilean conformal field theories and flat\n holography: We obtain the reflected entropy for bipartite states in a class of\n$(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) through a\nreplica technique. Furthermore we compare our results with the entanglement\nwedge cross section (EWCS) obtained for the dual (2+1) dimensional\nasymptotically flat geometries in the context of flat holography. We find that\nour results are consistent with the duality between the reflected entropy and\nthe bulk EWCS for flat holographic scenarios.", "category": "hep-th" }, { "text": "Scattering in Twisted Yangians: We study the bulk and boundary scattering of the sl(N) twisted Yangian spin\nchain via the solution of the Bethe ansatz equations in the thermodynamic\nlimit. Explicit expressions for the scattering amplitudes are obtained and the\nfactorization of the bulk scattering is shown. The issue of defects in twisted\nYangians is also briefly discussed.", "category": "hep-th" }, { "text": "Tunneling Mechanism in Kerr-Newman Black Hole and Dimensional Reduction\n near the Horizon: It is shown that the derivation of the Hawking radiation from a rotating\nblack hole on the basis of the tunneling mechanism is greatly simplified by\nusing the technique of the dimensional reduction near the horizon. This\ntechnique is illustrated for the original derivation by Parikh and Wilczek, but\nit is readily applied to a variant of the method such as suggested by Banerjee\nand Majhi.", "category": "hep-th" }, { "text": "Conformal multi-Regge theory: We propose and explore the Regge limit for correlation functions of five\nlocal primary operators in conformal field theories. After reviewing some\nfeatures of Regge theory for flat-space scattering amplitudes, we analyse the\nanalytic structure of conformal blocks both in position and Mellin space in the\nRegge limit and propose an extension of conformal Regge theory for five-point\nfunctions. As a byproduct of our analysis we also introduce a new basis of\nthree-point correlation functions for operators with spin and the associated\nEuclidean conformal blocks.", "category": "hep-th" }, { "text": "Holographic Entanglement Entropy for the Most General Higher Derivative\n Gravity: The holographic entanglement entropy for the most general higher derivative\ngravity is investigated. We find a new type of Wald entropy, which appears on\nentangling surface without the rotational symmetry and reduces to usual Wald\nentropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for\nthe most general higher derivative gravity and work it out exactly for some\nsquashed cones. As an important application, we derive HEE for gravitational\naction with one derivative of the curvature when the extrinsic curvature\nvanishes. We also study some toy models with non-zero extrinsic curvature. We\nprove that our formula yields the correct universal term of entanglement\nentropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and\nSmolkin that the logarithmic term of entanglement entropy derived from Weyl\nanomaly of CFTs does not match the holographic result even if the extrinsic\ncurvature vanishes. We find that such mismatch comes from the `anomaly of\nentropy' of the derivative of curvature. After considering such contributions\ncarefully, we resolve the puzzle successfully. In general, we need to fix the\nsplitting problem for the conical metrics in order to derive the holographic\nentanglement entropy. We find that, at least for Einstein gravity, the\nsplitting problem can be fixed by using equations of motion. How to derive the\nsplittings for higher derivative gravity is a non-trivial and open question.\nFor simplicity, we ignore the splitting problem in this paper and find that it\ndoes not affect our main results.", "category": "hep-th" }, { "text": "Bound states in the three dimensional phi^4 model: We discuss the spectrum of the three dimensional phi^4 theory in the broken\nsymmetry phase. In this phase the effective potential between the elementary\nquanta of the model is attractive and bound states of two or more of them may\nexist. We give theoretical and numerical evidence for the existence of these\nbound states. Looking in particular at the Ising model realization of the phi^4\ntheory we show, by using duality, that these bound states are in one-to-one\ncorrespondence with the glueball states of the gauge Ising model. We discuss\nsome interesting consequences of this identification.", "category": "hep-th" }, { "text": "Black holes on cylinders are not algebraically special: We give a Petrov classification for five-dimensional metrics. We classify\nRicci-flat metrics that are static, have an SO(3) isometry group and have\nPetrov type 22. We use this classification to look for the metric of a black\nhole on a cylinder, i.e. a black hole with asymptotic geometry four-dimensional\nMinkowski space times a circle. Although a black string wrapped around the\ncircle and the five-dimensional black hole are both algebraically special, it\nturns out that the black hole on a cylinder is not.", "category": "hep-th" }, { "text": "Matching gluon scattering amplitudes and Wilson loops in off-shell\n regularization: We construct a regularization for light-like polygonal Wilson loops in ${\\cal\nN}=4$ SYM, which matches them to the off-shell MHV gluon scattering amplitudes.\nExplicit calculations are performed for the 1-loop four gluon case. The off\nlight cone extrapolation has to be based on the local supersymmetric Wilson\nloop. The observed matching concerns Feynman gauge. Furthermore, the leading\ninfrared divergent term is shown to be gauge parameter independent on 1-loop\nlevel.", "category": "hep-th" }, { "text": "An Alternative to Compactification: Conventional wisdom states that Newton's force law implies only four\nnon-compact dimensions. We demonstrate that this is not necessarily true in the\npresence of a non-factorizable background geometry. The specific example we\nstudy is a single 3-brane embedded in five dimensions. We show that even\nwithout a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and\ngeneral relativistic gravity is reproduced to more than adequate precision.", "category": "hep-th" }, { "text": "Superconformally covariant operators and super W algebras: We study superdifferential operators of order $2n+1$ which are covariant with\nrespect to superconformal changes of coordinates on a compact super Riemann\nsurface. We show that all such operators arise from super M\\\"obius covariant\nones. A canonical matrix representation is presented and applications to\nclassical super W algebras are discussed.", "category": "hep-th" }, { "text": "Two-Dimensional Quantum Poincar\u00c9 Group: Quantum Poincar\\'e-Weyl group in two dimensional quantum Minkowski space-time\nis considered and an appriopriate relativistic kinematics is investigated. It\nis claimed that a consistent approach to the above questions demands a kind of\na ``quantum geometry'' in the $q$-deformed space-time.", "category": "hep-th" }, { "text": "Exact Results in 5D from Instantons and Deconstruction: We consider non-perturbative effects in theories with extra dimensions and\nthe deconstructed versions of these theories. We establish the rules for\ninstanton calculations in 5D theories on the circle, and use them for an\nexplicit one-instanton calculation in a supersymmetric gauge theory. The\nresults are then compared to the known exact Seiberg-Witten type solution for\nthis theory, confirming the validity both of the exact results and of the rules\nfor instanton calculus for extra dimensions introduced here. Next we consider\nthe non-perturbative results from the perspective of deconstructed extra\ndimensions. We show that the non-perturbative results of the deconstructed\ntheory do indeed reproduce the known results for the continuum extra\ndimensional theory, thus providing the first non-perturbative evidence in favor\nof deconstruction. This way deconstruction also allows us to make exact\npredictions in higher dimensional theories which agree with earlier results,\nand helps to clarify the interpretation of 5D instantons.", "category": "hep-th" }, { "text": "Higher derivative corrections to DBI action at $ \u03b1'^2$ order: We use the compatibility of D-brane action with linear off-shell T-duality\nand linear on-shell S-duality as guiding principles to find all world volume\ncouplings of one massless closed and three massless open strings at order\n$\\alpha'^2$ in type II superstring theories in flat space-time.", "category": "hep-th" }, { "text": "Covariant - tensor method for quantum groups and applications I:\n $SU(2)_{q}$: A covariant - tensor method for $SU(2)_{q}$ is described. This tensor method\nis used to calculate q - deformed Clebsch - Gordan coefficients. The connection\nwith covariant oscillators and irreducible tensor operators is established.\nThis approach can be extended to other quantum groups.", "category": "hep-th" }, { "text": "Comments on gauge invariant overlaps for marginal solutions in open\n string field theory: We calculate the gauge invariant overlaps for\nSchnabl/Kiermaier-Okawa-Rastelli-Zwiebach's marginal solution with nonsingular\ncurrent. The obtained formula is the same as that for\nFuchs-Kroyter-Potting/Kiermaier-Okawa's marginal solution, which was already\ncomputed by Ellwood. Our result is consistent with the expectation that they\nmay be gauge equivalent. We also comment on a gauge invariant overlap for\nrolling tachyon solutions in cubic open string field theory.", "category": "hep-th" }, { "text": "Interactions of Charged Spin-2 Fields: In light of recent progress in ghost-free theories of massive gravity and\nmulti-gravity, we reconsider the problem of constructing a ghost-free theory of\nan interacting spin-2 field charged under a U(1) gauge symmetry. Our starting\npoint is the theory originally proposed by Federbush, which is essentially\nFierz-Pauli generalized to include a minimal coupling to a U(1) gauge field. We\nshow the Federbush theory with a dynamical U(1) field is in fact ghost-free and\ncan be treated as a healthy effective field theory to describe a massive\ncharged spin-2 particle. It can even potentially have healthy dynamics above\nits strong-coupling scale. We then construct candidate gravitational extensions\nto the Federbush theory both by using Dimensional Deconstruction, and by\nconstructing a general non-linear completion. However, we find that the U(1)\nsymmetry forces us to modify the form of the Einstein-Hilbert kinetic term. By\nperforming a constraint analysis directly in the first-order form, we show that\nthese modified kinetic terms inevitably reintroduce the Boulware-Deser ghost.\nAs a by-product of our analysis, we present a new proof for ghost-freedom of\nbi-gravity in 2+1 dimensions (also known as Zwei-Dreibein gravity). We also\ngive a complementary algebraic argument that the Einstein-Hilbert kinetic term\nis incompatible with a U(1) symmetry, for a finite number of gravitons.", "category": "hep-th" }, { "text": "Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory: We study the U(N) non-commutative Yang-Mills theory at the one-loop\napproximation. We check renormalizability and gauge invariance of the model and\ncalculate the one-loop beta function. The interaction of the SU(N) gauge bosons\nwith the U(1) gauge boson plays an important role in the consistency check. In\nparticular, the SU(N) theory by itself is not consistent. We also find that the\ntheta --> 0 limit of the U(N) theory does not converge to the ordinary SU(N) x\nU(1) commutative theory, even at the planar limit. Finally, we comment on the\nUV/IR mixing.", "category": "hep-th" }, { "text": "From positive geometries to a coaction on hypergeometric functions: It is well known that Feynman integrals in dimensional regularization often\nevaluate to functions of hypergeometric type. Inspired by a recent proposal for\na coaction on one-loop Feynman integrals in dimensional regularization, we use\nintersection numbers and twisted homology theory to define a coaction on\ncertain hypergeometric functions. The functions we consider admit an integral\nrepresentation where both the integrand and the contour of integration are\nassociated with positive geometries. As in dimensionally-regularized Feynman\nintegrals, endpoint singularities are regularized by means of exponents\ncontrolled by a small parameter $\\epsilon$. We show that the coaction defined\non this class of integral is consistent, upon expansion in $\\epsilon$, with the\nwell-known coaction on multiple polylogarithms. We illustrate the validity of\nour construction by explicitly determining the coaction on various types of\nhypergeometric ${}_{p+1}F_p$ and Appell functions.", "category": "hep-th" }, { "text": "The Berry-Tabor conjecture for spin chains of Haldane-Shastry type: According to a long-standing conjecture of Berry and Tabor, the distribution\nof the spacings between consecutive levels of a \"generic'' integrable model\nshould follow Poisson's law. In contrast, the spacings distribution of chaotic\nsystems typically follows Wigner's law. An important exception to the\nBerry-Tabor conjecture is the integrable spin chain with long-range\ninteractions introduced by Haldane and Shastry in 1988, whose spacings\ndistribution is neither Poissonian nor of Wigner's type. In this letter we\nargue that the cumulative spacings distribution of this chain should follow the\n\"square root of a logarithm'' law recently proposed by us as a characteristic\nfeature of all spin chains of Haldane-Shastry type. We also show in detail that\nthe latter law is valid for the rational counterpart of the Haldane-Shastry\nchain introduced by Polychronakos.", "category": "hep-th" }, { "text": "Lessons from All Logs Summation in Yukawa Theories: Some features of old results in the total summation of all logarithmic\ncontributions of all diagrams in Yukawa theory are presented. We discuss some\nlessons from this picture for the description of Pomeron, odderon, etc. in QCD.", "category": "hep-th" }, { "text": "Fermion vacuum energies in brane world models: The fermion representations and boundary conditions in five dimensional anti\nde Sitter space are described in detail. In each case the one loop effective\naction is calculated for massless fermions. The possibility of topological or\nWilson loop symmetry breaking is discussed.", "category": "hep-th" }, { "text": "Linear $r$-matrix algebra for classical separable systems: We consider a hierarchy of the natural type Hamiltonian systems of $n$\ndegrees of freedom with polynomial potentials separable in general ellipsoidal\nand general paraboloidal coordinates. We give a Lax representation in terms of\n$2\\times 2$ matrices for the whole hierarchy and construct the associated\nlinear $r$-matrix algebra with the $r$-matrix dependent on the dynamical\nvariables. A Yang-Baxter equation of dynamical type is proposed. Using the\nmethod of variable separation we provide the integration of the systems in\nclassical mechanics conctructing the separation equations and, hence, the\nexplicit form of action variables. The quantisation problem is discussed with\nthe help of the separation variables.", "category": "hep-th" }, { "text": "Detecting topological sectors in continuum Yang-Mills theory and the\n fate of BRST symmetry: In this work, motivated by Laplacian type center gauges in the lattice,\ndesigned to avoid the Gribov problem, we introduce a new family of gauge\nfixings for pure Yang-Mills theories in the continuum. This procedure separates\nthe partition function into partial contributions associated with different\nsectors, containing center vortices and correlated monopoles. We show that, on\neach sector, the gauge fixed path-integral displays a BRST symmetry, however,\nit cannot be globally extended due to sector dependent boundary conditions on\nthe ghost fields. These are nice features as they would permit to discuss the\nindependence of the partial contributions on gauge parameters,, while opening a\nwindow for the space of quantum states to be different from the perturbative\none, which would be implied if topological configurations were removed.", "category": "hep-th" }, { "text": "Opers and TBA: In this note we study the \"conformal limit\" of the TBA equations which\ndescribe the geometry of the moduli space of four-dimensional N=2 gauge\ntheories compactified on a circle. We argue that the resulting conformal TBA\nequations describe a generalization of the oper submanifold in the space of\ncomplex flat connections on a Riemann surface. In particular, the conformal TBA\nequations for theories in the A1 class produce solutions of the Schr\\\"odinger\nequation with a rational potential.", "category": "hep-th" }, { "text": "On the canonical structure and extra mode of generalized unimodular\n gravity: We consider a recently proposed generalization of unimodular gravity, where\nthe lapse function is constrained to be equal to a function of the determinant\nof the spatial metric $f(h)$, as a potential origin of a dark fluid with a\ngenerally $h$-dependent equation of state parameter. We establish the\nHamiltonian analysis and the canonical path integral for the theory. All the\nspecial cases that do not match unimodular gravity involve violation of general\ncovariance, and consequently the physical content of the theory is changed\nsignificantly. Particularly, the case of a constant function $f$ is shown to\ncontain an extra physical degree of freedom in each point of space. Physical\nconsequences of the extra degree of freedom are studied in a linearized theory,\nwhere the extra mode is carried by the trace of the metric perturbation. The\ntrace mode does not propagate as a wave, since it satisfies an elliptic partial\ndifferential equation in spacetime. Consequently, the trace perturbation is\nshown to grow exponentially with time, which implies instability. The case of a\ngeneral $f(h)$ involves additional second-class constraints, which implies the\npresence of an extra global degree of freedom that depends only on time\n(instead of the extra local degree of freedom in the case of a constant $f$).", "category": "hep-th" }, { "text": "Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space: We show that standard Einstein gravity coupled to a free conformal field\ntheory (CFT) in Anti de Sitter space can undergo a Higgs phenomenon whereby the\ngraviton acquires a nonzero mass (and three extra polarizations). We show that\nthe essential ingredients of this mechanism are the discreteness of the energy\nspectrum in AdS space, and unusual boundary conditions on the elementary fields\nof the CFT. These boundary conditions can be interpreted as implying the\nexistence of a 3-d defect CFT living at the boundary of the AdS space. Our\nfree-field computation sheds light on the essential, model-independent features\nof AdS that give rise to massive gravity.", "category": "hep-th" }, { "text": "Non-Einstein geometries in Chiral Gravity: We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive\nGravity at \\mu l = 1 with Brown-Henneaux boundary conditions) focusing on\nnon-Einstein metrics. A class of such solutions admits curvature singularities\nin the interior which are reflected as singularities or infinite bulk energy of\nthe corresponding linear solutions. A non-linear solution is found exactly. The\nback-reaction induces a repulsion of geodesics and a shielding of the\nsingularity by an event horizon but also introduces closed timelike curves.", "category": "hep-th" }, { "text": "Fermion scattering on topological solitons in the $\\mathbb{CP}^{N-1}$\n model: The scattering of Dirac fermions in the background fields of topological\nsolitons of the $(2+1)$-dimensional $\\mathbb{CP}^{N-1}$ model is studied using\nanalytical and numerical methods. It is shown that the exact solutions for\nfermionic wave functions can be expressed in terms of the confluent Heun\nfunctions. The question of the existence of bound states for the\nfermion-soliton system is then investigated. General formulae describing\nfermion scattering are obtained, and a symmetry property for the partial phase\nshifts is derived. The amplitudes and cross-sections of the fermion-soliton\nscattering are obtained in an analytical form within the framework of the Born\napproximation, and the symmetry properties and asymptotic forms of the Born\namplitudes are investigated. The dependences of the first few partial phase\nshifts on the fermion momentum are obtained by numerical methods, and some of\ntheir properties are investigated and discussed.", "category": "hep-th" }, { "text": "Non-Abelian tensor gauge fields and new topological invariants: In this article we shall consider the tensor gauge fields which are possible\nto embed into the existing framework of generalized YM theory and therefore\nallows to construct the gauge invariant and metric independent forms in 2n+4\nand 2n+2 dimensions. These new forms are analogous to the\nPontryagin-Chern-Simons densities in YM gauge theory and to the corresponding\nseries of densities in 2n+3 dimensions constructed recently in arXiv:1205.0027.", "category": "hep-th" }, { "text": "Flux-Induced Baryon Asymmetry: I propose that the primordial baryon asymmetry of the universe was induced by\nthe presence of a non-vanishing antisymmetric field background H_ijk across the\nthree space dimensions. This background creates a dilute (B-L)-number density\nin the universe cancelling the contribution from baryons and leptons. This\nsituation naturally appears if the U(1)_{B-L} symmetry is gauged and the\ncorresponding gauge boson gets a Stuckelberg mass by combining with an\nantisymmetric field B_ij. All these ingredients are present in D-brane models\nof particle physics. None of the Sakharov conditions are required.", "category": "hep-th" }, { "text": "Mesoscopic Fluctuations in Stochastic Spacetime: Mesoscopic effects associated with wave propagation in spacetime with metric\nstochasticity are studied. We show that the scalar and spinor waves in a\nstochastic spacetime behave similarly to the electrons in a disordered system.\nViewing this as the quantum transport problem, mesoscopic fluctuations in such\na spacetime are discussed. The conductance and its fluctuations are expressed\nin terms of a nonlinear sigma model in the closed time path formalism. We show\nthat the conductance fluctuations are universal, independent of the volume of\nthe stochastic region and the amount of stochasticity.", "category": "hep-th" }, { "text": "Matching three-point functions of BMN operators at weak and strong\n coupling: The agreement between string theory and field theory is demonstrated in the\nleading order by providing the first calculation of the correlator of three\ntwo-impurity BMN states with all non-zero momenta. The calculation is performed\nin two completely independent ways: in field theory by using the large-$N$\nperturbative expansion, up to the terms subleading in finite-size, and in\nstring theory by using the Dobashi-Yoneya 3-string vertex in the leading order\nof the Penrose expansion. The two results come out to be completely identical.", "category": "hep-th" }, { "text": "Winding Tachyons and Stringy Black Holes: We study string theory on $\\mathbb{R}^d\\times \\mathbb{S}^1$. For applications\nto thermodynamics, the circumference of the $\\mathbb{S}^1$ is the inverse\ntemperature, $\\beta$. We show that for $d=6$, the low energy effective field\ntheory at the inverse Hagedorn temperature, $\\beta=\\beta_H$, has a one\nparameter family of normalizable spherically symmetric solutions that break the\nwinding symmetry around the $\\mathbb{S}^1$. The resulting backgrounds exhibit\nan enhanced symmetry, with the symmetry breaking pattern $SU(2)_L\\times\nSU(2)_R\\to SU(2)_{\\rm diagonal}$. The effective field theory analysis of these\nbackgrounds is reliable for some range of parameters. More generally, they are\ndescribed by a worldsheet CFT, which corresponds to the free theory on\n$\\mathbb{R}^6\\times \\mathbb{S}^1$ perturbed by a non-abelian Thirring\ndeformation with an $r$-dependent coupling. We propose that, in a certain\nscaling limit, string theory in these backgrounds is described by the\n$SL(2,\\mathbb{R})/U(1)$ cigar, and provides a thermodynamic description of\nweakly coupled highly excited fundamental strings. We also discuss the relation\nof these backgrounds to Euclidean black holes with near-Hagedorn Hawking\ntemperature, and possible generalizations to other $d$.", "category": "hep-th" }, { "text": "Transverse Goldstone mode in holographic fluids with broken translations: In this paper we investigate the low energy shear modes in fluid systems with\nspontaneously broken translations by a specific holographic model. In absence\nof momentum relaxation, we find that there exist two decoupled gapless modes in\nthe transverse channel, one of which is purely diffusive and the other\ncorresponds to vortex like excitations. The diffusive mode is associated with\nthe conservation of momentum and the vortex mode can be viewed as the Goldstone\nmode of the spontaneous symmetry breaking. Switching on an external source\nwhich breaks the translations explicitly but weakly, the would-be gapless modes\nboth get relaxed and acquire a tiny mass gap. Finally, in the strong momentum\nrelaxation regime, we find a (pseudo-)diffusive-to-sound crossover that is set\nby a momentum gap.", "category": "hep-th" }, { "text": "Unification of Gravity, Gauge and Higgs Fields by Confined Quantum\n Fields II -Effective Theory-: Dynamics of quantized free fields ( of spin 0 and 1/2 ) contained in a\nsubspace $V_*$ of an N+4 dimensional flat space $V$ is studied. The space $V_*$\nis considered as a neighborhood of a four dimensional submanifold $M$\narbitrarily embedded into $V$. We show that Einstein SO(N)-Yang-Mills Higgs\ntheory is induced as a low energy effective theory of the system. Gravity,\nSO(N) gauge fields and Higgs fields are obtained from embedding functions of\n$M$.", "category": "hep-th" }, { "text": "Exotic Dark Spinor Fields: Exotic dark spinor fields are introduced and investigated in the context of\ninequivalent spin structures on arbitrary curved spacetimes, which induces an\nadditional term on the associated Dirac operator, related to a Cech cohomology\nclass. For the most kinds of spinor fields, any exotic term in the Dirac\noperator can be absorbed and encoded as a shift of the electromagnetic vector\npotential representing an element of the cohomology group H^1(M, Z_2). The\npossibility of concealing such an exotic term does not exist in case of dark\n(ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the\nfull topological analysis must be evaluated. Since exotic dark spinor fields\nalso satisfy Klein-Gordon propagators, the dynamical constraints related to the\nexotic term in the Dirac equation can be explicitly calculated. It forthwith\nimplies that the non-trivial topology associated to the spacetime can\ndrastically engender --- from the dynamics of dark spinor fields ---\nconstraints in the spacetime metric structure. Meanwhile, such constraints may\nbe alleviated, at the cost of constraining the exotic spacetime topology.\nBesides being prime candidates to the dark matter problem, dark spinor fields\nare shown to be potential candidates to probe non-trivial topologies in\nspacetime, as well as probe the spacetime metric structure.", "category": "hep-th" }, { "text": "The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure\n Spinors: Using the results recently obtained for computing integrals over\n(non-minimal) pure spinor superspace, we compute the coefficient of the\nmassless two-loop four-point amplitude from first principles. Contrasting with\nthe mathematical difficulties in the RNS formalism where unknown normalizations\nof chiral determinant formulae force the two-loop coefficient to be determined\nonly indirectly through factorization, the computation in the pure spinor\nformalism can be smoothly carried out.", "category": "hep-th" }, { "text": "Multivalued Fields on the Complex Plane and Conformal Field Theories: In this paper a class of conformal field theories with nonabelian and\ndiscrete group of symmetry is investigated. These theories are realized in\nterms of free scalar fields starting from the simple $b-c$ systems and scalar\nfields on algebraic curves. The Knizhnik-Zamolodchikov equations for the\nconformal blocks can be explicitly solved. Besides of the fact that one obtains\nin this way an entire class of theories in which the operators obey a\nnonstandard statistics, these systems are interesting in exploring the\nconnection between statistics and curved space-times, at least in the two\ndimensional case.", "category": "hep-th" }, { "text": "Novel Analysis of Spinor Interactions and non-Riemannian Geometry: A novel analysis of the gauge theory of the local Lorentz group is\nimplemented both in flat and in curved space-time, and the resulting dynamics\nis analyzed in view of the geometrical interpretation of the gauge potential.\nThe Yang-Mills picture of local Lorentz transformations is first approached in\na second-order formalism. For the Lagrangian approach to reproduce the second\nCartan structure equation as soon as the Lorentz gauge connections are\nidentified with the contortion tensor, an interaction term between the Lorentz\ngauge fields and the spin connections has to be postulated. The full picture\ninvolving gravity, torsion and spinors is described by a coupled set of field\nequations, which allows one to interpret both gravitational spin connections\nand matter spin density as the source term for the Yang-Mills equations. The\ncontortion tensor acquires a propagating character, because of its non-Abelian\nfeature, and the pure contact interaction is restored in the limit of vanishing\nLorentz connections.", "category": "hep-th" }, { "text": "On the integrability of Wilson loops in AdS_5 x S^5: Some periodic\n ansatze: Wilson loops are calculated within the AdS/CFT correspondence by finding a\nclassical solution to the string equations of motion in AdS_5 x S^5 and\nevaluating its action. An important fact is that this sigma-model used to\nevaluate the Wilson loops is integrable, a feature that has gained relevance\nthrough the study of spinning strings carrying large quantum numbers and\nspin-chains. We apply the same techniques used to solve the equations for\nspinning strings to find the minimal surfaces describing a wide class of Wilson\nloops. We focus on different cases with periodic boundary conditions on the\nAdS_5 and S^5 factors and find a rich array of solutions. We examine the\ndifferent phases that appear in the problem and comment on the applicability of\nintegrability to the general problem.", "category": "hep-th" }, { "text": "Black Holes and U-duality in Diverse Dimensions: In this paper we review some properties of BPS black holes of supergravities\nwith n=32,16 supersymmetries. The BPS condition, a condition on the eigenvalues\nof the central charge matrix, can be shown to be U-duality invariant. We\nexplicitly work out D=4, N=8 and D=5, N=4 supergravities.", "category": "hep-th" }, { "text": "Quantum Field Theory of Topological Defects as Inhomogeneous Condensates: In the framework of the Closed-Time-Path formalism, we show how topological\ndefects may arise in Quantum Field Theory as result of a localized\n(inhomogeneous) condensation of particles. We demonstrate our approach on two\nexamples; kinks in the $2D \\lambda \\psi^{4}$ theory (both at zero and finite\ntemperature) and vortices in the complex $4D \\lambda \\psi^{4} $ theory.", "category": "hep-th" }, { "text": "Derivation of String Field Theory from the Large N BMN Limit: We continue the development of a systematic procedure for deriving closed\nstring pp wave string field theory from the large N\nBerenstein-Maldacena-Nastase limit. In the present paper the effects of the\nYang-Mills interaction are considered in detail for general BMN states. The SFT\ninteraction with the appropriate operator insertion at the interaction point is\ndemonstrated.", "category": "hep-th" }, { "text": "Renormalization and asymptotic safety in truncated quantum Einstein\n gravity: A perturbative quantum theory of the 2-Killing vector reduction of general\nrelativity is constructed. Although non-renormalizable in the standard sense,\nwe show that to all orders of the loop expansion strict cut-off independence\ncan be achieved in a space of Lagrangians differing only by a field dependent\nconformal factor. In particular the Noether currents and the quantum\nconstraints can be defined as finite composite operators. The form of the field\ndependence in the conformal factor changes with the renormalization scale and a\nclosed formula is obtained for the beta functional governing its flow. The flow\npossesses a unique fixed point at which the trace anomaly is shown to vanish.\nThe approach to the fixed point adheres to Weinberg's ``asymptotic safety''\nscenario, both in the gravitational wave/cosmological sector and in the\nstationary sector.", "category": "hep-th" }, { "text": "An equivalence of two mass generation mechanisms for gauge fields: Two mass generation mechanisms for gauge theories are studied. It is proved\nthat in the abelian case the topological mass generation mechanism introduced\nin hep-th/9301060, hep-th/9512216 is equivalent to the mass generation\nmechanism defined in hep-th/0510240, hep-th/0605050 with the help of\n``localization'' of a nonlocal gauge invariant action. In the nonabelian case\nthe former mechanism is known to generate a unitary renormalizable quantum\nfield theory describing a massive vector field.", "category": "hep-th" }, { "text": "Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge\n Theories: The correspondence between supergravity (and string theory) on $AdS$ space\nand boundary conformal field theory relates the thermodynamics of ${\\cal N}=4$\nsuper Yang-Mills theory in four dimensions to the thermodynamics of\nSchwarzschild black holes in Anti-de Sitter space. In this description, quantum\nphenomena such as the spontaneous breaking of the center of the gauge group,\nmagnetic confinement, and the mass gap are coded in classical geometry. The\ncorrespondence makes it manifest that the entropy of a very large $AdS$\nSchwarzschild black hole must scale ``holographically'' with the volume of its\nhorizon. By similar methods, one can also make a speculative proposal for the\ndescription of large $N$ gauge theories in four dimensions without\nsupersymmetry.", "category": "hep-th" }, { "text": "Integrable N=2 Supersymmetric Field Theories: Some additional references are included on the last 3 pages.", "category": "hep-th" }, { "text": "Supersymmetric field theories and geometric Langlands: The other side of\n the coin: This note announces results on the relations between the approach of\nBeilinson and Drinfeld to the geometric Langlands correspondence based on\nconformal field theory, the approach of Kapustin and Witten based on $N=4$ SYM,\nand the AGT-correspondence. The geometric Langlands correspondence is described\nas the Nekrasov-Shatashvili limit of a generalisation of the AGT-correspondence\nin the presence of surface operators. Following the approaches of Kapustin -\nWitten and Nekrasov - Witten we interpret some aspects of the resulting picture\nusing an effective description in terms of two-dimensional sigma models having\nHitchin's moduli spaces as target-manifold.", "category": "hep-th" }, { "text": "Algebraic inversion of the Dirac equation for the vector potential in\n the non-abelian case: We study the Dirac equation for spinor wavefunctions minimally coupled to an\nexternal field, from the perspective of an algebraic system of linear equations\nfor the vector potential. By analogy with the method in electromagnetism, which\nhas been well-studied, and leads to classical solutions of the Maxwell-Dirac\nequations, we set up the formalism for non-abelian gauge symmetry, with the\nSU(2) group and the case of four-spinor doublets. An extended isospin-charge\nconjugation operator is defined, enabling the hermiticity constraint on the\ngauge potential to be imposed in a covariant fashion, and rendering the\nalgebraic system tractable. The outcome is an invertible linear equation for\nthe non-abelian vector potential in terms of bispinor current densities. We\nshow that, via application of suitable extended Fierz identities, the solution\nof this system for the non-abelian vector potential is a rational expression\ninvolving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial\nvector current densities, albeit in the non-closed form of a Neumann series.", "category": "hep-th" }, { "text": "Collective Motion of Micro-organisms from Field Theoretical Viewpoint: We analyze the collective motion of micro-organisms in the fluid and consider\nthe problem of the red tide. The red tide is produced by the condensation of\nthe micro-organisms, which might be a similar phenomenon to the condensation of\nthe strings. We propose a model of the generation of the red tide. By\nconsidering the interaction between the micro- organisms mediated by the\nvelocity fields in the fluid, we derive the Van der Waals type equation of\nstate, where the generation of the red tide can be regarded as a phase\ntransition from the gas of micro-organisms to the liquid. (The number density\nof micro-organisms which generates the red tide is order estimated.)", "category": "hep-th" }, { "text": "Momentum space topology of QCD: We discuss the possibility to consider quark matter as the topological\nmaterial. We consider hadronic phase (HP), the quark - gluon plasma phase\n(QGP), and the hypothetical color - flavor locking (CFL) phase. In those phases\nwe identify the relevant topological invariants in momentum space. The\nformalism is developed, which relates those invariants and massless fermions\nthat reside on vortices and at the interphases. This formalism is illustrated\nby the example of vortices in the CFL phase.", "category": "hep-th" }, { "text": "Stability of the quantum supermembrane in a manifold with boundary: We point out an effect which may stabilize a supersymmetric membrane moving\non a manifold with boundary, and lead to a light-cone Hamiltonian with a\ndiscrete spectrum of eigenvalues. The analysis is carried out explicitly for a\nclosed supermembrane in the regularized $SU(N)$ matrix model version.", "category": "hep-th" }, { "text": "Aspects of critical O$(N)$ model with boundary and defect: In this thesis, we explore the critical phenomena in the presence of extended\nobjects, which we call defects, aiming for a better understanding of the\nproperties of non-local objects ubiquitous in our world and a more practical\nand realistic study of criticality. To this end, we study the statistical\nO$(N)$ vector model in $(4-\\epsilon)$ dimensions with three kinds of defects: a\nline defect constructed by smearing an O$(N)$ vector field along one direction\nand Dirichlet and Neumann boundaries. A conventional approach to critical\nphenomena would be to perform perturbative calculations using Feynman diagrams\nand doing renormalization group analysis. But we here also take a different but\ncomplementary approach based on three axioms that include conformal symmetry of\nthe theory at the criticality. We apply this axiomatic framework to the\ncritical O$(N)$ model with a defect and reproduce the perturbative results at\nthe leading non-trivial order in $\\epsilon$, substantiating the validity of our\napproach. Along the way, we develop and refine the axiomatic framework to\nderive anomalous dimensions of the composite operators on the defect that have\nnot been accessible in the existing literature by focusing on the analyticity\nof the correlation functions.", "category": "hep-th" }, { "text": "Observations on Integral and Continuous U-duality Orbits in N=8\n Supergravity: One would often like to know when two a priori distinct extremal black\np-brane solutions are in fact U-duality related. In the classical supergravity\nlimit the answer for a large class of theories has been known for some time.\nHowever, in the full quantum theory the U-duality group is broken to a discrete\nsubgroup and the question of U-duality orbits in this case is a nuanced matter.\nIn the present work we address this issue in the context of N=8 supergravity in\nfour, five and six dimensions. The purpose of this note is to present and\nclarify what is currently known about these discrete orbits while at the same\ntime filling in some of the details not yet appearing in the literature. To\nthis end we exploit the mathematical framework of integral Jordan algebras and\nFreudenthal triple systems. The charge vector of the dyonic black string in D=6\nis SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified\nby a set of two arithmetic U-duality invariants. Similarly, the black hole\n(string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge\ncanonical form, again uniquely fixed by a set of three arithmetic U-duality\ninvariants. The situation in four dimensions is less clear: while black holes\npreserving more than 1/8 of the supersymmetries may be fully classified by\nknown arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield\nincreasingly subtle orbit structures, which remain to be properly understood.\nHowever, for the very special subclass of projective black holes a complete\nclassification is known. All projective black holes are E_{7(7)}(Z) related to\na four or five charge canonical form determined uniquely by the set of known\narithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the\ncharge vectors of black holes with a given leading-order entropy.", "category": "hep-th" }, { "text": "The Search for the Origins of M Theory : Loop Quantum Mechanics,\n Loops/Strings and Bulk/Boundary Dualities: The construction of a $covariant$ Loop Wave functional equation in a 4D\nspacetime is attained by introducing a generalized $eleven$ dimensional\ncategorical {\\bf C}-space comprised of $8\\times 8$ antisymmetric matrices. The\nlatter matrices encode the generalized coordinates of the histories of points,\nloops and surfaces $combined$. Spacetime Topology change and the Holographic\nprinciple are natural consequences of imposing the principle of $covariance$ in\n{\\bf C}-space. The Planck length is introduced as a necessary rescaling\nparameter to establish the correspondence limit with the physics of\npoint-histories in ordinary Minkowski space, in the limit $l_P\\to 0$. Spacetime\nquantization should appear in discrete units of Planck length, area, volume\n,....All this seems to suggest that the generalized principle of covariance,\nrepresenting invariance of proper $area$ intervals in {\\bf C}-space, under\nmatrix-coordinate transformations, could be relevant in discovering the\nunderlying principle behind the origins of $M$ theory. We construct an ansatz\nfor the $SU(\\infty)$ Yang-Mills vacuum wavefunctional as a solution of the\nSchroedinger Loop Wave equation associated with the Loop Quantum Mechanical\nformulation of the Eguchi-Schild String . The Strings/Loops ($SU(\\infty)$ gauge\nfield) correspondence implements one form of the Bulk/Boundary duality\nconjecture in this case.", "category": "hep-th" }, { "text": "Some aspects of quantum correlations and decoherence in the cosmological\n spacetimes: This thesis presents a theoretical investigation into the quantum field\ntheoretic aspects of quantum correlations and decoherence in the cosmological\nspacetimes. We shall focus on the inflationary or dark energy dominated phase\nof the universe, and we shall take the spacetime background to be de Sitter.\nThe primary objective of this thesis is to study the physics of the very early\nuniverse and to gain insight into the interesting interplay among quantum\ncorrelations, entanglement and decoherence which can affect the evolution of\nour universe.", "category": "hep-th" }, { "text": "$\u03b8$-diagram technique for $\\mathcal{N}=1$, $d=4$ superfields: We describe a diagrammatic procedure to carry out the Grassmann integration\nin super-Feynman diagrams of 4d theories expressed in terms of $\\mathcal{N}=1$\nsuperfields. This method is alternative to the well known $D$-algebra approach.\nWe develop it in detail for theories containing vector, chiral and anti-chiral\nsuperfields, with the type of interactions which occur in $\\mathcal{N}=2$ SYM\ntheories with massless matter, but it would be possible to extend it to other\ncases. The main advantage is that this method is algorithmic; we implemented it\nas a Mathematica program that, given the description of a super Feynman diagram\nin momentum space, returns directly the polynomial in the momenta produced by\nthe Grassmann integration.", "category": "hep-th" }, { "text": "Holographic description of vacuum bubbles: We discuss a holographic description of vacuum bubbles, with possible\nimplications for a consistent description of the multiverse. In particular, we\nelaborate on the recent observation by Maldacena, that the interior of AdS\nbubbles can be described in terms of CFT degrees of freedom living on the\nworldsheet of the bubble wall. We consider the scattering of bulk gravitons in\nthe ambient parent vacuum, off the bubble wall. In the dual description, the\ntransmission coefficient is interpreted as the probability that a graviton is\nabsorbed by the worldsheet CFT degrees of freedom. The result is in agreement\nwith intuitive expectations. Conformal invariance is not exact in this setup,\nand the leading corrections due to the IR and UV cut-offs are displayed. Aside\nfrom bulk scattering states, we find that when a bubble nucleates within a\nparent dS vacuum, there is a zero mode of the graviton which describes lower\ndimensional gravity with a finite Newton's constant. This massless graviton\nlives within one Hubble radius away from the bubble wall. Possible implications\nfor a fully holographic description of the inflating multiverse are briefly\ndiscussed.", "category": "hep-th" }, { "text": "Free Fermions at Finite Temperature: An Application of the\n Non-Commutative Algebra: Charret et. al. applied the properties of the Grassmann generators to develop\na new method to calculate the coefficients of the high temperature expansion of\nthe grand canonical partition function of self-interacting fermionic models in\nany d-dimensions (d>=1). The method explores the anti-commuting nature of\nfermionic fields and avoids the calculation of the fermionic path integral. We\napply this new method to the relativistic free Dirac fermions and recover the\nknown results in the literature.", "category": "hep-th" }, { "text": "Cohomology of Lie Superalgebras: Forms, Pseudoforms, and Integral Forms: We study the cohomology of Lie superalgebras for the full complex of forms:\nsuperforms, pseudoforms and integral forms. We use the technique of spectral\nsequences to abstractly compute the Chevalley-Eilenberg cohomology. We first\nfocus on the superalgebra $\\mathfrak{osp}(2|2)$ and show that there exist\nnon-empty cohomology spaces among pseudoforms related to sub-superalgebras. We\nthen extend some classical theorems by Koszul, as to include pseudoforms and\nintegral forms. Further, we conjecture that the algebraic Poincar\\'e duality\nextends to Lie superalgebras, as long as all the complexes of forms are taken\ninto account and we prove that this holds true for $\\mathfrak{osp}(2|2)$. We\nfinally construct the cohomology representatives explicitly by using a\ndistributional realisation of pseudoforms and integral forms. On one hand,\nthese results show that the cohomology of Lie superalgebras is actually larger\nthan expected, whereas one restricts to superforms only; on the other hand, we\nshow the emergence of completely new cohomology classes represented by\npseudoforms. These classes realise as integral form classes of\nsub-superstructures.", "category": "hep-th" }, { "text": "The extremal black hole bomb: We analyze the spectrum of massive scalar bound states in the background of\nextremal Kerr black holes, focusing on modes in the superradiant regime, which\ngrow exponentially in time and quickly deplete the black hole's mass and spin.\nPrevious analytical estimates for the growth rate of this instability were\nlimited to the $\\mu M\\ll1$ and $\\mu M\\gg1$ regimes, where $\\mu$ and $M$ denote\nthe scalar field and black hole masses, respectively. In this work, we discuss\nan analytical method to compute the superradiant spectrum for generic values of\nthese parameters, namely in the phenomenologically interesting regime $\\mu\nM\\sim 1$. To do this, we solve the radial mode equation in two overlapping\nregions and match the solutions in their common domain of validity. We show\nthat matching the functional forms of these functions involves approximations\nthat are not valid for the whole range of scalar masses, exhibiting unphysical\npoles that produce a large enhancement of the growth rate. Alternatively, we\nmatch the functions at a single point and show that, despite the uncertainty in\nthe choice of the match point, this method eliminates the spurious poles and\nagrees with previous numerical computations of the spectrum using a\ncontinued-fraction method.", "category": "hep-th" }, { "text": "Discrete scale invariance in holography and an argument against the\n complexity=action proposal: The AdS/CFT correspondence often motivates research on questions in\ngravitational physics whose relevance might not be immediately clear from a\npurely GR-perspective, but which are nevertheless interesting. In these\nproceedings, we summarise two such results recently obtained by the author. One\nconcerns, broadly speaking, the possible isometry-groups of a spacetime sourced\nby physical matter. The other one provides a possible argument against the\nrecently proposed complexity=action conjecture.", "category": "hep-th" }, { "text": "Positivity, low twist dominance and CSDR for CFTs: We consider a crossing symmetric dispersion relation (CSDR) for CFT four\npoint correlation with identical scalar operators, which is manifestly\nsymmetric under the cross-ratios $u,v$ interchange. This representation has\nseveral features in common with the CSDR for quantum field theories. It enables\na study of the expansion of the correlation function around $u=v=1/4$, which is\nused in the numerical conformal bootstrap program. We elucidate several\nremarkable features of the dispersive representation using the four point\ncorrelation function of $\\Phi_{1,2}$ operators in 2d minimal models as a\ntest-bed. When the dimension of the external scalar operator ($\\Delta_\\sigma$)\nis less than $\\frac{1}{2}$, the CSDR gets contribution from only a single tower\nof global primary operators with the second tower being projected out. We find\nthat there is a notion of low twist dominance (LTD) which, as a function of\n$\\Delta_\\sigma$, is maximized near the 2d Ising model as well as the\nnon-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the\nTaylor expansion coefficients of the correlation function around the crossing\nsymmetric point and lead to universal predictions for specific ratios of these\ncoefficients. These results carry over to the epsilon expansion in $4-\\epsilon$\ndimensions. We also conduct a preliminary investigation of geometric function\ntheory ideas, namely the Bieberbach-Rogosinski bounds.", "category": "hep-th" }, { "text": "Spacetime Subsystem Symmetries: One characteristic feature of many fractonic lattice models, and a defining\nproperty of the exotic field theories developed to describe them, are subsystem\nsymmetries including a conservation of not just net electric charge but also\nelectric dipole moments or charges living on submanifolds. So far all such\ntheories were based on internal subsystem symmetries. In this work we\ngeneralize the notion of subsystem symmetries to system with subsystem\nspacetime symmetries with locally conserved energies.", "category": "hep-th" }, { "text": "Eikonal phase matrix, deflection angle and time delay in effective field\n theories of gravity: The eikonal approximation is an ideal tool to extract classical observables\nin gauge theory and gravity directly from scattering amplitudes. Here we\nconsider effective theories of gravity where in addition to the\nEinstein-Hilbert term we include non-minimal couplings of the type $R^3$, $R^4$\nand $FFR$. In particular, we study the scattering of gravitons and photons of\nfrequency $\\omega$ off heavy scalars of mass $m$ in the limit $m\\gg \\omega \\gg\n|\\vec{q}\\,|$, where $\\vec{q}$ is the momentum transfer. The presence of\nnon-minimal couplings induces helicity-flip processes which survive the eikonal\nlimit, thereby promoting the eikonal phase to an eikonal phase matrix. We\nobtain the latter from the relevant two-to-two helicity amplitudes that we\ncompute up to one-loop order, and confirm that the leading-order terms in\n$\\omega$ exponentiate \\`{a} la Amati, Ciafaloni and Veneziano. From the\neigenvalues of the eikonal phase matrix we then extract two physical\nobservables, to 2PM order: the classical deflection angle and Shapiro time\ndelay/advance. Whenever the classical expectation of helicity conservation of\nthe massless scattered particle is violated, i.e. the eigenvalues of the\neikonal matrix are non-degenerate, causality violation due to time advance is a\ngeneric possibility for small impact parameter. We show that for graviton\nscattering in the $R^4$ and $FFR$ theories, time advance is circumvented if the\ncouplings of these interactions satisfy certain positivity conditions, while it\nis unavoidable for graviton scattering in the $R^3$ theory and photon\nscattering in the $FFR$ theory. The scattering processes we consider mimic the\ndeflection of photons and gravitons off spinless heavy objects such as\nblack~holes.", "category": "hep-th" }, { "text": "Classicalization and unitarization of wee partons in QCD and Gravity:\n The CGC-Black Hole correspondence: We discuss a remarkable correspondence between the description of Black Holes\nas highly occupied condensates of $N$ weakly interacting gravitons and that of\nColor Glass Condensates (CGCs) as highly occupied gluon states. In both cases,\nthe dynamics of \"wee partons\" in Regge asymptotics is controlled by emergent\nsemi-hard scales that lead to perturbative unitarization and classicalization\nof $2\\rightarrow N$ particle amplitudes at weak coupling. In particular, they\nattain a maximal entropy permitted by unitarity, bounded by the inverse\ncoupling $\\alpha$ of the respective constituents. Strikingly, this entropy is\nequal to the area measured in units of the Goldstone constant corresponding to\nthe spontaneous breaking of Poincar{\\'{e}} symmetry by the corresponding\ngraviton or gluon condensate. In gravity, the Goldstone constant is the Planck\nscale, and gives rise to the Bekenstein-Hawking entropy. Likewise, in the CGC,\nthe corresponding Goldstone scale is determined by the onset of gluon\nscreening. We point to further similarities in Black Hole formation,\nthermalization and decay, to that of the Glasma matter formed from colliding\nCGCs in ultrarelativistic nuclear collisions, which decays into a Quark-Gluon\nPlasma.", "category": "hep-th" }, { "text": "Twistorial monopoles & chiral algebras: We initiate the study of how the insertion of magnetically charged states in\n4d self-dual gauge theories impacts the 2d chiral algebras supported on the\ncelestial sphere at asymptotic null infinity, from the point of view of the\n4d/2d twistorial correspondence introduced by Costello and the second author.\nBy reducing the 6d twistorial theory to a 3d holomorphic-topological theory\nwith suitable boundary conditions, we can motivate certain non-perturbative\nenhancements of the celestial chiral algebra corresponding to extensions by\nmodules arising from 3d boundary monopole operators. We also identify the\ninsertion of 4d (non-abelian) monopoles with families of spectral flow\nautomorphisms of the celestial chiral algebra.", "category": "hep-th" }, { "text": "Accelerating Black Holes and Spinning Spindles: We study solutions in the Pleba\\'nski--Demia\\'nski family which describe an\naccelerating, rotating and dyonically charged black hole in $AdS_4$. These are\nsolutions of $D=4$ Einstein-Maxwell theory with a negative cosmological\nconstant and hence minimal $D=4$ gauged supergravity. It is well known that\nwhen the acceleration is non-vanishing the $D=4$ black hole metrics have\nconical singularities. By uplifting the solutions to $D=11$ supergravity using\na regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters\ncan be chosen to eliminate the conical singularities. Topologically, the $D=11$\nsolutions incorporate an $SE_7$ fibration over a two-dimensional weighted\nprojective space, $\\mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which\nis labelled by two integers that determine the conical singularities of the\n$D=4$ metrics. We also discuss the supersymmetric and extremal limit and show\nthat the near horizon limit gives rise to a new family of regular\nsupersymmetric $AdS_2\\times Y_9$ solutions of $D=11$ supergravity, which\ngeneralise a known family by the addition of a rotation parameter. We calculate\nthe entropy of these black holes and argue that it should be possible to derive\nthis from certain ${\\cal N}=2$, $d=3$ quiver gauge theories compactified on a\nspinning spindle with appropriate magnetic flux.", "category": "hep-th" }, { "text": "Algebraic deformations of toric varieties II. Noncommutative instantons: We continue our study of the noncommutative algebraic and differential\ngeometry of a particular class of deformations of toric varieties, focusing on\naspects pertinent to the construction and enumeration of noncommutative\ninstantons on these varieties. We develop a noncommutative version of twistor\ntheory, which introduces a new example of a noncommutative four-sphere. We\ndevelop a braided version of the ADHM construction and show that it\nparametrizes a certain moduli space of framed torsion free sheaves on a\nnoncommutative projective plane. We use these constructions to explicitly build\ninstanton gauge bundles with canonical connections on the noncommutative\nfour-sphere that satisfy appropriate anti-selfduality equations. We construct\nprojective moduli spaces for the torsion free sheaves and demonstrate that they\nare smooth. We define equivariant partition functions of these moduli spaces,\nfinding that they coincide with the usual instanton partition functions for\nsupersymmetric gauge theories on C^2.", "category": "hep-th" }, { "text": "A Meandering Inflaton: If the cosmological inflationary scenario took place in the cosmic landscape\nin string theory, the inflaton, the scalar mode responsible for inflation,\nwould have meandered in a complicated multi-dimensional potential. We show that\nthis meandering property naturally leads to many e-folds of inflation, a\nnecessary condition for a successful inflationary scenario. This behavior also\nleads to fluctuations in the primordial power spectrum of the cosmic microwave\nbackground radiation, which may be detected in a near future cosmic variance\nlimited experiment like PLANCK.", "category": "hep-th" }, { "text": "Structure of deformations in Jackiw-Teitelboim black holes with matter: We consider Jackiw-Teitelboim gravity with a massless matter field and turn\non bulk excitations leading to a nontrivial vev of the corresponding dual\nboundary operator. To leading order, we realize the corresponding deformation\nof thermofield double state by explicitly identifying their Hilbert space. The\ndeformed state can be prepared with an operator insertion at the mid-point of\nthe Euclidean time evolution in the context of Hartle-Hawking construction. We\nshow that the inserted operators form an SL(2,{\\bf R}) representation. We\nconstruct a specific orthonormal basis that is directly related to the operator\nbasis of the vev deformations. If we include the higher order corrections, the\nbulk geometry is no longer left-right symmetric. We argue that, classically,\nthe mode coefficients in the bulk deformation cannot be fully recovered from\nthe data collected along the boundary cutoff\n trajectories. Then the bulk seems to contain more information than the cutoff\nboundary, and this might be responsible for nontrivial behind-horizon degrees\nof freedom.", "category": "hep-th" }, { "text": "$L_\\infty$ algebras and Tensor Hierarchies in Exceptional Field Theory\n and Gauged Supergravity: We show how the gauge and field structure of the tensor hierarchies in Double\nand $E_{7(7)}$ Exceptional Field Theory fits into $L_\\infty$ algebras. Special\nattention is paid to redefinitions, the role of covariantly constrained fields\nand intertwiners. The results are connected to Gauged Supergravities through\ngeneralized Scherk-Schwarz reductions. We find that certain gauging-dependent\nparameters generate trivial gauge transformations, giving rise to novel\nsymmetries for symmetries that are absent in their ungauged counterparts.", "category": "hep-th" }, { "text": "How one can obtain unambiguous predictions for the S-matrix in\n non-renormalizable theories: The usual Bogolyubov R-operation works in non-renormalizable theories in the\nsame way as in renormalizable ones. However, in the non-renormalizable case,\nthe counter-terms eliminating ultraviolet divergences do not repeat the\nstructure of the original Lagrangian but contain new terms with a higher degree\nof fields and derivatives increasing from order to order of PT. If one does not\naim to obtain finite off-shell Green functions but limits oneself only to the\nfiniteness of the S-matrix, then one can use the equations of motion and\ndrastically reduce the number of independent counter-terms. For example, it is\npossible to reduce all counter-terms to a form containing only operators with\nfour fields and an arbitrary number of derivatives. And although there will\nstill be infinitely many such counter-terms, in order to fix the arbitrariness\nof the subtraction procedure, one can normalize the on-shell 4-point amplitude,\nwhich must be known for arbitrary kinematics, plus the 6-point amplitude at one\npoint. All other multiparticle amplitudes will be calculated unambiguously.\nWithin the framework of perturbation theory, the number of independent\ncounter-terms in a given order is limited, so does the number of normalization\nconditions. The constructed counter-terms are not absorbed into the\nnormalization of a single coupling constant, the Lagrangian contains an\ninfinite number of terms, but after fixing the arbitrariness, it allows one to\nobtain unambiguous predictions for observables.", "category": "hep-th" }, { "text": "Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds: We derive the Free Differential Algebra for type IIA supergravity in 10\ndimensions in the string frame. We provide all fermionic terms for all\ncurvatures. We derive the Green-Schwarz sigma model for type IIA superstring\nbased on the FDA construction and we check its invariance under kappa-symmetry.\nFinally, we derive the pure spinor sigma model and we check the BRST\ninvariance. The present derivation has the advantage that the resulting sigma\nmodel is constructed in terms of the superfields appearing in the FDA and\ntherefore one can directly relate a supergravity background with the\ncorresponding sigma model. The complete explicit form of the BRST\ntransformations is given and some new pure spinor constraints are obtained.\nFinally, the explicit form of the action is given.", "category": "hep-th" }, { "text": "Vertex algebras and 4-manifold invariants: We propose a way of computing 4-manifold invariants, old and new, as chiral\ncorrelation functions in half-twisted 2d $\\mathcal{N}=(0,2)$ theories that\narise from compactification of fivebranes. Such formulation gives a new\ninterpretation of some known statements about Seiberg-Witten invariants, such\nas the basic class condition, and gives a prediction for structural properties\nof the multi-monopole invariants and their non-abelian generalizations.", "category": "hep-th" }, { "text": "Classical Gravity Coupled to Liouville Theory: We consider the two dimensional Jackiw-Teitelboim model of gravity. We first\ncouple the model to the Liouville action and $c$ scalar fields and show,\ntreating the combined system as a non linear sigma model, that the resulting\ntheory can be interpreted as a critical string moving in a target space of\ndimension $D=c+2$. We then analyse perturbatively a generalised model\ncontaining a kinetic term and an arbitrary potential for the auxiliary field.\nWe use the background field method and work with covariant gauges. We show that\nthe renormalisability of the theory depends on the form of the potential. For a\ngeneral potential, the theory can be renormalised as a non linear sigma model.\nIn the particular case of a Liouville-like potential, the theory is\nrenormalisable in the usual sense.", "category": "hep-th" }, { "text": "Semiclassical Bethe Ansatz and AdS/CFT: The Bethe ansatz can be used to compute anomalous dimensions in N=4 SYM\ntheory. The classical solutions of the sigma-model on AdS(5)xS(5) can also be\nparameterized by an integral equation of Bethe type. In this note the\nrelationship between the two Bethe ansaetze is reviewed following\nhep-th/0402207.", "category": "hep-th" }, { "text": "Rotating Rotated Branes: We present a class of spacetime rotations that preserve a proportion of\nspacetime supersymmetry. We then give the rules for superposing these rotations\nwith various branes to construct rotating brane solutions which preserve exotic\nfractions of supersymmetry. We also investigate the superposition of rotations\nwith intersecting branes at angles and we find new rotating intersecting branes\nat angles configurations. We demonstrate this with two examples of such\nsolutions one involving intersecting NS-5-branes on a string at $Sp(2)$ angles\nsuperposed with fundamental strings and pp-waves, and the other involving\nintersecting M-5-branes on a string at $Sp(2)$ angles superposed with membranes\nand pp-waves. We find that the geometry of some of these solutions near the\nintersection region of every pair of 5-branes is $AdS_3\\times S^3\\times\nS^3\\times \\bE$ and $AdS_3\\times S^3\\times S^3\\times\\bE^2$, respectively. We\nalso present a class of solutions that can be used for null string and M-theory\ncompactifications preserving supersymmetry.", "category": "hep-th" }, { "text": "$SO/Sp$ Chern-Simons Gauge Theories At Large $N$, $SO/Sp$ Penner Models\n And The Gauge Group Volumes: We construct a deformed $SO/Sp$ Penner generating function responsible for\nthe close connection between $SO/Sp$ Chern-Simons gauge theories at large $N$\nand the $SO/Sp$ Penner models. This construction is then shown to follow from a\nsector of a Chern-Simons gauge theory with coupling constant $\\lambda$. The\nfree energy and its continuum limit of the perturbative Chern-Simons gauge\ntheory are obtained from the Penner model. Finally, asymptotic expansions for\nthe logarithm of the gauge group volumes are given for every genus $g\\geq 0$\nand shown to be equivalent to the continuum limits of the $SO/Sp$ Chern-Simons\ngauge theories and the $SO/Sp$ Penner models", "category": "hep-th" }, { "text": "Cancellation of soft and collinear divergences in noncommutative QED: In this paper, we investigate the behavior of non-commutative IR divergences\nand will also discuss their cancellation in the physical cross sections. The\ncommutative IR (soft) divergences existing in the non-planar diagrams will be\nexamined in order to prove an all order cancellation of these divergences using\nthe Weinberg's method. In non-commutative QED, collinear divergences due to\ntriple photon splitting vertex, were encountered, which are shown to be\ncanceled out by the non-commutative version of KLN theorem. This guarantees\nthat there is no mixing between the Collinear, soft and non-commutative IR\ndivergences.", "category": "hep-th" }, { "text": "Fast scrambling in holographic Einstein-Podolsky-Rosen pair: We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair\nexhibits fast scrambling. Strongly entangled quark and antiquark in\n$\\mathcal{N}=4$ super Yang-Mills theory are considered. Their gravity dual is a\nfundamental string whose endpoints are uniformly accelerated in opposite\ndirection. We slightly increase the acceleration of the endpoint and show that\nit quickly destroys the correlation between the quark and antiquark. The proper\ntime scale of the destruction is $\\tau_\\ast\\sim \\beta \\ln S$ where $\\beta$ is\nthe inverse Unruh temperature and $S$ is the entropy of the accelerating quark.\nWe also evaluate the Lyapunov exponent from correlation function as\n$\\lambda_L=2\\pi/\\beta$, which saturates the Lyapunov bound. Our results suggest\nthat the fast scrambling or saturation of the Lyapunov bound do not directly\nimply the existence of an Einstein dual. When we slightly decrease the\nacceleration, the quark and antiquark are causally connected and an \"one-way\ntraversable wormhole\" is created on the worldsheet. It causes the divergence of\nthe correlation function between the quark and antiquark.", "category": "hep-th" }, { "text": "Dual Path Integral: a non-perturbative approach to strong coupling: We develop a non-perturbative method for calculating partition functions of\nstrongly coupled quantum mechanical systems with interactions between\nsubsystems described by a path integral of a dual system. The dual path\nintegral is derived starting from non-interacting subsystems at zeroth order\nand then by introducing couplings of increasing complexity at each order of an\niterative procedure. These orders of interactions play the role of a dual time\nand the full quantum partition function is expressed as a transition amplitude\nin the dual system. More precisely, it is expressed as a path integral from a\ndeformation-operators dependent initial state at zero time/order to the\ninverse-temperature dependent final state at later time/order. We provide three\nexamples of strongly coupled systems with first-order, second-order and\nhigher-order interactions and discuss a possible emergence of space-time,\nquantum field theories and general relativity in context of the dual path\nintegral.", "category": "hep-th" }, { "text": "S-matrix on effective string and compactified membrane: Expanding Nambu-Goto action near infinitely long string vacuum one can\ncompute scattering amplitudes of 2d massless fields representing transverse\nstring coordinates. As was shown in arXiv:1203.1054, the resulting S-matrix is\nintegrable, in agreement with the known free string spectrum and also with an\ninterpretation of the static-gauge NG action as a $T\\bar T$ deformation of a\nfree massless theory. We consider a generalization of this computation to the\ncase of a membrane, expanding its 3d action near an infinite membrane vacuum\nthat has cylindrical $\\mathbb R \\times S^1$ shape (we refer to such membrane as\n\"compactified\"). Representing 3d fields as Fourier series in $S^1$ coordinate\nwe get an effective 2d model in which the massless string modes are coupled to\nan infinite KK tower of massive 2d modes. We find that the resulting 2d\nS-matrix is not integrable already at the tree level. We also compute 1-loop\nscattering amplitude of massless string modes with all compactified membrane\nmodes propagating in the loop. The result is UV finite and is a non-trivial\nfunction of the kinematic variables. In the large momentum limit or when the\nradius of $S^1$ is taken to infinity we recover the expression for the 1-loop\nscattering amplitude of the uncompactified $\\mathbb R^2$ membrane. We also\nconsider a 2d model which is the $T\\bar T$ deformation to the free theory with\nthe same massless plus infinite massive tower of modes. The corresponding 2d\nS-matrix is found, as expected, to be integrable.", "category": "hep-th" }, { "text": "The Conformal Limit of the 0A Matrix Model and String Theory on AdS(2): We analyze the conformal limit of the matrix model describing flux\nbackgrounds of two dimensional type 0A string theory. This limit is believed to\nbe dual to an AdS(2) background of type 0A string theory. We show that the\nspectrum of this limit is identical to that of a free fermion on AdS(2),\nsuggesting that there are no closed string excitations in this background.", "category": "hep-th" }, { "text": "Quantum Mechanics on S^n and Meron Solution: A particle in quantum mechanics on manifolds couples to the induced\ntopological gauge field that characterises the possible inequivalent\nquantizations. For instance, the gauge potential induced on $S^2$ is that of a\nmagnetic monopole located at the center of $S^2$. We find that the gauge\npotential induced on $S^3$ ($S^{2n+1}$) is that of a meron (generalized meron)\nalso sitting at the center of $S^3$ ($S^{2n+1}$).", "category": "hep-th" }, { "text": "Finite-size effects of Membranes on AdS_4 x S_7: We consider semi-classical solution of membranes on the AdS_4 x S^7. This is\nsupposed to be dual to the N=6 super Chern-Simons theory with k=1 in a planar\nlimit recently proposed by Aharony, Bergmann, Jafferis, and Maldacena (ABJM).\nWe have identified giant magnon and single spike states on the membrane by\nreducing them to the Neumamm - Rosochatius integrable system. We also connect\nthese to the complex sine-Gordon integrable model. Based on this approach, we\nfind finite-size membrane solutions and obtain their images in the complex\nsine-Gordon system along with the leading finite-size corrections to the\nenergy-charge relations.", "category": "hep-th" }, { "text": "Hamiltonian structure of three-dimensional gravity in Vielbein formalism: Considering Chern-Simons like gravity theories in three dimensions as first\norder systems, we analyze the Hamiltonian structure of three theories\nTopological massive gravity, New massive gravity, and Zwei-Dreibein Gravity.We\nshow that these systems demonstrate a new feature of the constrained systems in\nwhich a new kind of constraints emerge due to factorization of determinant of\nthe matrix of Poisson brackets of constraints. We find the desired number of\ndegrees of freedom as well as the generating functional of local Lorentz\ntransformations and diffeomorphism through canonical structure of the system.\nWe also compare the Hamiltonian structure of linearized version of the\nconsidered models with the original ones.", "category": "hep-th" }, { "text": "Reflections on Virasoro circuit complexity and Berry phase: Recently, the notion of circuit complexity defined in symmetry group\nmanifolds has been related to geometric actions which generally arise in the\ncoadjoint orbit method in representation theory and play an important role in\ngeometric quantization. On the other hand, it is known that there exists a\nprecise relation between geometric actions and Berry phases defined in group\nrepresentations. Motivated by these connections, we elaborate on a relation\nbetween circuit complexity and the group theoretic Berry phase. As the simplest\nsetup relevant for holography, we discuss the case of two dimensional conformal\nfield theories. In the large central charge limit, we identify the\ncomputational cost function with the Berry connection in the unitary\nrepresentation of the Virasoro group. We then use the latter identification to\nexpress the Berry phase in terms of the Virasoro circuit complexity. The former\ncan be seen as the holonomy of the Berry connection along the path in the group\nmanifold which defines the protocol. In addition, we derive a proportionality\nrelation between Virasoro circuit complexity and the logarithm of the inner\nproduct between a particularly chosen reference state and the prepared target\nstate. In this sense, the logarithmic formula turns out to be approximating the\ncomplexity up to some additive constant if the building blocks of the circuit\nare taken to be the underlying symmetry gates. Predictions based on this\nformula have recently been shown to coincide with the holographic complexity\nproposals and the path integral optimization procedure. The found connections\nmay therefore help to better understand such coincidences. We also discuss that\nour findings, put together with earlier observations, may suggest a connection\nbetween the Virasoro Berry phase and the complexity measure in the path\nintegral optimization proposal.", "category": "hep-th" }, { "text": "Anomaly Cancellations in the Type I D9-anti-D9 System and the USp(32)\n String Theory: We check some consistency conditions for the D9-anti-D9 system in type I\nstring theory. The gravitational anomaly and gauge anomaly for SO(n) x SO(m)\ngauge symmetry are shown to be cancelled when n-m=32. In addition, we find that\na string theory with USp(n) x USp(m) gauge symmetry also satisfies the anomaly\ncancellation conditions. After tachyon condensation, the theory reduces to a\ntachyon-free USp(32) string theory, though there is no spacetime supersymmetry.", "category": "hep-th" }, { "text": "Slowly rotating black holes in Quasi-topological gravity: While cubic Quasi-topological gravity is unique, there is a family of quartic\nQuasi-topological gravities in five dimensions. These theories are defined by\nleading to a first order equation on spherically symmetric spacetimes,\nresembling the structure of the equations of Lovelock theories in\nhigher-dimensions, and are also ghost free around AdS. Here we construct slowly\nrotating black holes in these theories, and show that the equations for the\noff-diagonal components of the metric in the cubic theory are automatically of\nsecond order, while imposing this as a restriction on the quartic theories\nallows to partially remove the degeneracy of these theories, leading to a\nthree-parameter family of Lagrangians of order four in the Riemann tensor. This\nshows that the parallel with Lovelock theory observed on spherical symmetry,\nextends to the realm of slowly rotating solutions. In the quartic case, the\nequations for the slowly rotating black hole are obtained from a consistent,\nreduced action principle. These functions admit a simple integration in terms\nof quadratures. Finally, in order to go beyond the slowly rotating regime, we\nexplore the consistency of the Kerr-Schild ansatz in cubic Quasi-topological\ngravity. Requiring the spacetime to asymptotically match with the rotating\nblack hole in GR, for equal oblateness parameters, the Kerr-Schild deformation\nof an AdS vacuum, does not lead to a solution for generic values of the\ncoupling. This result suggests that in order to have solutions with finite\nrotation in Quasi-topological gravity, one must go beyond the Kerr-Schild\nansatz.", "category": "hep-th" }, { "text": "Surgical invariants of four-manifolds: A new topological invariant of closed connected orientable four-dimensional\nmanifolds is proposed. The invariant, constructed via surgery on a special\nlink, is a four-dimensional counterpart of the celebrated SU(2) three-manifold\ninvariant of Reshetikhin, Turaev and Witten.", "category": "hep-th" }, { "text": "Brane solutions in strings with broken supersymmetry and dilaton\n tadpoles: The tachyon-free nonsupersymmetric string theories in ten dimensions have\ndilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally\nsymmetric backgrounds for the $USp(32)$ Type I string and the $SO(16)\\times\nSO(16)$ heterotic string. The static solutions exhibit nine dimensional\nPoincar\\'e symmetry and have finite 9D Planck and Yang-Mills constants. The low\nenergy geometry is given by a ten dimensional manifold with two boundaries\nseparated by a finite distance which suggests a spontaneous compactification of\nthe ten dimensional string theory.", "category": "hep-th" }, { "text": "Superconformal mechanics, black holes, and non-linear realizations: The OSp(2|2)-invariant planar dynamics of a D=4 superparticle near the\nhorizon of a large mass extreme black hole is described by an N=2\nsuperconformal mechanics, with the SO(2) charge being the superparticle's\nangular momentum. The {\\it non-manifest} superconformal invariance of the\nsuperpotential term is shown to lead to a shift in the SO(2) charge by the\nvalue of its coefficient, which we identify as the orbital angular momentum.\nThe full SU(1,1|2)-invariant dynamics is found from an extension to N=4\nsuperconformal mechanics.", "category": "hep-th" }, { "text": "The Standard Model, The Exceptional Jordan Algebra, and Triality: Jordan, Wigner and von Neumann classified the possible algebras of quantum\nmechanical observables, and found they fell into 4 \"ordinary\" families, plus\none remarkable outlier: the exceptional Jordan algebra. We point out an\nintriguing relationship between the complexification of this algebra and the\nstandard model of particle physics, its minimal left-right-symmetric\n$SU(3)\\times SU(2)_{L}\\times SU(2)_{R}\\times U(1)$ extension, and $Spin(10)$\nunification. This suggests a geometric interpretation, where a single\ngeneration of standard model fermions is described by the tangent space\n$(\\mathbb{C}\\otimes\\mathbb{O})^{2}$ of the complex octonionic projective plane,\nand the existence of three generations is related to $SO(8)$ triality.", "category": "hep-th" }, { "text": "Closed Superstrings in a Uniform Magnetic Field and Regularization\n Criterion: We summarize exact solutions of closed superstrings in a constant magnetic\nfield, from a view point of the regularization criterion. Some models will be\nexcluded according to this criterion. The spectrum-generating algebra is also\nconstructed in these interacting models.", "category": "hep-th" }, { "text": "Fluctuations of inflationary magnetogenesis: This analysis aims at exploring what can be said about the growth rate of\nmagnetized inhomogeneities under two concurrent hypotheses: a phase of quasi-de\nSitter dynamics driven by a single inflaton field and the simultaneous presence\nof a spectator field coupled to gravity and to the gauge sector. Instead of\ninvoking ad hoc correlations between the various components, the system of\nscalar inhomogeneities is diagonalized in terms of two gauge-invariant\nquasi-normal modes whose weighted sum gives the curvature perturbations on\ncomoving orthogonal hypersurfaces. The predominance of the conventional\nadiabatic scalar mode implies that the growth rate of magnetized\ninhomogeneities must not exceed 2.2 in Hubble units if the conventional\ninflationary phase is to last about 70 efolds and for a range of slow roll\nparameters between 0.1 and 0.001. Longer and shorter durations of the quasi-de\nSitter stage lead, respectively, either to tighter or to looser bounds which\nare anyway more constraining than the standard backreaction demands imposed on\nthe gauge sector. Since a critical growth rate of order 2 leads to a quasi-flat\nmagnetic energy spectrum, the upper bounds on the growth rate imply a lower\nbound on the magnetic spectral index. The advantages of the uniform curvature\ngauge are emphasized and specifically exploited throughout the treatment of the\nmulticomponent system characterizing this class of problems.", "category": "hep-th" }, { "text": "Explaining the Electroweak Scale and Stabilizing Moduli in M Theory: In a recent paper \\cite{Acharya:2006ia} it was shown that in $M$ theory vacua\nwithout fluxes, all moduli are stabilized by the effective potential and a\nstable hierarchy is generated, consistent with standard gauge unification. This\npaper explains the results of \\cite{Acharya:2006ia} in more detail and\ngeneralizes them, finding an essentially unique de Sitter (dS) vacuum under\nreasonable conditions. One of the main phenomenological consequences is a\nprediction which emerges from this entire class of vacua: namely gaugino masses\nare significantly suppressed relative to the gravitino mass. We also present\nevidence that, for those vacua in which the vacuum energy is small, the\ngravitino mass, which sets all the superpartner masses, is automatically in the\nTeV - 100 TeV range.", "category": "hep-th" }, { "text": "On the instability of 3d null singularities: String propagation on a three-dimensional Lorentzian string orbifold with a\nnull singularity has been studied by Horowitz and Steif, and more recently by\nLiu, Moore and Seiberg. We analyze the target space as a classical\ngravitational background. The singularity becomes spacelike when an arbitrarily\nsmall amount of matter is thrown at the singularity. This can be seen directly\nby studying the null singularity as a limit of the M=0, J=0 BTZ black hole\nmetric.", "category": "hep-th" }, { "text": "Decomposing the SU(N) Connection and the Wu-Yang Potential: Based on the decomposition of SU(2) gauge field, we derive a generalization\nof the decomposition theory for the SU(N) gauge field. We thus obtain the\ninvariant electro-magnetic tensors of SU(N) groups and the extended Wu-Yang\npotentials. The sourceless solutions are also discussed.", "category": "hep-th" }, { "text": "Aspects of the Holographic Study of Flavor Dynamics: This thesis is dedicated to the holographic study of flavor dynamics. The\ntechnique employed is a D7-brane probing of various D3-brane backgrounds. The\nfirst topic covered studies the influence of an external magnetic field on a\nflavored large N Yang-Mills theory. The theory exhibits spontaneous chiral\nsymmetry breaking. The meson spectrum exhibits Zeeman splitting and\ncharacteristic GMOR relation. The second topic examines thermal properties of\nthe dual gauge theory. The third topic studies the phase structure of the\nfinite temperature dual gauge theory in the presence of magnetic field. A phase\ndiagram of the theory is obtained and the meson spectrum is explored. The\nfourth topic studies the addition of an external electric field. The observed\neffect is dissociation of the bound quarks, favoring the meson melting, the\ndissociation of mesons corresponds to an insulator/conductor phase transition.\nThe fifth topic studies the addition of an R-charge chemical potential via\nbrane probing of the spinning D3-brane geometry. The corresponding phase\ndiagram is obtained. The chemical potential favors the dissociation of mesons.\nThe last topic explores universal properties of gauge theories dual to the\nDp/Dq system. A universal discrete self-similar behavior associated to the\ninsulator/conductor phase transition is observed and the corresponding scaling\nexponents are computed.", "category": "hep-th" }, { "text": "Moduli space volume of vortex and localization: Volume of moduli space of BPS vortices on a compact genus h Riemann surface\nSigma_h is evaluated by means of topological field theory and localization\ntechnique. Vortex in Abelian gauge theory with a single charged scalar field\n(ANO vortex) is studied first and is found that the volume of the moduli space\nagrees with the previous results obtained more directly by integrating over the\nmoduli space metric. Next we extend the evaluation to non-Abelian gauge groups\nand multi-flavors of scalar fields in the fundamental representation. We find\nthat the result of localization can be consistently understood in terms of\nmoduli matrix formalism wherever possible. More details are found in our paper\nin Prog.Theor.Phys.126 (2011) 637.", "category": "hep-th" }, { "text": "Calculating Casimir Energies in Renormalizable Quantum Field Theory: Quantum vacuum energy has been known to have observable consequences since\n1948 when Casimir calculated the force of attraction between parallel uncharged\nplates, a phenomenon confirmed experimentally with ever increasing precision.\nCasimir himself suggested that a similar attractive self-stress existed for a\nconducting spherical shell, but Boyer obtained a repulsive stress. Other\ngeometries and higher dimensions have been considered over the years. Local\neffects, and divergences associated with surfaces and edges have been studied\nby several authors. Quite recently, Graham et al. have re-examined such\ncalculations, using conventional techniques of perturbative quantum field\ntheory to remove divergences, and have suggested that previous self-stress\nresults may be suspect. Here we show that the examples considered in their work\nare misleading; in particular, it is well-known that in two dimensions a\ncircular boundary has a divergence in the Casimir energy for massless fields,\nwhile for general dimension $D$ not equal to an even integer the corresponding\nCasimir energy arising from massless fields interior and exterior to a\nhyperspherical shell is finite. It has also long been recognized that the\nCasimir energy for massive fields is divergent for $D\\ne1$. These conclusions\nare reinforced by a calculation of the relevant leading Feynman diagram in $D$\nand three dimensions. There is therefore no doubt of the validity of the\nconventional finite Casimir calculations.", "category": "hep-th" }, { "text": "Unification of twistors and Ramond vectors: We generalize the idea of supertwistors and introduce a new supersymmetric\nobject - the $\\theta$-twistor which includes the composite Ramond vector [11]\nwell known from the spinning string dynamics. The symmetries of the chiral\n$\\theta$-twistor superspace are studied. It is shown that the chiral spin\nstructure introduced by the $\\theta$-twistor breaks the superconformal boost\nsymmetry but preserves the scale symmetry and the super-Poincare symmetry. This\ngeometrical effect of breaking correlates with the Gross-Wess effect of the\nconformal boost breaking for bosonic scattering amplitudes.", "category": "hep-th" }, { "text": "Preheating with Fractional Powers: We consider preheating in models in which the potential for the inflaton is\ngiven by a fractional power, as is the case in axion monodromy inflation. We\nassume a standard coupling between the inflaton field and a scalar matter\nfield. We find that in spite of the fact that the oscillation of the inflaton\nabout the field value which minimizes the potential is anharmonic, there is\nnevertheless a parametric resonance instability, and we determine the Floquet\nexponent which describes this instability as a function of the parameters of\nthe inflaton potential.", "category": "hep-th" }, { "text": "Metric and coupling reversal in string theory: Invariance under reversing the sign of the metric G_{MN}(x) and/or the sign\nof the string coupling field H(x), where = g_s, leads to four possible\nUniverses denoted 1,I,J,K according as (G,H) goes to (G,H), (-G,H), (-G,-H),\n(G,-H), respectively. Universe 1 is described by conventional string/M theory\nand contains all M, D, F and NS branes. Universe I contains only D(-1), D3 and\nD7. Universe J contains only D1, D5, D9 and Type I. Universe K contains only F1\nand NS5 of IIB and Heterotic SO(32).", "category": "hep-th" }, { "text": "String versus Einstein frame in an AdS/CFT induced quantum dilatonic\n brane-world universe: AdS/CFT induced quantum dilatonic brane-world where 4d boundary is flat or de\nSitter (inflationary) or Anti-de Sitter brane is considered. The classical\nbrane tension is fixed but boundary QFT produces the effective brane tension\nvia the account of corresponding conformal anomaly induced effective action.\nThis results in inducing of brane-worlds in accordance with AdS/CFT set-up as\nwarped compactification. The explicit, independent construction of quantum\ninduced dilatonic brane-worlds in two frames: string and Einstein one is done.\nIt is demonstrated their complete equivalency for all quantum cosmological\nbrane-worlds under discussion, including several examples of classical\nbrane-world black holes. This is different from quantum corrected 4d dilatonic\ngravity where de Sitter solution exists in Einstein but not in Jordan (string)\nframe. The role of quantum corrections on massive graviton perturbations around\nAnti-de Sitter brane is briefly discussed.", "category": "hep-th" }, { "text": "The Casimir effect with quantized charged spinor matter in background\n magnetic field: We study the influence of a background uniform magnetic field and boundary\nconditions on the vacuum of a quantized charged spinor matter field confined\nbetween two parallel neutral plates; the magnetic field is directed\northogonally to the plates. The admissible set of boundary conditions at the\nplates is determined by the requirement that the Dirac Hamiltonian operator be\nself-adjoint. It is shown that, in the case of a sufficiently strong magnetic\nfield and a sufficiently large separation of the plates, the generalized\nCasimir force is repulsive, being independent of the choice of a boundary\ncondition, as well as of the distance between the plates. The detection of this\neffect seems to be feasible in the foreseeable future.", "category": "hep-th" }, { "text": "Brackets, Sigma Models and Integrability of Generalized Complex\n Structures: It is shown how derived brackets naturally arise in sigma-models via Poisson-\nor antibracket, generalizing a recent observation by Alekseev and Strobl. On\nthe way to a precise formulation of this relation, an explicit coordinate\nexpression for the derived bracket is obtained. The generalized Nijenhuis\ntensor of generalized complex geometry is shown to coincide up to a de-Rham\nclosed term with the derived bracket of the structure with itself, and a new\ncoordinate expression for this tensor is presented. The insight is applied to\ntwo known two-dimensional sigma models in a background with generalized complex\nstructure. Introductions to geometric brackets on the one hand and to\ngeneralized complex geometry on the other hand are given in the appendix.", "category": "hep-th" }, { "text": "Thermodynamics of accelerating AdS$_4$ black holes from the covariant\n phase space: We study the charges and first law of thermodynamics for accelerating,\nnon-rotating black holes with dyonic charges in AdS$_4$ using the covariant\nphase space formalism. In order to apply the formalism to these solutions\n(which are asymptotically locally AdS and admit a non-smooth conformal boundary\n$\\mathscr{I}$) we make two key improvements: 1) We relax the requirement to\nimpose Dirichlet boundary conditions and demand merely a well-posed variational\nproblem. 2) We keep careful track of the codimension-2 corner term induced by\nthe holographic counterterms, a necessary requirement due to the presence of\n\"cosmic strings\" piercing $\\mathscr{I}$. Using these improvements we are able\nto match the holographic Noether charges to the Wald Hamiltonians of the\ncovariant phase space and derive the first law of black hole thermodynamics\nwith the correct \"thermodynamic length\" terms arising from the strings. We\ninvestigate the relationship between the charges imposed by supersymmetry and\nshow that our first law can be consistently applied to various classes of\nnon-supersymmetric solutions for which the cross-sections of the horizon are\nspindles.", "category": "hep-th" }, { "text": "A note about a new class of two-kinks: We present a model of two-kinks resulting from an explicit composition of two\nstandards kinks of the $\\phi^4$ model based on the procedure of Ref.\n\\cite{uchiyama}. The two-kinks have an additional parameter accounting for the\nseparation of the standard kinks of $\\phi^4$ model. We have shown that the\ntwo-kinks have two discrete internal modes besides the zeroth mode and the\ncontinuous spectrum. This new feature signalizes that the head-on collision a\ntwo-kinks/two-antikinks pair exhibits a rich and complex behavior due to the\nadditional channel from which the energy of the system can be stored. We have\nexhibited the fractal structure associated with the main configurations after\nthe collision. We have inferred the fractality as the imprint of the nonlinear\nexchange of energy into the two discrete internal modes.", "category": "hep-th" }, { "text": "Schwinger Pair Production in dS_2 and AdS_2: We study Schwinger pair production in scalar QED from a uniform electric\nfield in dS_2 with scalar curvature R_{dS} = 2 H^2 and in AdS_2 with R_{AdS} =\n- 2 K^2. With suitable boundary conditions, we find that the pair-production\nrate is the same analytic function of the scalar curvature in both cases.", "category": "hep-th" }, { "text": "Multiple Membranes in M-theory: We review developments in the theory of multiple, parallel membranes in\nM-theory. After discussing the inherent difficulties pertaining to a maximally\nsupersymmetric lagrangian formulation with the appropriate field content and\nsymmetries, we discuss how introducing the concept of 3-algebras allows for\nsuch a description. Different choices of 3-algebras lead to distinct classes of\n2+1 dimensional theories with varying degrees of supersymmetry. We then\ndescribe how these are equivalent to a type of conventional superconformal\nChern-Simons gauge theories at level k, coupled to bifundamental matter.\nAnalysing the physical properties of these theories leads to the identification\nof a certain subclass of models with configurations of M2-branes in Z_k\norbifolds of M-theory. In addition these models give rise to a whole new sector\nof the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We\nalso discuss mass deformations, higher derivative corrections as well as the\npossibility of extracting information about M5-brane physics.", "category": "hep-th" }, { "text": "The Hydrohedron: Bootstrapping Relativistic Hydrodynamics: As an effective theory, relativistic hydrodynamics is fixed by symmetries up\nto a set of transport coefficients. A lot of effort has been devoted to\nexplicit calculations of these coefficients. Here we propose a shift in\nperspective: we deploy bootstrap techniques to rule out theories that are\ninconsistent with microscopic causality. What remains is a universal convex\ngeometry in the space of transport coefficients, which we call the hydrohedron.\nThe landscape of all consistent theories necessarily lie inside or on the edges\nof the hydrohedron. We analytically construct cross-sections of the hydrohedron\ncorresponding to bounds on transport coefficients that appear in sound and\ndiffusion modes for theories without stochastic fluctuations.", "category": "hep-th" }, { "text": "Standard Models and Split Supersymmetry from Intersecting Brane\n Orbifolds: We construct four dimensional three generation non-supersymmetric $SU(3)_c\n\\times SU(2)_L \\times U(1)_Y$ intersecting D6-brane models with $\\nu_R$\\rq{s}.\nAt three stacks we find exactly the MSSM chiral fermion matter spectrum. At 4-,\n5-stacks we find models with the massless fermion spectrum of the N=1 Standard\nModel and massive exotic non-chiral matter; these models flow also to only the\nSM. At 8-stacks we find MSSM-like models, with minimal massless exotics, made\nfrom two different N=1 sectors. Exotic triplet masses put a lower bound on the\nstring scale of $2.79/2.89 \\times 10^6$ GeV for a Higgs 124/126 GeV. It\\rq{}s\nthe first appearance of N=0 stringy quivers with the MSSM and matter in\nantisymmetric representations and perturbatively missing Yukawa couplings. The\npresent models are based on orientifolds of ${\\bf T^6/(Z_3 \\times Z_3)}$\ncompactifications of IIA theory based on the torus lattice AAA; all complex\nmoduli are fixed by the orbifold symmetry. We also present the spectrum rules +\nGS anomaly cancellation for the ABB lattice. Moreover, we point out the\nrelevance of intersecting/and present D6-brane constructions on ideas related\nto existence of split supersymmetry in nature. In this context we present\nnon-susy models with only the SM-matter and also MSSM-matter dominated models,\nwith massive gauginos and light higgsinos, that achieve the correct\nsupersymmetric GUT value for the Weinberg angle $sin^2 \\theta = \\frac{3}{8}$ at\na string scale $5 \\cdot 10^{13} \\ GeV < M_{S} < 1.4 \\cdot 10^{17}$ GeV. It\nappears that if only the SM survives at low energy the unification scale is\npreserved at $5.03 \\times 10^{13}$ GeV when n$_H$ =1, 3, 6. These models\nsupport the existence of split supersymmetry scenario in string theory.", "category": "hep-th" }, { "text": "Reggeized gluon states in Quantum Chromodynamics: The reggeized gluon states, which are also called Reggeons, appear in the\nscattering amplitude of hadrons in Regge limit. The wave-function of Reggeons\nsatisfy the BKP equation, which in multi-colour limit of Quantum Chromodynamics\nis equivalent to the Schrodinger equation of the XXX Heisenberg SL(2,C) spin\nchain model. In this work we solve the BKP equation, show the spectrum of the\nenergy and other integrals of motion for a number of Reggeons N=2,...,8.\nMoreover, we consider deep inelastic scattering where due to the reggeized\ngluons states we are able to calculate anomalous dimensions and corresponding\nto their twists.", "category": "hep-th" }, { "text": "Kac-Moody Algebras in M-theory: In this thesis, we consider several aspects of over-extended and\nvery-extended Kac-Moody algebras in relation with theories of gravity coupled\nto matter. In the first part, we focus on the occurrence of KM algebras in the\ncosmological billiards. We analyse the billiards in the simplified situation of\nspatially homogeneous cosmologies. The most generic cases lead to the same\nalgebras as those met in the general inhomogeneous case, but also sub-algebras\nof the \"generic\" ones appear. Next, we consider particular gravitational\ntheories which, upon toroidal compactification to D=3 space-time dimensions,\nreduce to a theory of gravity coupled to a symmetric space non-linear\nsigma-model. We show that the billiard analysis gives direct information on\npossible dimensional oxidations (or on their obstructions) and field content of\nthe oxidation endpoint. We also consider all hyperbolic Kac-Moody algebras and\ncompletely answer the question of whether or not a specific theory exists\nadmitting a billiard characterised by the given hyperbolic algebra. In the\nsecond part, we turn to the set up of such gravity-matter theories through the\nbuilding of an action explicitly invariant under a Kac-Moody group. As a first\nstep to include fermions, we check the compatibility of the presence of a Dirac\nfermion with the (hidden duality) symmetries appearing in the toroidal\ncompactification down to 3 space-time dimensions. Next, we investigate how the\nfermions (with spin 1/2 or 3/2) fit in the conjecture for hidden over-extended\nsymmetry G++. Finally, in the context of G+++ invariant actions, we derive all\nthe possible signatures for all the GB++ theories that can be obtained from the\nconventional one (1,D-1) by \"dualities\" generated by Weyl reflections. This\ngeneralizes the results obtained for E8++.", "category": "hep-th" }, { "text": "Coulomb interaction from the interplay between Confinement and Screening: It has been noticed that confinement effects can be described by the addition\nof a $ \\sqrt {- F_{\\mu \\nu}^a F^{a\\mu \\nu}} $ term in the Lagrangian density.\nWe now study the combined effect of such \"confinement term\" and that of a mass\nterm. The surprising result is that the interplay between these two terms gives\nrise to a Coulomb interaction. Our picture has a certain correspondence with\nthe quasiconfinement picture described by Giles, Jaffe and de Rujula for QCD\nwith symmetry breaking.", "category": "hep-th" }, { "text": "Emergent Gravity from Noncommutative Spacetime: We showed before that self-dual electromagnetism in noncommutative (NC)\nspacetime is equivalent to self-dual Einstein gravity. This result implies a\nstriking picture about gravity: Gravity can emerge from electromagnetism in NC\nspacetime. Gravity is then a collective phenomenon emerging from gauge fields\nliving in fuzzy spacetime. We elucidate in some detail why electromagnetism in\nNC spacetime should be a theory of gravity. In particular, we show that NC\nelectromagnetism is realized through the Darboux theorem as a diffeomorphism\nsymmetry G which is spontaneously broken to symplectomorphism H due to a\nbackground symplectic two-form $B_{\\mu\\nu}=(1/\\theta)_{\\mu\\nu}$, giving rise to\nNC spacetime. This leads to a natural speculation that the emergent gravity\nfrom NC electromagnetism corresponds to a nonlinear realization G/H of the\ndiffeomorphism group, more generally its NC deformation. We also find some\nevidences that the emergent gravity contains the structure of generalized\ncomplex geometry and NC gravity. To illuminate the emergent gravity, we\nillustrate how self-dual NC electromagnetism nicely fits with the twistor space\ndescribing curved self-dual spacetime. We also discuss derivative corrections\nof Seiberg-Witten map which give rise to higher order gravity.", "category": "hep-th" }, { "text": "Optical Properties of a \u03b8-Vacuum: Chern-Simons (CS) forms generalize the minimal coupling between gauge\npotentials and point charges, to sources represented by charged extended\nobjects (branes). The simplest example of such a CS-brane coupling is a domain\nwall coupled to the electromagnetic CS three-form. This describes a\ntopologically charged interface where the CS form AdA is supported, separating\ntwo three-dimensional spatial regions in 3+1 spacetime. Electrodynamics at\neither side of the brane is described by the same Maxwell's equations, but\nthose two regions have different vacua, characterized by a different value of\nthe \\theta-parameter multiplying the Pontryagin form F ^ F. The \\theta-term is\nthe abelian version of the concept introduced by 't Hooft for the resolution of\nthe U(1) problem in QCD. We point out that CS-generalized classical\nelectrodynamics shows new phenomena when two neighboring regions with different\n\\theta-vacua are present. These topological effects result from surface effects\ninduced by the boundary and we explore the consequences of such boundary\neffects for the propagation of the electromagnetic field in Maxwell theory.\nSeveral features, including optical and electrostatic/magnetostatic responses,\nwhich may be observable in condensed matter systems, like topological\ninsulators, are discussed.", "category": "hep-th" }, { "text": "String creation in D6-brane background: The production of string charge during a crossing of certain oriented\nD-branes is studied. We compute the string charge in the system of a probe\nD2-brane and a background D6-brane by use of the equations of motion in the\nten-dimensions. We confirm the creation of string charge as inflow from the\nbackground D6-brane.", "category": "hep-th" }, { "text": "Hamiltonian Dynamics of Cosmological Quintessence Models: The time-evolution dynamics of two nonlinear cosmological real gas models has\nbeen reexamined in detail with methods from the theory of Hamiltonian dynamical\nsystems. These examples are FRWL cosmologies, one based on a gas, satisfying\nthe van der Waals equation and another one based on the virial expansion gas\nequation. The cosmological variables used are the expansion rate, given by the\nHubble parameter, and the energy density. The analysis is aided by the\nexistence of global first integral as well as several special (second)\nintegrals in each case. In addition, the global first integral can serve as a\nHamiltonian for a canonical Hamiltonian formulation of the evolution equations.\nThe conserved quantities lead to the existence of stable periodic solutions\n(closed orbits) which are models of a cyclic Universe. The second integrals\nallow for explicit solutions as functions of time on some special trajectories\nand thus for a deeper understanding of the underlying physics. In particular,\nit is shown that any possible static equilibrium is reachable only for infinite\ntime.", "category": "hep-th" }, { "text": "Magnetic monopoles and symmetries in noncommutative space: In this paper, we review the progress in the analysis of magnetic monopoles\nas generalized states in quantum mechanics. We show that the considered model\ncontains rich algebraic structure that generates symmetries which have been\nutilized in different physical contexts. Even though are we focused on quantum\nmechanics in noncommutative space $\\textbf{R}_\\lambda^3$, the results can be\nreconstructed in ordinary quantum mechanics in $\\textbf{R}^3$ as well.", "category": "hep-th" }, { "text": "BPS Equations and the Stress Tensor: We exploit the relationship between the space components of the\nenergy-momentum tensor and the supercurrent to discuss the connection between\nthe BPS equations and the vanishing of the components of the stress tensor in\nvarious supersymmetric theories with solitons.\n Using the fact that certain combination of supercharges annihilate BPS\nstates, we show that $T_{ij}=0$ for kinks, vortices and dyons, displaying the\nconnection between supersymmetry and non-interacting BPS solitons.", "category": "hep-th" }, { "text": "Nonsupersymmetric Brane/Antibrane Configurations in Type IIA and M\n Theory: We study metastable nonsupersymmetric configurations in type IIA string\ntheory, obtained by suspending D4-branes and anti-D4-branes between\nholomorphically curved NS5's, which are related to those of hep-th/0610249 by\nT-duality. When the numbers of branes and antibranes are the same, we are able\nto obtain an exact M theory lift which can be used to reliably describe the\nvacuum configuration as a curved NS5 with dissolved RR flux for g_s<<1 and as a\ncurved M5 for g_s>>1. When our weakly coupled description is reliable, it is\nrelated by T-duality to the deformed IIB geometry with flux of hep-th/0610249\nwith moduli exactly minimizing the potential derived therein using special\ngeometry. Moreover, we can use a direct analysis of the action to argue that\nthis agreement must also hold for the more general brane/antibrane\nconfigurations of hep-th/0610249. On the other hand, when our strongly coupled\ndescription is reliable, the M5 wraps a nonholomorphic minimal area curve that\ncan exhibit quite different properties, suggesting that the residual structure\nremaining after spontaneous breaking of supersymmetry at tree level can be\nfurther broken by the effects of string interactions. Finally, we discuss the\nboundary condition issues raised in hep-th/0608157 for nonsupersymmetric IIA\nconfigurations, their implications for our setup, and their realization on the\ntype IIB side.", "category": "hep-th" }, { "text": "On orbifolds and free fermion constructions: This work develops the correspondence between orbifolds and free fermion\nmodels. A complete classification is obtained for orbifolds X/G with X the\nproduct of three elliptic curves and G an abelian extension of a group (Z_2)^2\nof twists acting on X. Each such quotient X/G is shown to give a geometric\ninterpretation to an appropriate free fermion model, including the geometric\nNAHE+ model. However, the semi-realistic NAHE free fermion model is proved to\nbe non-geometric: its Hodge numbers are not reproduced by any orbifold X/G. In\nparticular cases it is shown that X/G can agree with some Borcea-Voisin\nthreefolds, an orbifold limit of the Schoen threefold, and several further\norbifolds thereof. This yields free fermion models with geometric\ninterpretations on such special threefolds.", "category": "hep-th" }, { "text": "Baxter operators for arbitrary spin II: This paper presents the second part of our study devoted to the construction\nof Baxter operators for the homogeneous closed XXX spin chain with the quantum\nspace carrying infinite or finite-dimensional $s\\ell_2$ representations. We\nconsider the Baxter operators used in \\cite{BLZ,Shortcut}, formulate their\nconstruction uniformly with the construction of our previous paper. The\nbuilding blocks of all global chain operators are derived from the general\nYang-Baxter operators and all operator relations are derived from general\nYang-Baxter relations. This leads naturally to the comparison of both\nconstructions and allows to connect closely the treatment of the cases of\ninfinite-dimensional representation of generic spin and finite-dimensional\nrepresentations of integer or half-integer spin. We proof not only the\nrelations between the operators but present also their explicit forms and\nexpressions for their action on polynomials representing the quantum states.", "category": "hep-th" }, { "text": "Multiboson Expansions for the q-Oscillator and $SU(1,1)_q$: All the hermitian representations of the ``symmetric\" $q$-oscillator are\nobtained by means of expansions. The same technique is applied to characterize\nin a systematic way the $k$-order boson realizations of the $q$-oscillator and\n$su(1,1)_q$. The special role played by the quadratic realizations of\n$su(1,1)_q$ in terms of boson and $q$-boson operators is analysed and\nclarified.", "category": "hep-th" }, { "text": "Some inequalities bridging stringy parameters and cosmological\n observables: By demanding the validity of an effective field theory description during\ninflation, in this note we derive some peculiar inequalities among the three\ninteresting stringy and cosmological parameters, namely the tensor-to-scalar\nratio ($r$), the string coupling ($g_s$) and the compactification volume\n(${\\cal V}$). In deriving these inequalities, we explicitly demand that the\ninflationary scale and the Hubble parameter during inflation are well below the\nKaluza-Klein (KK) mass scale, string scale, and the four dimensional Planck\nmass. For the inflationary models developed within the framework of type IIB\norientifold comapctification, we investigate the regions of parameters space\nspanned by the three parameters $(r, g_s, {\\cal V})$ by satisfying our\ninequalities, and we find that the same can reduce the size of available\nparameter space quite significantly. Moreover, we comment on obtaining further\nconstraints on the parameters by comparing gravitino mass ($m_{3/2}$) with the\nHubble scale ($H$), which also provides a lower bound on tensor-to-scalar ratio\n($r$), for the cases when $m_{3/2} 4$,\n$Im(\\omega / T_H)$ vanishes in the scalar perturbation. For the gravitational\nperturbation it is shown that $Re(\\omega / T_H) = \\ln 3$ is reproduced when $n\n= 0$ and $n = 4$. For different $n$, however, $Re(\\omega / T_H)$ is smaller\nthan $\\ln 3$. When $n = \\infty$, for example, $Re(\\omega / T_H)$ approaches to\n$\\ln (1 + 2 \\cos \\sqrt{5} \\pi) \\approx 0.906$. Unlike the scalar perturbation\n$Im(\\omega / T_H)$ does not vanish regradless of the number of extra\ndimensions.", "category": "hep-th" }, { "text": "Towards Natural Inflation in String Theory: We provide type IIB string embeddings of two axion variants of natural\ninflation. We use a combination of RR 2 form axions as the inflaton field and\nhave its potential generated by non perturbative effects in the superpotential.\nBesides giving rise to inflation, the models developed take into account the\nstabilization of the compact space, both in the KKLT and large volume scenario\nregimes, an essential condition for any semi-realistic model of string\ninflation.", "category": "hep-th" }, { "text": "Wick rotation and the positivity of energy in quantum field theory: We propose a new axiom system for unitary quantum field theories on curved\nspace-time backgrounds, by postulating that the partition function and the\ncorrelators extend analytically to a certain domain of complex-valued metrics.\nOrdinary Riemannian metrics are contained in the allowable domain, while\nLorentzian metrics lie on its boundary.", "category": "hep-th" }, { "text": "An extended standard model and its Higgs geometry from the matrix model: We find a simple brane configuration in the IKKT matrix model which resembles\nthe standard model at low energies, with a second Higgs doublet and\nright-handed neutrinos. The electroweak sector is realized geometrically in\nterms of two minimal fuzzy ellipsoids, which can be interpreted in terms of\nfour point-branes in the extra dimensions. The electroweak Higgs connects these\nbranes and is an indispensable part of the geometry. Fermionic would-be zero\nmodes arise at the intersections with two larger branes, leading precisely to\nthe correct chiral matter fields at low energy, along with right-handed\nneutrinos which can acquire a Majorana mass due to a Higgs singlet. The larger\nbranes give rise to $SU(3)_c$, extended by $U(1)_B$ and another $U(1)$ which\nare anomalous at low energies and expected to disappear. At higher energies,\nmirror fermions and additional fields arise, completing the full ${\\cal N}=4$\nsupersymmetry. The brane configuration is a solution of the model, assuming a\nsuitable effective potential and a non-linear stabilization of the singlet\nHiggs. The basic results can be carried over to ${\\cal N}=4$ $SU(N)$\nsuper-Yang-Mills on ordinary Minkowski space with sufficiently large $N$.", "category": "hep-th" }, { "text": "Casimir Torque in Inhomogeneous Dielectric Plates: In this work, we consider a torque caused by the well known quantum\nmechanical Casimir effect arising from quantized field fluctuations between\nplates with inhomogeneous, sharply discontinuous, dielectric properties. While\nthe Casimir effect is a relatively well understood phenomenon, systems\nresulting in lateral or rotational forces are far less developed; to our\nknowledge, a theoretical study of discontinuous dielectric variants of such\nsystems has not been attempted. We utilize a Proximity Force Approximation in\nconjunction with the Lifshitz dielectric formula to perform theoretical\nanalyses of resultant torques in systems with bisected and quadrisected\ndielectric regions. We also develop a high precision Monte Carlo type numerical\nintegrator to approximate our derived expressions. Our calculations of an\nenergy density linear with the alignment angle result in a constant torque and\nhave implications in NEMS (nano electromechanical systems) and MEMS (micro\nelectromechanical systems), including a postulated nanoscale oscillating drive\nmechanism powered by quantum field interactions.", "category": "hep-th" }, { "text": "One-Loop Effective Action on the Four-Ball: This paper applies $\\zeta$-function regularization to evaluate the 1-loop\neffective action for scalar field theories and Euclidean Maxwell theory in the\npresence of boundaries. After a comparison of two techniques developed in the\nrecent literature, vacuum Maxwell theory is studied and the contribution of all\nperturbative modes to $\\zeta'(0)$ is derived: transverse, longitudinal and\nnormal modes of the electromagnetic potential, jointly with ghost modes. The\nanalysis is performed on imposing magnetic boundary conditions, when the\nFaddeev-Popov Euclidean action contains the particular gauge-averaging term\nwhich leads to a complete decoupling of all perturbative modes. It is shown\nthat there is no cancellation of the contributions to $\\zeta'(0)$ resulting\nfrom longitudinal, normal and ghost modes.", "category": "hep-th" }, { "text": "Anisotropic Dyonic Black Brane and its Effects on Hydrodynamics: We construct $SL(2,R)$ invariant in anisotropic medium, with a dual\nanisotropic charged black hole geometry in massive gravity. We show how to\nobtain $SL(2,R)$ elements in terms of new degrees of freedom for\nElectromagnetic configuration, and construct the general expressions for\nconductivity with $SL(2,R)$ invariant. The holographic conductivities can be\ncalculated using horizon data in an external magnetic field, and we show the\nnumerical results using the linear response theory.", "category": "hep-th" }, { "text": "$N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$: We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super\nYang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories\nshould have coefficients that are modular forms of these subgroups. In\nparticular, uniqueness arguments are sufficient to construct the $SU(3)$ curve,\nup to two numerical constants, which can be fixed by making some assumptions\nabout strong coupling behavior. We also discuss the situation for higher\ngroups. We also include a derivation of the closed form $\\beta$-function for\nthe $SU(2)$ and $SU(3)$ theories without matter, and the massless theories with\n$N_f=n$.", "category": "hep-th" }, { "text": "HS in flat spacetime. The effective action method: This is the first paper in a series of three dealing with HS theories in flat\nspacetime. It is divided in three parts. The first part is an elaboration on\nthe method of effective action, initiated in a previous paper. We study the\nproperties of correlators of currents in the free fermion coupled to external\nhigher spin (HS) potentials, and develop techniques for their explicit\ncalculation. In particular we show how they can be calculated via ordinary\nFeynman diagram techniques. We also introduce the concept of {\\it curved}\n$L_\\infty$ algebra and show how it can be realized in the context of the\nfermion model. In part II we compare the results of the scalar model and those\nof the fermion model (coupled to HS fields). We show that the HS field\nformulation coming from the scalar model is the `square' of the one ensuing\nfrom the fermion model. Finally, in part III, we analyze the possible\nobstructions that one may meet in constructing the effective action: these are\nthe analogs of anomalies in ordinary gauge theories. We provide explicit and\ncompact formulas of the latter.", "category": "hep-th" }, { "text": "Supersymmetry Breaking and the Cosmological Constant: I review three attempts to explain the small value of the cosmological\nconstant, and their connection to SUSY breaking. They are The String Landscape,\nSupersymmetric Large Extra Dimensions (SLED), and the Holographic Space-time\nFormalism invented by Fischler and myself.", "category": "hep-th" }, { "text": "AdS Black Holes with a Bouncing Interior: We construct planar black hole solutions of AdS gravity minimally coupled to\na scalar field with an even, super-exponential potential. We show that the\nevolution of the black hole interior exhibits an infinite sequence of Kasner\nepochs, as the scalar field rolls back and forth in its potential. We obtain an\nanalytic expression for the `bounces' between each Kasner epoch and also give\nan explicit formula for the times and strengths of the bounces at late interior\ntimes, thereby fully characterizing the interior evolution. In this way we show\nthat the interior geometry approaches the Schwarzschild singularity at late\ntimes, even as the scalar field is driven higher up its potential with each\nbounce.", "category": "hep-th" }, { "text": "SDiff(2) Toda equation -- hierarchy, $\u03c4$ function, and symmetries: A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda\nequation, is shown to have a Lax formalism and an infinite hierarchy of higher\nflows. The Lax formalism is very similar to the case of the self-dual vacuum\nEinstein equation and its hyper-K\\\"ahler version, however now based upon a\nsymplectic structure and the group SDiff(2) of area preserving diffeomorphisms\non a cylinder $S^1 \\times \\R$. An analogue of the Toda lattice tau function is\nintroduced. The existence of hidden SDiff(2) symmetries are derived from a\nRiemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function\nturn out to have commutator anomalies, hence give a representation of a central\nextension of the SDiff(2) algebra.", "category": "hep-th" }, { "text": "Field-theoretic Methods in Strongly-Coupled Models of General Gauge\n Mediation: An often-exploited feature of the operator product expansion (OPE) is that it\nincorporates a splitting of ultraviolet and infrared physics. In this paper we\nuse this feature of the OPE to perform simple, approximate computations of soft\nmasses in gauge-mediated supersymmetry breaking. The approximation amounts to\ntruncating the OPEs for hidden-sector current-current operator products. Our\nmethod yields visible-sector superpartner spectra in terms of vacuum\nexpectation values of a few hidden-sector IR elementary fields. We manage to\nobtain reasonable approximations to soft masses, even when the hidden sector is\nstrongly coupled. We demonstrate our techniques in several examples, including\na new framework where supersymmetry-breaking arises both from a hidden sector\nand dynamically.", "category": "hep-th" }, { "text": "Towards the description of anisotropic plasma at strong coupling: We initiate a study of anisotropic plasma at strong coupling using the\nAdS/CFT correspondence. We construct an exact dual geometry which represents a\nstatic uniform but anisotropic system and find, that although it is singular,\nit allows for a notion of `incoming' boundary conditions. We study small\nfluctuations around this background and find that the dispersion relation\ndepends crucially on the direction of the wave-vector relative to the shape of\nthe anisotropy reminiscent of similar behaviour at weak coupling. We do not\nfind explicit instabilities to the considered order but only a huge difference\nin the damping behaviour.", "category": "hep-th" }, { "text": "On the \"scattering law\" for Kasner parameters appearing in asymptotics\n of an exact S-brane solution: A multidimensional cosmological model with scalar and form fields [1-4] is\nstudied. An exact S-brane solution (either electric or magnetic) in a model\nwith l scalar fields and one antisymmetric form of rank m > 1 is considered.\nThis solution is defined on a product manifold containing n Ricci-flat factor\nspaces M_1, ..., M_n. In the case when the kinetic term for scalar fields is\npositive definite we singled out a special solution governed by the function\ncosh. It is shown that this special solution has Kasner-like asymptotics in the\nlimits \\tau \\to + 0 and \\tau \\to + \\infty, where \\tau is a synchronous time\nvariable. A relation between two sets of Kasner parameters \\alpha_{\\infty} and\n\\alpha_0 is found. This relation, named as ``scattering law'' (SL) formula, is\ncoinciding with the ``collision law'' (CL) formula obtained previously in [5]\nin a context of a billiard description of S-brane solutions near the\nsingularity. A geometric sense of SL formula is clarified: it is shown that SL\ntransformation is a map of a ``shadow'' part of the Kasner sphere S^{N-2} (N =\nn+l) onto ``illuminated'' part. This map is just a (generalized) inversion with\nrespect to a point v located outside the Kasner sphere S^{N-2}. The shadow and\nilluminated parts of the Kasner sphere are defined with respect to a point-like\nsource of light located at v. Explicit formulae for SL transformations\ncorresponding to SM2- and SM5-brane solutions in 11-dimensional supergravity\nare presented.", "category": "hep-th" }, { "text": "Noncommutative quantum mechanics as a constrained system: It is shown that quantum mechanics on noncommutative spaces (NQM) can be\nobtained by the canonical quantization of some underlying second class\nconstrained system formulated in extended configuration space. It leads, in\nparticular, to an intriguing possibility of quantization in terms of the\ninitial (noncommutative) variables. Two different formulations are discissed.\nThe first one is appropriate for at most quadratic potential. The\nnoncommutativity parameter and rank of matrix of the constraint brackets depend\non the potential. It explains appearance of two phases of the resulting NQM.\nThe second formulation is appropriate for an arbitrary potential. In both cases\nthe corresponding Lagrangian action is presented and quantized, which leads to\nquantum mechanics with ordinary product replaced by the Moyal product.", "category": "hep-th" }, { "text": "Area Operators in Holographic Quantum Gravity: We argue that the holographic formula relating entanglement entropy and the\narea of a minimal surface is the key to define the area of surfaces in the\n(emergent) spacetime from the dual theory on the boundary. So we promote the\nentropy/area relation to operators to define the \"area\" observable in a\nholographic formulation of quantum gravity, then we find a suitable geometric\nrepresentation for the states, and show that the Ryu-Takayanagi proposal is\nrecovered in the approximation of semi-classical gravity. Finally, we discuss\nthis picture in the example of a AdS-Black hole.", "category": "hep-th" }, { "text": "The NSVZ beta-function in supersymmetric theories with different\n regularizations and renormalization prescriptions: We briefly review the calculations of quantum corrections related with the\nexact NSVZ $\\beta$-function in ${\\cal N}=1$ supersymmetric theories, paying\nespecial attention to the scheme dependence of the results. It is explained,\nhow the NSVZ relation is obtained for the renormalization group functions\ndefined in terms of the bare coupling constant if a theory is regularized by\nhigher derivatives. Also we describe, how to construct a special\nrenormalization prescription which gives the NSVZ relation for the\nrenormalization group functions defined in terms of the renormalized coupling\nconstant exactly in all orders for Abelian supersymmetric theories, regularized\nby higher derivatives. The scheme dependence of the NSVZ $\\beta$-function (for\nthe renormalization group functions defined in terms of the renormalized\ncoupling constant) is discussed in the non-Abelian case. It is shown that in\nthis case the NSVZ $\\beta$-function leads to a certain scheme-independent\nequality.", "category": "hep-th" }, { "text": "Semiclassical circular strings in AdS_5 and \"long\" gauge field strength\n operators: We consider circular strings rotating with equal spins S_1=S_2=S in two\northogonal planes in AdS_5 and suggest that they may be dual to \"long\" gauge\ntheory operators built out of self-dual components of gauge field strength. As\nwas found in hep-th/0404187, the one-loop anomalous dimensions of the such\ngauge-theory operators are described by an anti-ferromagnetic XXX_1 spin chain\nand scale linearly with length L>>1. We find that in the case of rigid rotating\nstring both the classical energy E_0 and the 1-loop string correction E_1\ndepend linearly on the spin S (within the stability region of the solution).\nThis supports the relation between the rigid rotating string and the\ngauge-theory operator corresponding to the maximal-spin (ferromagnetic) state\nof the XXX_1 spin chain. The energy of more general rotating and pulsating\nstrings also happens to scale linearly with both the spin and the oscillation\nnumber. Such solutions should be dual to other lower-spin states of the spin\nchain, with the anti-ferromagnetic ground state presumably corresponding to the\nstring pulsating in two planes with no rotation.", "category": "hep-th" }, { "text": "From black holes to flux throats: polarization can resolve the\n singularity: Supersymmetry-breaking is a key ingredient for string theory models to be\nphenomenologically viable. We review the strong analogy in the physics and the\nmethods used for describing non-supersymmetric flux vacua and\nnon-supersymmetric black holes in string theory. We also show how the polarized\nstate could be the key to describing a well-behaved back-reaction of\nanti-branes in flux backgrounds, shedding a new light on a recent debate in the\nliterature.", "category": "hep-th" }, { "text": "Derivative Expansion of the Effective Action for Massless Scalar\n Electrodynamics in Arbitrary Gauge: It is shown how operator regularization can be used to obtain an expansion of\nthe effective action in powers of derivatives of the background field. This is\napplied to massless scalar electrodynamics to find the one-loop corrections to\nthe kinetic terms associated with both the scalar and vector fields in\narbitrary gauge. This allows us to examine the radiatively induced masses\narising in this model.", "category": "hep-th" }, { "text": "On Brane-Antibrane Forces: In this note, we will discuss two aspects of brane-antibrane forces. In one\naspect, we generalize the force calculation of D0-${\\bar {\\rm D}}$0 of Banks\nand Susskind to Dp-${\\bar {\\rm D}}p$ for $1\\le p \\leq 8$. In particular, we\nfind that the force is also divergent for p = 1 while for the other cases ($p\n\\ge 2$) the forces are in general finite when $Z \\to 0^+$, where $Z =\n\\frac{Y^2}{2\\pi^2\\alpha'} - 1$ with Y, the brane-antibrane separation. However,\nthe forces are divergent for all cases when Z < 0, signalling the occurrence of\nopen string tachyon condensation in this regime. The other deals with the\npuzzling static nature of the supergravity brane-antibrane configurations. We\nwill show that the force on a brane probe due to a brane-antibrane background\nvanishes when the probe is placed at the location of the coincident\nbrane-antibranes, thereby providing a direct evidence for the existence of\ngeneral static brane-antibrane configuration in the supergravity approximation.", "category": "hep-th" }, { "text": "Background Independent Field Quantization with Sequences of\n Gravity-Coupled Approximants II: Metric Fluctuations: We apply the new quantization scheme outlined in Phys. Rev. D102 (2020)\n125001 to explore the influence which quantum vacuum fluctuations of the\nspacetime metric exert on the universes of Quantum Einstein Gravity, which is\nregarded an effective theory here. The scheme promotes the principle of\nBackground Independence to the level of the regularized precursors of a quantum\nfield theory (\"approximants\") and severely constrains admissible regularization\nschemes. Without any tuning of parameters, we find that the zero point\noscillations of linear gravitons on maximally symmetric spacetimes do not\ncreate the commonly expected cosmological constant problem of a cutoff-size\ncurvature. On the contrary, metric fluctuations are found to reduce positive\ncurvatures to arbitrarily tiny and ultimately vanishing values when the cutoff\nis lifted. This suggests that flat space could be the distinguished groundstate\nof pure quantum gravity. Our results contradict traditional beliefs founded\nupon background-dependent calculations whose validity must be called into\nquestion therefore.", "category": "hep-th" }, { "text": "Complex linear superfields, Supercurrents and Supergravities: We present expressions for the supercurrents generated by a generic\n$4D,~\\mathcal{N}=1$ theory of complex linear superfield $\\Sigma$. We verify\nthat these expressions satisfy the appropriate superspace conservation\nequations. Furthermore, we discuss the component projection in order to derive\nexpressions for the energy-momentum tensor, the supersymmetry current and the\nR-symmetry current when available. In addition, we discuss aspects of the\ncoupling of the theory to supergravity. Specifically, we present a\nstraightforward method to select the appropriate formulations of supergravity\nthat one must use in order to do the coupling. This procedure is controlled by\na superfield X originating from the Super-Poincar\\'{e} invariance of the\ntheory. We apply these results to examples of theories with higher derivative\nterms.", "category": "hep-th" }, { "text": "Some Properties of Open - String Theories: Open-string theories may be related to suitable models of oriented closed\nstrings. The resulting construction of ``open descendants'' is illustrated in a\nfew simple cases that exhibit some of its key features.", "category": "hep-th" }, { "text": "A Deformation of Sasakian Structure in the Presence of Torsion and\n Supergravity Solutions: We discuss a deformation of Sasakian structure in the presence of totally\nskew-symmetric torsion by introducing odd dimensional manifolds whose metric\ncones are K\\\"ahler with torsion. It is shown that such a geometry inherits\nsimilar properties to those of Sasakian geometry. As an example of them, we\npresent an explicit expression of local metrics and see how Sasakian structure\nis deformed by the presence of torsion. We also demonstrate that our example of\nthe metrics admits the existence of hidden symmetries described by non-trivial\nodd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using\nthese metrics as an {\\it ansatz}, we construct exact solutions in five\ndimensional minimal (un-)gauged supergravity and eleven dimensional\nsupergravity. Finally, we discuss the global structures of the solutions and\nobtain regular metrics on compact manifolds in five dimensions, which give\nnatural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and\n$L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven\ndimensions.", "category": "hep-th" }, { "text": "One-loop divergences in the Galileon model: The investigation of UV divergences is a relevant step in better\nunderstanding of a new theory. In this work the one-loop divergences in the\nfree field sector are obtained for the popular Galileons model. The\ncalculations are performed by the generalized Schwinger-DeWitt technique and\nalso by means of Feynman diagrams. The first method can be directly generalized\nto curved space, but here we deal only with the flat-space limit. We show that\nthe UV completion of the theory includes the $\\pi \\Box^4\\pi$ term. According to\nour previous analysis in the case of quantum gravity, this means that the\ntheory can be modified to become superrenormalizable, but then its physical\nspectrum includes two massive ghosts and one massive scalar with positive\nkinetic energy. The effective approach in this theory can be perfectly\nsuccessful, exactly as in the higher derivative quantum gravity, and in this\ncase the non-renormalization theorem for Galileons remains valid in the\nlow-energy region.", "category": "hep-th" }, { "text": "Orbifold instantons, moment maps and Yang-Mills theory with sources: We revisit the problem of constructing instantons on ADE orbifolds R^4/\\Gamma\nand point out some subtle relations with the complex structure on the orbifold.\nWe consider generalized instanton equations on R^4/\\Gamma which are BPS\nequations for the Yang-Mills equations with an external current. The relation\nbetween level sets of the moment maps in the hyper-Kaehler quotient\nconstruction of the instanton moduli space and sources in the Yang-Mills\nequations is discussed. We describe two types of spherically-symmetric\n\\Gamma-equivariant connections on complex V-bundles over R^4/\\Gamma which are\ntailored to the way in which the orbifold group acts on the fibres. Some\nexplicit abelian and nonabelian SU(2)-invariant solutions to the nstanton\nequations on the orbifold are worked out.", "category": "hep-th" }, { "text": "A Variational Perturbation Approach to One-Point Functions in QFT: In this paper, we develop a variational perturbation (VP) scheme for\ncalculating vacuum expectation values (VEVs) of local fields in quantum field\ntheories. For a comparatively general scalar field model, the VEV of a\ncomparatively general local field is expanded and truncated at second order in\nthe VP scheme. The resultant truncated expressions (we call Gaussian smearing\nformulae) consist mainly of Gaussian transforms of the local-field function,\nthe model-potential function and their derivatives, and so can be used to skip\ncalculations on path integrals in a concrete theory. As an application, the VP\nexpansion series of the VEV of a local exponential field in the sine- and\nsinh-Gordon field theories is truncated and derived up to second order\nequivalently by directly performing the VP scheme, by finishing ordinary\nintegrations in the Gaussian smearing formulae, and by borrowing Feynman\ndiagrammatic technique, respectively. Furthermore, the one-order VP results of\nthe VEV in the two-dimensional sine- and sinh-Gordon field theories are\nnumerically calculated and compared with the exact results conjectured by\nLukyanov, Zamolodchikov $et al.$, or with the one-order perturbative results\nobtained by Poghossian. The comparisons provide a strong support to the\nconjectured exact formulae and illustrate non-perturbability of the VP scheme.", "category": "hep-th" }, { "text": "On Asymptotic Symmetries of 3d Extended Supergravities: We study asymptotic symmetry algebras for classes of three dimensional\nsupergravities with and without cosmological constant. In the first part we\ngeneralise some of the non-Dirichlet boundary conditions of $AdS_3$ gravity to\nextended supergravity theories, and compute their asymptotic symmetries. In\nparticular, we show that the boundary conditions proposed to holographically\ndescribe the chiral induced gravity and Liouville gravity do admit extension to\nthe supergravity contexts with appropriate superalgebras as their asymptotic\nsymmetry algebras. In the second part we consider generalisation of the 3d\n$BMS$ computation to extended supergravities without cosmological constant, and\nshow that their asymptotic symmetry algebras provide examples of nonlinear\nextended superalgebras containing the $BMS_3$ algebra.", "category": "hep-th" }, { "text": "Manifestations of Space-Time Multidimensionality in Scattering of Scalar\n Particles: We analyze a possibility of experimental detection of the contribution of the\nKaluza-Klein tower of heavy particles to scattering cross-section in a\nsix-dimensional scalar model with two dimensions being compactified to the\ntorus with the radii $R$. It is shown that there is a noticeable effect even\nfor the energies of colliding particles below $R^{-1}$ which may be observed in\nfuture collider experiments if $R^{-1}$ is of the order of $1 TeV$.", "category": "hep-th" }, { "text": "Black Holes at Exp-time: Classical GR governs the evolution of black holes for a long time, but at\nsome exponentially large time it must break down. The breakdown, and what comes\nafter it, is not well understood. In this paper I'll discuss the problem using\nconcepts drawn from complexity geometry. In particular the geometric concept of\ncut locus plays a key role.", "category": "hep-th" }, { "text": "The M-theory Archipelago: We combine supersymmetric localization results and the numerical conformal\nbootstrap technique to study the 3d maximally supersymmetric (${\\cal N} = 8$)\nCFT on $N$ coincident M2-branes (the $U(N)_k \\times U(N)_{-k}$ ABJM theory at\nChern-Simons level $k=1$). In particular, we perform a mixed correlator\nbootstrap study of the superconformal primaries of the stress tensor multiplet\nand of the next possible lowest-dimension half-BPS multiplet that is allowed by\n3d ${\\cal N} = 8$ superconformal symmetry. Of all known 3d ${\\cal N} = 8$\nSCFTs, the $k=1$ ABJM theory is the only one that contains both types of\nmultiplets in its operator spectrum. By imposing the values of the short OPE\ncoefficients that can be computed exactly using supersymmetric localization, we\nare able to derive precise islands in the space of semi-short OPE coefficients\nfor an infinite number of such coefficients. We find that these islands\ndecrease in size with increasing $N$. More generally, we also analyze 3d ${\\cal\nN} = 8$ SCFT that contain both aforementioned multiplets in their operator\nspectra without inputing any additional information that is specific to ABJM\ntheory. For such theories, we compute upper and lower bounds on the semi-short\nOPE coefficients as well as upper bounds on the scaling dimension of the lowest\nunprotected scalar operator. These latter bounds are more constraining than the\nanalogous bounds previously derived from a single correlator bootstrap of the\nstress tensor multiplet. This leads us to conjecture that the $U(N)_2 \\times\nU(N+1)_{-2}$ ABJ theory, and not the $k=1$ ABJM theory, saturates the single\ncorrelator bounds.", "category": "hep-th" }, { "text": "Anomaly-induced edge currents in hydrodynamics with parity anomaly: In this paper, we discuss relativistic hydrodynamics for a massless Dirac\nfermion in $(2+1)$ dimensions, which has the parity anomaly -- a global 't\nHooft anomaly between $\\mathrm{U}(1)$ and parity symmetries. We investigate how\nhydrodynamics implements the party anomaly, particularly focusing on the\ntransport phenomena at the boundary. Based on the parity anomaly matching and\nthe second law of local thermodynamics, we find $\\mathrm{U}(1)$ and entropy\ncurrents localized at the boundary as well as the bulk anomalous current with\nvanishing divergence. These edge currents are similar to the\n$(1+1)$-dimensional chiral transports, but the coefficients are given by half\nof theirs. We also generalize our discussion to more general anomalies among\nmultiple $\\mathrm{U}(1)$ symmetries and single $\\mathbb{Z}_2$ symmetry.", "category": "hep-th" }, { "text": "Aspects of three-dimensional C-metric: In this work, we present an extensive analysis of the thermodynamics and\nholographic properties of three-dimensional C-metrics in the FG gauge, where we\nfind that the free energy is equal to the Euclidean on-shell action with a\ngeneric conformal factor. For the black hole solutions we find that Smarr\nrelation and the first law of thermodynamics can be formulated when the\ncontributions of the boundary entropy are considered . We also compute\nholographic entanglement entropy following the AdS/BCFT formalism. By comparing\nthe free energies of different bulk solutions with a fixed flat torus boundary\ngeometry, we find that a specific type of accelerating black hole is dominant\nin the high temperature regime.", "category": "hep-th" }, { "text": "Time-dependent AdS/CFT Duality II: Holographic Reconstruction of Bulk\n Metric and Possible Resolution of Singularity: We continue the studies of our earlier proposal for an AdS/CFT correspondence\nfor time-dependent supergravity backgrounds. We note that by performing a\nsuitable change of variables, the dual super Yang-Mills theory lives on a flat\nbase space, and the time-dependence of the supergravity background is entirely\nencoded in the time-dependent couplings (gauge and axionic) and their\nsupersymmetric completion. This form of the SYM allows a detailed perturbative\nanalysis to be performed. In particular the one-loop Wilsonian effective action\nof the boundary SYM theory is computed. By using the holographic UV/IR\nrelation, we propose a way to extract the bulk metric from the Wilsonian\neffective action; and we find that the bulk metric of our supergravity\nsolutions can be reproduced precisely. While the bulk geometry can have various\nsingularities such as geodesic incompleteness, gauge theory quantum effects can\nintroduce higher derivative corrections in the effective action which can serve\nas a way to resolve the singularities.", "category": "hep-th" }, { "text": "Temperature, Topology and Quantum Fields: This thesis uses Path Integrals and Green's Functions to study Gravity,\nQuantum Field Theory and Statistical Mechanics, particularly with respect to:\nfinite temperature quantum systems of different spin in gravitational fields;\nfinite temperature interacting quantum systems in perturbative regime;\nself-interacting fermi models in non-trivial space-time of different\ndimensions; non-linear quantum models at finite temperatures in a background\ncurved space-time; 3-D topological field models in non-trivial space-time and\nat finite temperatures; thermal quantum systems in a background curved\nspace-time. Results include: Non-Equivalence of Inertial and Gravitational\nMass.", "category": "hep-th" }, { "text": "Jet suppression in non-conformal plasma using AdS/CFT: In this paper, we study suppression of light quark in strongly coupled\nnon-conformal plasmas using the AdS/CFT correspondence. The well-known falling\nstring profile in the bulk is considered as light quark moving through the\nplasma. The maximum distance which string with energy E can travel before\nfalling through the horizon is interpreted as thermalization distance of light\nquark in the hot-strongly coupled plasma. Our numerical results show that the\nthermalization distance of light quark increases by increasing deviation from\nconformal invariance. The relation between this distance and the energy of\nquark and the temperature of the plasma is analyzed numerically. The jet\nquenching parameter is also calculated in the non-conformal backgrounds and it\nis found that the jet quenching parameter is generally decreased by increasing\nthe non-conformality. Our results are compared with the results of N = 4 SYM\ntheory and also some available experimental data.", "category": "hep-th" }, { "text": "Nambu and the Ising Model: In 2021, to mark the occasion of 2021 was Y\\^oichir\\^o Nambu's birth\ncentenary, we engaged in writing a historical/scientific description of his\nmost incisive papers. Nambu was the humblest genius we have known, and we\nexpected to find some of his great but forgotten insights. We found one,\nwritten in 1947: ``A Note on the Eigenvalue Problem in Crystal Statistics\",\nwhere he formulates and solves the $(N\\times N)$ Ising model in a\n$2N$-dimensional Hilbert space", "category": "hep-th" }, { "text": "Caustics in Self-gravitating N-body systems and Cosmological Large Scale\n Structures: In this paper we demonstrate the generation of gravitational caustics that\nappear due to the geodesic focusing in a self-gravitating N-body system. The\ngravitational caustics are space regions where the density of particles is\nhigher than the average density in the surrounding space. It is suggested that\nthe intrinsic mechanism of caustics generation is responsible for the formation\nof the cosmological Large Scale Structure that consists of matter\nconcentrations in the form of galaxies, galactic clusters, filaments, and vast\nregions devoid of galaxies.\n In our approach the dynamics of a self-gravitating N-body system is\nformulated in terms of a geodesic flow on a curved Riemannian manifold of\ndimension 3N equipped by the Maupertuis's metric. We investigate the sign of\nthe sectional curvatures that defines the stability of geodesic trajectories in\ndifferent parts of the phase space. The regions of negative sectional\ncurvatures are responsible for the exponential instability of geodesic\ntrajectories, deterministic chaos and relaxation phenomena of globular clusters\nand galaxies, while the regions of positive sectional curvatures are\nresponsible for the gravitational geodesic focusing and generation of caustics.\nBy solving the Jacobi and the Raychaudhuri equations we estimated the\ncharacteristic time scale of generation of gravitational caustics, calculated\nthe density contrast on the caustics and compared it with the density contrasts\ngenerated by the Jeans-Bonnor-Lifshitz-Khalatnikov gravitational instability\nand that of the spherical top-hat model of Gunn and Gott.", "category": "hep-th" }, { "text": "N=2 Superstrings with (1,2m) Spacetime Signature: We show that the $N=2$ superstring in $d=2D\\ge6$ real dimensions, with\ncriticality achieved by including background charges in the two real time\ndirections, exhibits a ``coordinate-freezing'' phenomenon, whereby the momentum\nin one of the two time directions is constrained to take a specific value for\neach physical state. This effectively removes this time direction as a physical\ncoordinate, leaving the theory with $(1,d-2)$ real spacetime signature. Norm\ncalculations for low-lying physical states suggest that the theory is ghost\nfree.", "category": "hep-th" }, { "text": "Flows involving Lifshitz solutions: We construct gravity solutions describing renormalization group flows\nrelating relativistic and non-relativistic conformal theories. We work both in\na simple phenomenological theory with a massive vector field, and in an N=4,\nd=6 gauged supergravity theory, which can be consistently embedded in string\ntheory. These flows offer some further insight into holography for Lifshitz\ngeometries: in particular, they enable us to give a description of the field\ntheory dual to the Lifshitz solutions in the latter theory. We also note that\nsome of the AdS and Lifshitz solutions in the N=4, d=6 gauged supergravity\ntheory are dynamically unstable.", "category": "hep-th" }, { "text": "Couplings for Compactifications: A general formula is obtained for Yukawa couplings in compactification on\n\\LGO{s} and corresponding \\CY\\ spaces. Up to the kinetic term normalizations,\nthis equates the classical Koszul ring structure with the \\LGO\\ chiral ring\nstructure and the true super\\CFT\\ ring structure.", "category": "hep-th" }, { "text": "Entanglement entropy in Galilean conformal field theories and flat\n holography: We present the analytical calculation of entanglement entropy for a class of\ntwo dimensional field theories governed by the symmetries of the Galilean\nconformal algebra, thus providing a rare example of such an exact computation.\nThese field theories are the putative holographic duals to theories of gravity\nin three-dimensional asymptotically flat spacetimes. We provide a check of our\nfield theory answers by an analysis of geodesics. We also exploit the\nChern-Simons formulation of three-dimensional gravity and adapt recent\nproposals of calculating entanglement entropy by Wilson lines in this context\nto find an independent confirmation of our results from holography.", "category": "hep-th" }, { "text": "An \u00c9tude on the Regularization and Renormalization of Divergences in\n Primordial Observables: Many cosmological observables of interest derive from primordial vacuum\nfluctuations evolved to late times. These observables represent statistical\ndraws from some underlying quantum or statistical field theoretic framework\nwhere infinities arise and require regularization. After subtracting\ndivergences, renormalization conditions must be imposed by measurements or\nobservations at some scale, mindful of scheme and background dependence. We\nreview this process on backgrounds that transition from finite duration\ninflation to radiation domination, and show how in spite of the ubiquity of\nscaleless integrals, UV divergences can still be meaningfully extracted from\nquantities that nominally vanish when dimensionally regularized. In this way,\none can contextualize calculations with hard cutoffs, distinguishing between UV\nand IR scales corresponding to the beginning and end of inflation from UV and\nIR scales corresponding the unknown completion of the theory and its\nobservables. This distinction has significance as observable quantities cannot\ndepend on the latter although they will certainly depend on the former. One can\nalso explicitly show the scheme independence of the coefficients of UV\ndivergent logarithms. Furthermore, certain IR divergences can be shown to be an\nartifact of the de Sitter limit and are cured for finite duration inflation.\nFor gravitational wave observables, we stress the need to regularize stress\ntensors that do not presume a prior scale separation in their construction (as\nwith the standard Isaacson form), deriving an improved stress tensor fit to\npurpose. We conclude by highlighting the inextricable connection between\ninferring $N_{\\rm eff}$ bounds from vacuum tensor perturbations and the process\nof background renormalization.", "category": "hep-th" }, { "text": "Revisiting Gribov's Copies Inside The Horizon: In this work, we recover the problem of legitimate topologically trivial\nGribov copies inside the Gribov horizon. We avoid the reducibility problem\nwhich hampered the standard construction of van Baal, and then we are able to\nbuild a valid example with spherical symmetry. We also apply the same technique\nin the presence of a background of a Polyakov instanton in a Euclidian 3D\nspacetime, in order to study the effect of a non trivial environment in the\ngeneration of multiple copies inside the horizon.", "category": "hep-th" }, { "text": "A local and integrable lattice regularization of the massive Thirring\n model: The light--cone lattice approach to the massive Thirring model is\nreformulated using a local and integrable lattice Hamiltonian written in terms\nof discrete fermi fields. Several subtle points concerning boundary conditions,\nnormal--ordering, continuum limit, finite renormalizations and decoupling of\nfermion doublers are elucidated. The relations connecting the six--vertex\nanisotropy and the various coupling constants of the continuum are analyzed in\ndetail.", "category": "hep-th" }, { "text": "Sasaki-Ricci flow equation on five-dimensional Sasaki-Einstein space\n $Y^{p,q}$: We analyze the transverse K\\\"{a}hler-Ricci flow equation on Sasaki-Ein\\-stein\nspace $Y^{p,q}$. Explicit solutions are produced representing new\nfive-dimensional Sasaki structures. Solutions which do not modify the\ntransverse metric preserve the Sasaki-Einstein feature of the contact\nstructure. If the transverse metric is altered, the deformed metrics remain\nSasaki, but not Einstein.", "category": "hep-th" }, { "text": "Simple Current Extensions and Mapping Class Group Representations: The conjecture of Fuchs, Schellekens and Schweigert on the relation of\nmapping class group representations and fixed point resolution in simple\ncurrent extensions is investigated, and a cohomological interpretation of the\nuntwisted stabilizer is given.", "category": "hep-th" }, { "text": "Gauge Fields, Fermions and Mass Gaps in 6D Brane Worlds: We study fluctuations about axisymmetric warped brane solutions in 6D minimal\ngauged supergravity. Much of our analysis is general and could be applied to\nother scenarios. We focus on bulk sectors that could give rise to Standard\nModel gauge fields and charged matter. We reduce the dynamics to Schroedinger\ntype equations plus physical boundary conditions, and obtain exact solutions\nfor the Kaluza-Klein wave functions and discrete mass spectra. The power-law\nwarping, as opposed to exponential in 5D, means that zero mode wave functions\ncan be peaked on negative tension branes, but only at the price of localizing\nthe whole Kaluza-Klein tower there. However, remarkably, the codimension two\ndefects allow the Kaluza-Klein mass gap to remain finite even in the infinite\nvolume limit. In principle, not only gravity, but Standard Model fields could\n`feel' the extent of large extra dimensions, and still be described by an\neffective 4D theory.", "category": "hep-th" }, { "text": "Syncyclons or Solitonic Signals from Extra Dimensions: In theories where spacetime is a direct product of Minkowski space ($M^4$)\nand a d dimensional compact space ($K^d$), there can exist topological solitons\nthat simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the\ncompact dimensions. A paradigmatic non-gravitational example of such\n``co-winding\" solitons is furnished by Yang-Mills theory defined on $M^4 X\nS^1$. Pointlike, stringlike and sheetlike solitons can be identified by\ntranscribing and generalizing the proceedure used to construct the periodic\ninstanton (caloron) solutions. Asymptotically the classical pointlike objects\nhave non-Abelian magnetic dipole fields together with a non-Abelian scalar\npotential while the ``color\" electric charge is zero. However quantization of\ncollective coordinates associated with zeromodes and coupling to fermions can\nradically change these quantum numbers due to fermion number fractionalization\nand its non-Abelian generalization. Interpreting the YM group as color (or the\nElectroweak SU(2) group) and assuming that an extra circular dimension exists\nthus implies the existence of topologically stable solitonic objects which\ncarry baryon(lepton) number and a mass O($1/g^2R$), where R is the radius of\nthe compact dimension.", "category": "hep-th" }, { "text": "Gibbs entropy from entanglement in electric quenches: In quantum electrodynamics with charged fermions, a background electric field\nis the source of the chiral anomaly which creates a chirally imbalanced state\nof fermions. This chiral state is realized through the production of entangled\npairs of right-moving fermions and left-moving antifermions (or vice versa,\ndepending on the orientation of the electric field). Here we show that the\nstatistical Gibbs entropy associated with these pairs is equal to the entropy\nof entanglement between the right-moving particles and left-moving\nantiparticles. We then derive an asymptotic expansion for the entanglement\nentropy in terms of the cumulants of the multiplicity distribution of produced\nparticles and explain how to re-sum this asymptotic expansion. Finally, we\nstudy the time dependence of the entanglement entropy in a specific\ntime-dependent pulsed background electric field, the so-called \"Sauter pulse\",\nand illustrate how our resummation method works in this specific case. We also\nfind that short pulses (such as the ones created by high energy collisions)\nresult in an approximately thermal distribution for the produced particles.", "category": "hep-th" }, { "text": "Mesons from (non) Abelian T-dual backgrounds: In this work we study mesonic excitations in a Quantum Field Theory dual to\nthe non Abelian T-dual of $AdS_5\\times S^5$, using a D6 brane probe on the\nSfetsos-Thompson background. Before and after the duality, we observe\ninteresting differences between the spectra and interpret them. The spectrum of\nmasses and the interactions among mesonic excitations teach valuable lessons\nabout the character of non-Abelian T-duality and its implications for\nHolography. The case of Abelian T-duality is also studied.", "category": "hep-th" }, { "text": "Noncommutative differential geometry with higher order derivatives: We build a toy model of differential geometry on the real line, which\nincludes derivatives of the second order. Such construction is possible only\nwithin the framework of noncommutative geometry. We introduce the metric and\nbriefly discuss two simple physical models of scalar field theory and gauge\ntheory in this geometry.", "category": "hep-th" }, { "text": "Supersymmetry Enhancement of D-p-branes and M-branes: We examine the supersymmetry of classical D-brane and M-brane configurations\nand explain the dependence of Killing spinors on coordinates. We find that one\nhalf supersymmetry is broken in the bulk and that supersymmetry near the\nD-brane horizon is restored for $p\\leq 3$, for solutions in the stringy frame,\nbut only for $p=3$ in the10d canonical frame. We study the enhancement for the\ncase of four intersecting D-3-branes in 10 dimensions and the implication of\nthis for the size of the infinite throat of the near horizon geometry in\nnon-compactified theory. We found some indications of universality of near\nhorizon geometries of various intersecting brane configurations.", "category": "hep-th" }, { "text": "Gravity = Yang-Mills: This essay's title is justified by discussing a class of Yang-Mills-type\ntheories of which standard Yang-Mills theories are special cases but which is\nbroad enough to include gravity as a double field theory. We use the framework\nof homotopy algebras, where conventional Yang-Mills theory is the tensor\nproduct ${\\cal K}\\otimes \\frak{g}$ of a `kinematic' algebra ${\\cal K}$ with a\ncolor Lie algebra $\\frak{g}$. The larger class of Yang-Mills-type theories are\ngiven by the tensor product of ${\\cal K}$ with more general Lie-type algebras\nof which ${\\cal K}$ itself is an example, up to anomalies that can be cancelled\nfor the tensor product with a second copy $\\bar{\\cal K}$. Gravity is then given\nby ${\\cal K}\\otimes \\bar{\\cal K}$.", "category": "hep-th" }, { "text": "Coset Symmetries in Dimensionally Reduced Bosonic String Theory: We discuss the dimensional reduction of various effective actions,\nparticularly that of the closed Bosonic string and pure gravity, to two and\nthree dimensions. The result for the closed Bosonic string leads to coset\nsymmetries which are in agreement with those recently predicted and argued to\nbe present in a new unreduced formulation of this theory. We also show that\npart of the Geroch group appears in the unreduced duality symmetric formulation\nof gravity recently proposed. We conjecture that this formulation can be\nextended to a non-linear realisation based on a Kac-Moody algebra which we\nidentify. We also briefly discuss the proposed action of Bosonic M-theory.", "category": "hep-th" }, { "text": "3d mirror for Argyres-Douglas theories: 3d mirrors for all 4d $\\mathcal{N}=2$ Argyres-Douglas (AD) theories\nengineered using 6d $(2,0)$ theory are found. The basic steps are: 1): Find a\npunctured sphere representation for the AD theories (this is achieved in our\nprevious studies of S duality); 2): Attach a 3d theory for each puncture; 3):\nGlue together the 3d theory for each puncture. We found the 3d mirror quiver\ngauge theory for the AD theories engineered using 6d $A$ and $D$ type theories.\nThese 3d mirrors are useful for studying the properties of original 4d theory\nsuch as Higgs branch, S-duality, etc; We also construct many new 3d\n$\\mathcal{N}=4$ SCFTs.", "category": "hep-th" }, { "text": "Berry's phase in noncommutative spaces: We introduce the perturbative aspects of noncommutative quantum mechanics.\nThen we study the Berry's phase in the framework of noncommutative quantum\nmechanics. The results show deviations from the usual quantum mechanics which\ndepend on the parameter of space/space noncommtativity.", "category": "hep-th" }, { "text": "Moduli Thermalization and Finite Temperature Effects in \"Big\" Divisor\n Large Volume D3/D7 Swiss-Cheese Compactification: In the context of Type IIB compactified on a large volume Swiss-Cheese\norientifold in the presence of a mobile space-time filling D3-brane and stacks\nof fluxed D7-branes wrapping the \"big\" divisor Sigma_B of a Swiss-Cheese Calabi\nYau in WCP^4 [1,1,1,6,9], we explore various implications of moduli dynamics\nand discuss their couplings and decay into MSSM (-like) matter fields early in\nthe history of universe to reach thermal equilibrium. Like finite temperature\neffects in O'KKLT, we observe that the local minimum of zero-temperature\neffective scalar potential is stable against any finite temperature corrections\n(up to two-loops) in large volume scenarios as well. Also, we find that moduli\nare heavy enough to avoid any cosmological moduli problem.", "category": "hep-th" }, { "text": "Casimir force in noncommutative Randall-Sundrum models revisited: We propose another method to compute the Casimir force in noncommutative\nRandall-Sundrum braneworld model considered by K. Nouicer and Y. Sabri\nrecently. Our method can be used to compute the Casimir force to any order in\nthe noncommutative parameter. Contrary to the claim made by K. Nouicer and Y.\nSabri that repulsive Casimir force can appear in the first order approximation,\nwe show that the Casimir force is always attractive at any order of\napproximation.", "category": "hep-th" }, { "text": "Loops in AdS: From the Spectral Representation to Position Space II: We continue the study of AdS loop amplitudes in the spectral representation\nand in position space. We compute the finite coupling 4-point function in\nposition space for the large-$N$ conformal Gross Neveu model on $AdS_3$. The\nresummation of loop bubble diagrams gives a result proportional to a tree-level\ncontact diagram. We show that certain families of fermionic Witten diagrams can\nbe easily computed from their companion scalar diagrams. Thus, many of the\nresults and identities of [1] are extended to the case of external fermions. We\nderive a spectral representation for ladder diagrams in AdS. Finally, we\ncompute various bulk 2-point correlators, extending the results of [1].", "category": "hep-th" }, { "text": "The Standard Model with gravity couplings: In this paper, we examine the coupling of matter fields to gravity within the\nframework of the Standard Model of particle physics. The coupling is described\nin terms of Weyl fermions of a definite chirality, and employs only\n(anti)self-dual or left-handed spin connection fields. It is known from the\nwork of Ashtekar and others that such fields can furnish a complete description\nof gravity without matter. We show that conditions ensuring the cancellation of\nperturbative chiral gauge anomalies are not disturbed. We also explore a global\nanomaly associated with the theory, and argue that its removal requires that\nthe number of fundamental fermions in the theory must be multiples of 16. In\naddition, we investigate the behavior of the theory under discrete\ntransformations P, C and T; and discuss possible violations of these discrete\nsymmetries, including CPT, in the presence of instantons and the\nAdler-Bell-Jackiw anomaly.", "category": "hep-th" }, { "text": "Why is AI hard and Physics simple?: We discuss why AI is hard and why physics is simple. We discuss how physical\nintuition and the approach of theoretical physics can be brought to bear on the\nfield of artificial intelligence and specifically machine learning. We suggest\nthat the underlying project of machine learning and the underlying project of\nphysics are strongly coupled through the principle of sparsity, and we call\nupon theoretical physicists to work on AI as physicists. As a first step in\nthat direction, we discuss an upcoming book on the principles of deep learning\ntheory that attempts to realize this approach.", "category": "hep-th" }, { "text": "Many-Particle Quantum Cosmology: The Einstein-Friedmann Universe as whole quantum object can be treated as\nbosonic string mass groundstate, called a tachyon, having negative mass square\nand a speed more than the speed of light. I present a brief review of results\nobtained from this point of view called Many-Particle Quantum Gravity approach\n- the monodromy problem in the Fock space, thermodynamics of the Universe, and\nthe extremal tachyon mass model.", "category": "hep-th" }, { "text": "Higher Order Corrections to Holographic Black Hole Chemistry: We investigate the holographic Smarr relation beyond the large N limit. By\nmaking use of the holographic dictionary, we find that the bulk correlates of\nsub-leading 1/N corrections to this relation are related to the couplings in\nLovelock gravity theories. We likewise obtain a holographic equation of state,\nand check its validity for a variety of interesting and non-trivial black\nholes, including rotating planar black holes in Gauss-Bonnet-Born-Infeld\ngravity, and non-extremal rotating black holes in minimal 5d gauged\nsupergravity. We provide an explanation of the N-dependence of the holographic\nSmarr relation in terms of contributions due to planar and non-planar diagrams\nin the dual theory.", "category": "hep-th" }, { "text": "Effective long distance $q\\bar{q} $ potential in holographic RG flows: We study the $q\\bar{q}$ potential in strongly coupled non-conformal field\ntheories with a non-trivial renormalization group flow via holography. We focus\non the properties of this potential at an inter-quark separation $L$ large\ncompared to the characteristic scale of the field theory. These are determined\nby the leading order IR physics plus a series of corrections, sensitive to the\nproperties of the RG-flow. To determine those corrections, we propose a general\nmethod applying holographic Wilsonian renormalization to a dual string. We\napply this method to examine in detail two sets of examples, $3+1$-dimensional\ntheories with an RG flow ending in an IR fixed point; and theories that are\nconfining in the IR, in particular, the Witten QCD and Klebanov-Strassler\nmodels. In both cases, we find corrections with a universal dependence on the\ninter-quark separation. When there is an IR fixed point, that correction decays\nas a power $\\sim 1/L^4$. We explain that dependence in terms of a double-trace\ndeformation in a one-dimensional defect theory. For a confining theory, the\ndecay is exponential $\\sim e^{-ML}$, with $M$ a scale of the order of the\nglueball mass. We interpret this correction using an effective flux tube\ndescription as produced by a background internal mode excitation induced by\nsources localized at the endpoints of the flux tube. We discuss how these\nresults could be confronted with lattice QCD data to test whether the\ndescription of confinement via the gauge/gravity is qualitatively correct.", "category": "hep-th" }, { "text": "Quantized rotating Taub-bolt instantons: We argue that previously suggested metrics for rotating Taub-bolt instantons\ndo not satisfy all the necessary regularity conditions, and we present a family\nof new regular rotating Taub-bolts labelled by an odd integer $k$. There are\ntwo types of rotating bolt solutions. The first infinite sequence starts with\nnon-rotating Taub-NUT with positive mass $M_k=N$ for $a=0$ and goes to $(k-2)N$\nfor $|a|\\to \\infty$ (or $N$ for $k=1$), where $a$ is the rotation parameter.\nFor the second sequence of rotating Page bolts, the masses $M_k$ go through the\nvalue $M_k=5N/4$ for $a=0$ and asymptote to $(k+2)N$ for $|a|\\to \\infty$.", "category": "hep-th" }, { "text": "$S^7$ Current Algebras: We present $S^7$-algebras as generalized Kac-Moody algebras. A number of\nfree-field representations is found. We construct the octonionic projective\nspaces ${\\O}P^N$.", "category": "hep-th" }, { "text": "SU(2)/SL(2) knot invariants and KS monodromies: We review the Reshetikhin-Turaev approach to construction of non-compact knot\ninvariants involving R-matrices associated with infinite-dimensional\nrepresentations, primarily those made from Faddeev's quantum dilogarithm. The\ncorresponding formulas can be obtained from modular transformations of\nconformal blocks as their Kontsevich-Soibelman monodromies and are presented in\nthe form of transcendental integrals, where the main issue is manipulation with\nintegration contours. We discuss possibilities to extract more explicit and\nhandy expressions which can be compared with the ordinary (compact) knot\npolynomials coming from finite-dimensional representations of simple Lie\nalgebras, with their limits and properties. In particular, the quantum\nA-polynomials, difference equations for colored Jones polynomials should be the\nsame, just in non-compact case the equations are homogeneous, while they have a\nnon-trivial right-hand side for ordinary Jones polynomials.", "category": "hep-th" }, { "text": "Closed string exchanges on $C^2/Z_2$ in a background B-field: In an earlier work it was shown that the IR singularities arising in the\nnonplanar one loop two point function of a noncommutative ${\\cal N}=2$ gauge\ntheory can be reproduced exactly from the massless closed string exchanges. The\nnoncommutative gauge theory is realised on a fractional $D_3$ brane localised\nat the fixed point of the $C^2/Z_2$ orbifold. In this paper we identify the\ncontributions from each of the closed string modes. The sum of these adds upto\nthe nonplanar two-point function.", "category": "hep-th" }, { "text": "Supersymmetric index on T^2 x S^2 and elliptic genus: We study partition function of four-dimensional $\\mathcal{N}=1$\nsupersymmetric field theory on $T^2 \\times S^2$. By applying supersymmetry\nlocalization, we show that the $T^2 \\times S^2$ partition function is given by\nelliptic genus of certain two-dimensional $\\mathcal{N}=(0,2)$ theory. As an\napplication, we discuss a relation between 4d Seiberg duality duality and 2d\n$(0,2)$ triality, proposed by Gadde, Gukov and Putrov. In other examples, we\nidentify 4d theories giving elliptic genera of K3, M-strings and E-strings. In\nthe example of K3, we find that there are two 4d theories giving the elliptic\ngenus of K3. This would imply new four-dimensional duality.", "category": "hep-th" }, { "text": "General covariance, and supersymmetry without supersymmetry: An unusual four-dimensional generally covariant and supersymmetric SU(2)\ngauge theory is described. The theory has propagating degrees of freedom, and\nis invariant under a local (left-handed) chiral supersymmetry, which is half\nthe supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the\ntheory reveals the remarkable feature that the local supersymmetry is a\nconsequence of Yang-Mills symmetry, in a manner reminiscent of how general\ncoordinate invariance in Chern-Simons theory is a consequence of Yang-Mills\nsymmetry. It is possible to write down an infinite number of conserved\ncurrents, which strongly suggests that the theory is classically integrable. A\npossible scheme for non-perturbative quantization is outlined. This utilizes\nideas that have been developed and applied recently to the problem of\nquantizing gravity.", "category": "hep-th" }, { "text": "Chasing the cuprates with dilatonic dyons: Magnetic field and momentum dissipation are key ingredients in describing\ncondensed matter systems. We include them in gauge/gravity and systematically\nexplore the bottom-up panorama of holographic IR effective field theories based\non bulk Einstein-Maxwell Lagrangians plus scalars. The class of solutions here\nexamined appear insufficient to capture the phenomenology of charge transport\nin the cuprates. We analyze in particular the temperature scaling of the\nresistivity and of the Hall angle. Keeping an open attitude, we illustrate weak\nand strong points of the approach.", "category": "hep-th" }, { "text": "One-dimensional sigma-models with N=5,6,7,8 off-shell supersymmetries: We computed the actions for the 1D N=5 sigma-models with respect to the two\ninequivalent (2,8,6) multiplets. 4 supersymmetry generators are manifest, while\nthe constraint originated by imposing the 5-th supersymmetry automatically\ninduces a full N=8 off-shell invariance. The resulting action coincides in the\ntwo cases and corresponds to a conformally flat 2D target satisfying a special\ngeometry of rigid type. To obtain these results we developed a computational\nmethod (for Maple 11) which does not require the notion of superfields and is\ninstead based on the nowadays available list of the inequivalent\nrepresentations of the 1D N-extended supersymmetry. Its application to\nsystematically analyze the sigma-models off-shell invariant actions for the\nremaining N=5,6,7,8 (k,8,8-k) multiplets, as well as for the N>8\nrepresentations,only requires more cumbersome computations.", "category": "hep-th" }, { "text": "A Lorentz-violating SO(3) model: discussing the unitarity, causality and\n the 't Hooft-Polyakov monopoles: In this paper, we extend the analysis of the Lorentz-violating Quantum\nEletrodynamics to the non-Abelian case: an SO(3) Yang-Mills Lagrangian with the\naddition of the non-Abelian Chern-Simons-type term. We consider the spontaneous\nsymmetry breaking of the model and inspect its spectrum in order to check if\nunitarity and causality are respected. An analysis of the topological structure\nis also carried out and we show that a 't Hooft-Polyakov solution for monopoles\nis still present.", "category": "hep-th" }, { "text": "Superstring scattering amplitudes in higher genus: In this paper we continue the program pioneered by D'Hoker and Phong, and\nrecently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the\nchiral superstring measure by constructing modular forms satisfying certain\nfactorization constraints. We give new expressions for their proposed ans\\\"atze\nin genera 2 and 3, respectively, which admit a straightforward generalization.\nWe then propose an ansatz in genus 4 and verify that it satisfies the\nfactorization constraints and gives a vanishing cosmological constant. We\nfurther conjecture a possible formula for the superstring amplitudes in any\ngenus, subject to the condition that certain modular forms admit holomorphic\nroots.", "category": "hep-th" }, { "text": "$\u03b5$-Expansion in the Gross-Neveu Model from Conformal Field\n Theory: We compute the anomalous dimensions of a class of operators of the form\n$(\\bar\\psi\\psi)^p$ and $(\\bar\\psi\\psi)^p\\psi$ to leading order in $\\epsilon$ in\nthe Gross-Neveu model in $2+\\epsilon$ dimensions. We use the techniques\ndeveloped in arXiv: 1505.00963.", "category": "hep-th" }, { "text": "Gravitating Cho-Maison Monopole: We study numerical solutions corresponding to spherically symmetric\ngravitating electroweak monopole and magnetically charged black holes of the\nEinstein-Weinberg-Salam theory. The gravitating electroweak monopole solutions\nare quite identical to the gravitating monopole solution in SU(2)\nEinsten-Yang-Mills-Higgs theory, but with distinctive characteristics. We also\nfound solutions representing radially excited monopole, which has no\ncounterpart in flat space. Both of these solutions exist up to a maximal\ngravitational coupling before they cease to exist. Lastly we also report on\nmagnetically charged non-Abelian black holes solutions that is closely related\nto the regular monopole solutions, which represents counterexample to the\n`no-hair' conjecture.", "category": "hep-th" }, { "text": "Gauge equivalent universes in 5d Kaluza-Klein theory: We examine in the framework of 5d Kaluza-Klein theory the gauge equivalence\nof $x^5$-dependent cosmological solutions each of which describes in the 4d\nsector an arbitrarily evolving isotropic, homogeneous universe with some pure\ngauge. We find that (1)within a certain time scale $\\tau_c$\n (which is characterized by the compactification radius $R_c$) any arbitrarily\nevolving 4d universe is allowed to exist by field equations, and these 4d\nuniverses with appropriate pure gauges are all gauge equivalent as long as they\nare of the same topology. (2)Outside $\\tau_c$ the gauge equivalence disappears\nand the evolution of the universe is fixed by field equations.", "category": "hep-th" }, { "text": "Constraints on the quantum state of pairs produced by semiclassical\n black holes: The pair-production process for a black hole (BH) is discussed within the\nframework of a recently proposed semiclassical model of BH evaporation. Our\nemphasis is on how the requirements of unitary evolution and strong\nsubadditivity act to constrain the state of the produced pairs and their\nentanglement with the already emitted BH radiation. We find that the state of\nthe produced pairs is indeed strongly constrained but that the semiclassical\nmodel is consistent with all requirements. We are led to the following picture:\nInitially, the pairs are produced in a state of nearly maximal entanglement\namongst the partners, with a parametrically small entanglement between each\npositive-energy partner and the outgoing radiation, similar to Hawking's model.\nBut, as the BH evaporation progresses past the Page time, each positive-energy\npartner has a stronger entanglement with the outgoing radiation and,\nconsequently, is less strongly entangled with its negative-energy partner. We\npresent some evidence that this pattern of entanglement does not require\nnon-local interactions, only EPR-like non-local correlations.", "category": "hep-th" }, { "text": "3d superconformal indices and isomorphisms of M2-brane theories: We test several expected isomorphisms between the U(N)xU(N) ABJM theory and\n(SU(N)xSU(N))/Z_N theory including the BLG theory by comparing their\nsuperconformal indices. From moduli space analysis, it is expected that this\nequivalence can hold if and only if the rank N and Chern-Simons level k are\ncoprime. We also calculate the index of the ABJ theory and investigate whether\nsome theories with identical moduli spaces are isomorphic or not.", "category": "hep-th" }, { "text": "Holographic line defects in F(4) gauged supergravity: In this note we construct a solution of six-dimensional $F(4)$ gauged\nsupergravity using $AdS_2\\times S^3$ warped over an interval as an ansatz. The\nsolution is completely regular, preserves eight of the sixteen supersymmetries\nof the $AdS_6$ vacuum and is a holographic realization of a line defect in a\ndual five-dimensional theory. We calculate the expectation value of the defect\nand the one-point function of the stress tensor in the presence of the defect\nusing holographic renormalization.", "category": "hep-th" }, { "text": "On the Non-renormalization of the AdS Radius: We show that the relation between the 't Hooft coupling and the radius of AdS\nis not renormalized at one-loop in the sigma model perturbation theory. We\nprove this by computing the quantum effective action for the superstring on\nAdS_5 x S^5 and showing that it does not receive any finite alpha' corrections.\nWe also show that the central charge of the interacting worldsheet conformal\nfield theory vanishes at one-loop.", "category": "hep-th" }, { "text": "Twistors and supertwistors for exceptional field theory: As a means of examining the section condition and its possible solutions and\nrelaxations, we perform twistor transforms related to versions of exceptional\nfield theory with Minkowski signature. The spinor parametrisation of the\nmomenta naturally solves simultaneously both the mass-shell condition and the\n(weak) section condition. It is shown that the incidence relations for\nmulti-particle twistors force them to share a common section, but not to be\northogonal. The supersymmetric extension contains additional scalar fermionic\nvariables shown to be kappa-symmetry invariants. We speculate on some\nimplications, among them a possible relation to higher spin theory.", "category": "hep-th" }, { "text": "On RG-flow and the Cosmological Constant: The AdS/CFT correspondence implies that the effective action of certain\nstrongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation\nof 5d gravity. Using an analogy with the relativistic point particle, I\nconstruct a low energy effective action that includes the Einstein action and\nobeys a Callan-Symanzik-type RG-flow equation. It follows from the flow\nequation that under quite general conditions the Einstein equations admit a\nflat space-time solution, but other solutions with non-zero cosmological\nconstant are also allowed. I discuss the geometric interpretation of this\nresult in the context of warped compactifications.", "category": "hep-th" }, { "text": "Holographic free energy and thermodynamic geometry: We analytically obtain the free energy and thermodynamic geometry of\nholographic superconductors in $2+1$-dimensions. The gravitational theory in\nthe bulk dual to this $2+1$-dimensional strongly coupled theory lives in the\n$3+1$-dimensions and is that of a charged $AdS$ black hole together with a\nmassive charged scalar field. The matching method is applied to obtain the\nnature of the fields near the horizon using which the holographic free energy\nis computed through the gauge/gravity duality. The critical temperature is\nobtained for a set of values of the matching point of the near horizon and the\nboundary behaviour of the fields. The thermodynamic geometry is then computed\nfrom the free energy of the boundary theory. From the divergence of the\nthermodynamic scalar curvature, the critical temperature is obtained once\nagain. We then compare this result for the critical temperature with that\nobtained from the matching method.", "category": "hep-th" }, { "text": "Gauge theory in deformed N=(1,1) superspace: We review the non-anticommutative Q-deformations of N=(1,1) supersymmetric\ntheories in four-dimensional Euclidean harmonic superspace. These deformations\npreserve chirality and harmonic Grassmann analyticity. The associated field\ntheories arise as a low-energy limit of string theory in specific backgrounds\nand generalize the Moyal-deformed supersymmetric field theories. A\ncharacteristic feature of the Q-deformed theories is the half-breaking of\nsupersymmetry in the chiral sector of the Euclidean superspace. Our main focus\nis on the chiral singlet Q-deformation, which is distinguished by preserving\nthe SO(4) Spin(4) ``Lorentz'' symmetry and the SU(2) R-symmetry. We present the\nsuperfield and component structures of the deformed N=(1,0) supersymmetric\ngauge theory as well as of hypermultiplets coupled to a gauge superfield:\ninvariant actions, deformed transformation rules, and so on. We discuss quantum\naspects of these models and prove their renormalizability in the abelian case.\nFor the charged hypermultiplet in an abelian gauge superfield background we\nconstruct the deformed holomorphic effective action.", "category": "hep-th" }, { "text": "The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed\n of Primordial Near-Extremal Black Holes: In a recent publication we studied the decay rate of primordial black holes\nperceiving the dark dimension, an innovative five-dimensional (5D) scenario\nthat has a compact space with characteristic length-scale in the micron range.\nWe demonstrated that the rate of Hawking radiation of 5D black holes slows down\ncompared to 4D black holes of the same mass. Armed with our findings we showed\nthat for a species scale of ${\\cal O} (10^{9}~{\\rm GeV})$, an all-dark-matter\ninterpretation in terms of primordial black holes should be feasible for black\nhole masses in the range $10^{14} \\lesssim M/{\\rm g} \\lesssim 10^{21}$. As a\nnatural outgrowth of our recent study, herein we calculate the Hawking\nevaporation of near-extremal 5D black holes. Using generic entropy arguments we\ndemonstrate that Hawking evaporation of higher-dimensional near-extremal black\nholes proceeds at a slower rate than the corresponding Schwarzschild black\nholes of the same mass. Assisted by this result we show that if there were 5D\nprimordial near-extremal black holes in nature, then a PBH all-dark-matter\ninterpretation would be possible in the mass range $10^{7}\\sqrt{\\beta} \\lesssim\nM/{\\rm g} \\lesssim 10^{21}$, where $\\beta$ is a parameter that controls the\ndifference between mass and charge of the associated near-extremal black hole.", "category": "hep-th" }, { "text": "Multiple Soft Limits of Cosmological Correlation Functions: We derive novel identities satisfied by inflationary correlation functions in\nthe limit where two external momenta are taken to be small. We derive these\nstatements in two ways: using background-wave arguments and as Ward identities\nfollowing from the fixed-time path integral. Interestingly, these identities\nallow us to constrain some of the O(q^2) components of the soft limit, in\ncontrast to their single-soft analogues. We provide several nontrivial checks\nof our identities both in the context of resonant non-Gaussianities and in\nsmall sound speed models. Additionally, we extend the relation at lowest order\nin external momenta to arbitrarily many soft legs, and comment on the many-soft\nextension at higher orders in the soft momentum. Finally, we consider how\nhigher soft limits lead to identities satisfied by correlation functions in\nlarge-scale structure.", "category": "hep-th" }, { "text": "Constructing near-horizon geometries in supergravities with hidden\n symmetry: We consider the classification of near-horizon geometries in a general\ntwo-derivative theory of gravity coupled to abelian gauge fields and uncharged\nscalars in four and five dimensions, with one and two commuting rotational\nsymmetries respectively. Assuming that the theory of gravity reduces to a 3d\nnon-linear sigma model (as is typically the case for ungauged supergravities),\nwe show that the functional form of any such near-horizon geometry may be\ndetermined. As an example we apply this to five dimensional minimal\nsupergravity. We also construct an example of a five parameter near-horizon\ngeometry solution to this theory with S^1 X S^2 horizon topology. We discuss\nits relation to the near-horizon geometries of the yet to be constructed\nextremal black rings with both electric and dipole charges.", "category": "hep-th" }, { "text": "States and amplitudes for finite regions in a two-dimensional Euclidean\n quantum field theory: We quantize the Helmholtz equation (plus perturbative interactions) in two\ndimensions to illustrate a manifestly local description of quantum field\ntheory. Using the general boundary formulation we describe the quantum dynamics\nboth in a traditional time evolution setting as well as in a setting referring\nto finite disk (or annulus) shaped regions of spacetime. We demonstrate that\nboth descriptions are equivalent when they should be.", "category": "hep-th" }, { "text": "Stringy Cosmic Strings and Axion Cohomology: The static stationary axially symmetric background (\"infinite cosmic string\")\nof the $D=4$ string theory provided with an axion charge is studied in the\neffective theory approach. The most general exact solution is constructed. It\nis found that the Kalb-Ramond axion charge, present in the string topology\n$R^{3} \\times S^{1}$, produces nontrivial gravitational field configurations\nwhich feature horizons. The corresponding ``no-hair'' theorems are proved which\nstress uniqueness of black strings. Connection of the solutions with the gauged\nWZWN sigma model constructions on the world sheet is discussed since they are\nthe only target spaces which hide their singularities behind horizons, and thus\nobey the cosmic censorship conjecture.", "category": "hep-th" }, { "text": "On the Liouville 2D dilaton gravity models with sinh-Gordon matter: We study 1+1 dimensional dilaton gravity models which take into account\nbackreaction of the sinh-Gordon matter field. We found a wide class of exact\nsolutions which generalizes black hole solutions of the Jackiw-Teitelboim\ngravity model and its hyperbolic deformation.", "category": "hep-th" }, { "text": "Odd Nambu bracket on Grassmann algebra: The Grassmann-odd Nambu bracket on the Grassmann algebra is proposed.", "category": "hep-th" }, { "text": "Wigner Representation Theory of the Poincare Group, Localization,\n Statistics and the S-Matrix: It has been known that the Wigner representation theory for positive energy\norbits permits a useful localization concept in terms of certain lattices of\nreal subspaces of the complex Hilbert -space. This ''modular localization'' is\nnot only useful in order to construct interaction-free nets of local algebras\nwithout using non-unique ''free field coordinates'', but also permits the study\nof properties of localization and braid-group statistics in low-dimensional\nQFT. It also sheds some light on the string-like localization properties of the\n1939 Wigner's ''continuous spin'' representations.We formulate a constructive\nnonperturbative program to introduce interactions into such an approach based\non the Tomita-Takesaki modular theory. The new aspect is the deep relation of\nthe latter with the scattering operator.", "category": "hep-th" }, { "text": "String duality and massless string states: We are discussing the $S$ \\& $T$ duality for special class of heterotic\nstring configurations. This class of solutions includes various types of black\nhole solutions and Taub-NUT geometries. It allows a self-dual point for both\ndualities which corresponds to massless configurations. As string state this\npoint corresponds to $N_R=1/2$ and $N_L=0$. The string/string duality is\nshortly discussed.", "category": "hep-th" }, { "text": "Improved Holographic QCD: We provide a review to holographic models based on Einstein-dilaton gravity\nwith a potential in 5 dimensions. Such theories, for a judicious choice of\npotential are very close to the physics of large-N YM theory both at zero and\nfinite temperature. The zero temperature glueball spectra as well as their\nfinite temperature thermodynamic functions compare well with lattice data. The\nmodel can be used to calculate transport coefficients, like bulk viscosity, the\ndrag force and jet quenching parameters, relevant for the physics of the\nQuark-Gluon Plasma.", "category": "hep-th" }, { "text": "The Gribov problem in presence of background field for $SU(2)$\n Yang-Mills theory: The Gribov problem in the presence of a background field is analyzed: in\nparticular, we study the Gribov copies equation in the Landau-De Witt gauge as\nwell as the semi-classical Gribov gap equation. As background field, we choose\nthe simplest non-trivial one which corresponds to a constant gauge potential\nwith non-vanishing component along the Euclidean time direction. This kind of\nconstant non-Abelian background fields is very relevant in relation with (the\ncomputation of) the Polyakov loop but it also appears when one considers the\nnon-Abelian Schwinger effect. We show that the Gribov copies equation is\naffected directly by the presence of the background field, constructing an\nexplicit example. The analysis of the Gribov gap equation shows that the larger\nthe background field, the smaller the Gribov mass parameter. These results\nstrongly suggest that the relevance of the Gribov copies (from the path\nintegral point of view) decreases as the size of the background field\nincreases.", "category": "hep-th" }, { "text": "Calculation of Green-Schwarz Superstring Amplitudes Using the N=2\n Twistor-String Formalism: The manifestly SU(4)xU(1) super-Poincare invariant free-field N=2 twistor-\nstring action for the ten-dimensional Green-Schwarz superstring is quantized\nusing standard BRST methods. Unlike the light-cone and semi-light-cone\ngauge-fixed Green-Schwarz actions, the twistor-string action does not require\ninteraction-point operators at the zeroes of the light-cone momentum, $\\dz\nx^+$, which complicated all previous calculations. After defining the vertex\noperator for the massless physical supermultiplet, as well as two\npicture-changing operators and an instanton-number-changing operator,\nscattering amplitudes for an arbitrary number of loops and external massless\nstates are explicitly calculated by evaluating free-field correlation functions\nof these operators on N=2 super-Riemann surfaces of the appropriate topology,\nand integrating over the global moduli. Although there is no sum over spin\nstructures, only discrete values of the global U(1) moduli contribute to the\namplitudes. Because the spacetime supersymmetry generators do not contain ghost\nfields, the amplitudes are manifestly spacetime supersymmetric, there is no\nmultiloop ambiguity, and the non-renormalization theorem is easily proven. By\nchoosing the picture-changing operators to be located at the zeroes of $\\dz\nx^+$, these amplitudes are shown to agree with amplitudes obtained using the\nmanifestly unitary light-cone gauge formalism.", "category": "hep-th" }, { "text": "Two interacting conformal Carroll particles: In this note we analyse two different models of two interacting conformal\nCarroll particles that can be obtained as the Carrollian limit of two\nrelativistic conformal particles. The first model describes particles with zero\nvelocity and exhibits infinite dimensional symmetries which are reminiscent of\nthe BMS symmetries. A second model of interaction of Carrollian particles is\nproposed, where the particles have non zero velocity and therefore, as a\nconsequence of the limit c to 0, are tachyons. Infinite dimensional symmetries\nare present also in this model.", "category": "hep-th" }, { "text": "The ultrarelativistic limit of Kerr: The massless (or ultrarelativistic) limit of a Schwarzschild black hole with\nfixed energy was determined long ago in the form of the Aichelburg-Sexl\nshockwave, but the status of the same limit for a Kerr black hole is less\nclear. In this paper, we explore the ultrarelativistic limit of Kerr in the\nclass of Kerr-Schild impulsive pp-waves by exploiting a relation between the\nmetric profile and the eikonal phase associated with scattering between a\nscalar and the source of the metric. This gives a map between candidate metrics\nand tree-level, 4-point scattering amplitudes. At large distances from the\nsource, we find that all candidates for the massless limit of Kerr in this\nclass do not have spin effects. This includes the metric corresponding to the\nmassless limit of the amplitude for gravitational scattering between a scalar\nand a massive particle of infinite spin. One metric, discovered by Balasin and\nNachbagauer, does have spin and finite size effects at short distances, leading\nto a remarkably compact scattering amplitude with many interesting properties.\nWe also discuss the classical single copy of the ultrarelativistic limit of\nKerr in electromagnetism.", "category": "hep-th" }, { "text": "Angular Momentum Induced In The Fermionic Vacuum On A\n Rotationally-Symmetric Noncompact Riemann Surface: The influence of spatial geometry on the vacuum polarization in\n2+1-dimensional spinor electrodynamics is investigated. The vacuum angular\nmomentum induced by an external static magnetic field is found to depend on\nglobal geometric surface characteristics connected with curvature. The\nrelevance of the results obtained for the fermion number fractionization is\ndiscussed.", "category": "hep-th" }, { "text": "Bifurcation and pattern changing with two real scalar fields: This work deals with bifurcation and pattern changing in models described by\ntwo real scalar fields. We consider generic models with quartic potentials and\nshow that the number of independent polynomial coefficients affecting the\nratios between the various domain wall tensions can be reduced to 4 if the\nmodel has a superpotential. We then study specific one-parameter families of\nmodels and compute the wall tensions associated with both BPS and non-BPS\nsectors. We show how bifurcation can be associated to modification of the\npatterns of domain wall networks and illustrate this with some examples which\nmay be relevant to describe realistic situations of current interest in high\nenergy physics. In particular, we discuss a simple solution to the cosmological\ndomain wall problem.", "category": "hep-th" }, { "text": "Moduli Spaces for D-branes at the Tip of a Cone: For physicists: We show that the quiver gauge theory derived from a\nCalabi-Yau cone via an exceptional collection of line bundles on the base has\nthe original cone as a component of its classical moduli space. For\nmathematicians: We use data from the derived category of sheaves on a Fano\nsurface to construct a quiver, and show that its moduli space of\nrepresentations has a component which is isomorphic to the anticanonical cone\nover the surface.", "category": "hep-th" }, { "text": "Supersymmetric Intersecting Branes in Time-dependent Backgrounds: We construct a family of supersymmetric solutions in time-dependent\nbackgrounds in supergravity theories. One class of the solutions are\nintersecting brane solutions and another class are brane solutions in pp-wave\nbackgrounds, and their intersection rules are also given. The relation to\nexisting literature is also discussed. An example of D1-D5 with linear null\ndilaton together with its possible dual theory is briefly discussed.", "category": "hep-th" }, { "text": "Vulcanized Vortex: We investigate vortex configurations with the \"vulcanization\" term inspired\nby the renormalization of $\\phi_\\star^4$ theory in the canonical\n$\\theta$-deformed noncommutativity. We focus on the classical limit of the\ntheory described by a single parameter which is the ratio of the vulcanization\nand the noncommutativity parameters. We perform numerical calculations and find\nthat nontopological vortex solutions exist as well as Q-ball type solutions,\nbut topological vortex solutions are not admitted.", "category": "hep-th" }, { "text": "Bootstrapping the String KLT Kernel: We show that a generalized version of the 4-point string theory KLT\ndouble-copy map is the most general solution to the minimal-rank double-copy\nbootstrap in effective field theory. This follows from significant restrictions\nof the 4-point map resulting from the 6-point bootstrap analysis. The\ngeneralized 4-point double-copy map is defined by a function with only two\nparameters times a simple function that is symmetric in $s,t,u$. The two\nparameters can be interpreted as independent choices of $\\alpha'$, one for each\nof the two sets of amplitudes double-copied with the map. Specifically, each of\nthose two sets of amplitudes must obey either the string monodromy relations or\nthe field theory KK & BCJ relations; there are no other options. We propose a\nclosed form of the new double-copy map that interpolates between the original\nKLT string double-copy and the open & closed string period integrals. The\nconstruction clarifies the \"single-valued projection\" property of the Riemann\nzeta-function values for the 4-point string theory double copy.", "category": "hep-th" }, { "text": "Generating Vector Boson Masses: If the Higgs particle is never found, one will need an alternative theory for\nvector boson masses. I propose such a theory involving an antisymmetric tensor\npotential coupled to a gauge field.", "category": "hep-th" }, { "text": "T-duality and U-duality in toroidally-compactified strings: We address the issue of T-duality and U-duality symmetries in the\ntoroidally-compactified type IIA string. It is customary to take as a starting\npoint the dimensionally-reduced maximal supergravity theories, with certain\nfield strengths dualised such that the classical theory exhibits a global\n$E_{n(n)}$ symmetry, where n=11-D in D dimensions. A discrete subgroup then\nbecomes the conjectured U-duality group. In dimensions D\\le 6, these necessary\ndualisations include NS-NS fields, whose potentials, rather than merely their\nfield strengths, appear explicitly in the couplings to the string worldsheet.\nThus the usually-stated U-duality symmetries act non-locally on the fundamental\nfields of perturbative string theory. At least at the perturbative level, it\nseems to be more appropriate to consider the symmetries of the versions of the\nlower-dimensional supergravities in which no dualisations of NS-NS fields are\nrequired, although dualisations of the R-R fields are permissible since these\ncouple to the string through their field strengths. Taking this viewpoint, the\nusual T-duality groups survive unscathed, as one would hope since T-duality is\na perturbative symmetry, but the U-duality groups are modified in D\\le 6.", "category": "hep-th" }, { "text": "A Note on a Generalized AHM Model with Analytical Vortex Solutions: We study topological vortex solutions in a generalized Abelian Higgs model\nwith non-polynomial dielectric and potential functions. These quantities are\nchosen by requiring integrability of the self-dual limit of the theory for all\nvalues of the magnetic flux. All the vortex profiles are described by exact\nanalytical expressions that solve the self-dual vortex equations. There is only\na symmetry-breaking superconducting phase and the model sustains regular\nphenomenology.", "category": "hep-th" }, { "text": "Generalized heat kernel coefficients: Following Osipov and Hiller, a generalized heat kernel expansion is\nconsidered for the effective action of bosonic operators. In this\ngeneralization, the standard heat kernel expansion, which counts inverse powers\nof a c-number mass parameter, is extended by allowing the mass to be a matrix\nin flavor space. We show that the generalized heat kernel coefficients can be\nrelated to the standard ones in a simple way. This holds with or without trace\nand integration over spacetime, to all orders and for general flavor spaces.\nGauge invariance is manifest.", "category": "hep-th" }, { "text": "Entanglement of Purification and Projective Measurement in CFT: We investigate entanglement of purification in conformal field theory. By\nusing Reeh-Schlieder theorem, we construct a set of the purification states for\n$\\rho_{AB}$, where $\\rho_{AB}$ is reduced density matrix for subregion $AB$ of\na global state $\\rho$. The set can be approximated by acting all the unitary\nobservables,located in the complement of subregion $AB$, on the global state\n$\\rho$, as long as the global state $\\rho$ is \\text{cyclic} for every local\nalgebra, e.g., the vacuum state. Combining with the gravity explanation of\nunitary operations in the context of the so-called surface/state\ncorrespondence, we prove the holographic EoP formula. We also explore the\nprojective measurement with the conformal basis in conformal field theory and\nits relation to the minimization procedure of EoP. Interestingly, though the\nprojective measurement is not a unitary operator, the difference in some limits\nbetween holographic EoP and the entanglement entropy after a suitable\nprojective measurement is a constant $\\frac{c}{3}\\log 2$ up to some\ncontributions from boundary. This suggests the states after projective\nmeasurements may approximately be taken as the purification state corresponding\nto the minimal value of the procedure.", "category": "hep-th" }, { "text": "Smooth non-extremal D1-D5-P solutions as charged gravitational\n instantons: We present an alternative and more direct construction of the\nnon-supersymmetric D1-D5-P supergravity solutions found by Jejjala, Madden,\nRoss and Titchener. We show that these solutions --- with all three charges and\nboth rotations turned on --- can be viewed as a charged version of the\nMyers-Perry instanton. We present an inverse scattering construction of the\nMyers-Perry instanton metric in Euclidean five-dimensional gravity. The angular\nmomentum bounds in this construction turn out to be precisely the ones\nnecessary for the smooth microstate geometries. We add charges on the\nMyers-Perry instanton using appropriate SO(4,4) hidden symmetry\ntransformations. The full construction can be viewed as an extension and\nsimplification of a previous work by Katsimpouri, Kleinschmidt and Virmani.", "category": "hep-th" }, { "text": "Ambiguity in mana and magic definition and knot states: We study the Mana and Magic for quantum states. They have a standard\ndefinition through the Clifford group, which is finite and thus classically\ncomputable. We introduce a modified Mana and Magic, which keep their main\nproperty of classical computability, while making other states classically\ncomputable. We also apply these new definitions to the studies of knot states\nof 2-strand knots.", "category": "hep-th" }, { "text": "Quantum corrected gravitational potential beyond monopole-monopole\n interactions: We investigate spin- and velocity-dependent contributions to the\ngravitational inter-particle potential. The methodology adopted here is based\non the expansion of the effective action in terms of form factors encoding\nquantum corrections. Restricting ourselves to corrections up to the level of\nthe graviton propagator, we compute, in terms of general form factors, the\nnon-relativistic gravitational potential associated with the scattering of\nspin-0 and -1/2 particles. We discuss comparative aspects concerning different\ntypes of scattered particles and we also establish some comparisons with the\ncase of electromagnetic potentials. Moreover, we apply our results to explicit\nexamples of form factors based on non-perturbative approaches for quantum\ngravity. Finally, the cancellation of Newtonian singularity is analysed in the\npresence of terms beyond the monopole-monopole sector.", "category": "hep-th" }, { "text": "Affine Symmetries for ABJM Partition Function and its Generalization: Partially motivated by the fact that the grand partition function of the ABJM\ntheory or its generalization is expressed by a spectral operator enjoying\nsymmetries of the Weyl group, it was found that the grand partition function\nsatisfies the q-Painleve equation, which is constructed from the affine Weyl\ngroup. In this paper we clarify the affine symmetries of the grand partition\nfunction. With the affine symmetries, we find that the grand partition function\nextends naturally outside the fundamental domain of duality cascades and once\nthe Painleve equation holds in the fundamental domain, so does it outside.", "category": "hep-th" }, { "text": "Self--dual Lorentzian wormholes in n--dimensional Einstein gravity: A family of spherically symmetric, static and self--dual Lorentzian wormholes\nis obtained in n--dimensional Einstein gravity. This class of solutions\nincludes the n--dimensional versions of the Schwarzschild black hole and the\nspatial--Schwarzschild traversable wormhole. Using isotropic coordinates we\nstudy the geometrical structure of the solution, and delineate the domains of\nthe free parameters for which wormhole, naked singular geometries and the\nSchwarzschild black hole are obtained. It is shown that, in the lower\ndimensional Einstein gravity without cosmological constant, we can not have\nself--dual Lorentzian wormholes.", "category": "hep-th" }, { "text": "The Canonical Symmetry and Hamiltonian Formalism. I. Conservation Laws: The properties of the canonical symmetry of the nonlinear Schr\\\"odinger\nequation are investigated. The densities of the local conservation laws for\nthis system are shown to change under the action of the canonical symmetry by\ntotal space derivatives.", "category": "hep-th" }, { "text": "A Web of 2d Dualities: ${\\bf Z}_2$ Gauge Fields and Arf Invariants: We describe a web of well-known dualities connecting quantum field theories\nin $d=1+1$ dimensions. The web is constructed by gauging ${\\bf Z}_2$ global\nsymmetries and includes a number of perennial favourites such as the\nJordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac\nfermion, and T-duality. There are also less-loved examples, such as non-modular\ninvariant $c=1$ CFTs that depend on a background spin structure.", "category": "hep-th" }, { "text": "Quantization Rules for Dynamical Systems: We discuss a manifestly covariant way of arriving at the quantization rules\nbased on causality, with no reference to Poisson or Peierls brackets of any\nkind.", "category": "hep-th" }, { "text": "The three-loop Adler $D$-function for ${\\cal N}=1$ SQCD with various\n renormalization prescriptions: The three-loop Adler $D$-function for ${\\cal N}=1$ SQCD in the\n$\\overline{\\mbox{DR}}$ scheme is calculated. It appears that the result does\nnot satisfy NSVZ-like equation which relates the $D$-function to the anomalous\ndimension of the matter superfields. However this NSVZ-like equation can be\nrestored by a special tuning of the renormalization scheme. Also we demonstrate\nthat the $D$-function defined in terms of the bare coupling does not satisfy\nthe NSVZ-like equation in the case of using the regularization by dimensional\nreduction. The scheme-dependence of the $D$-function written in the form of the\n$\\beta$-expansion is briefly discussed.", "category": "hep-th" }, { "text": "Breakdown of Cluster Decomposition in Instanton Calculations of the\n Gluino Condensate: A longstanding puzzle concerns the calculation of the gluino condensate\n<{tr\\lambda^2\\over 16\\pi^2}> = c\\Lambda^3 in N=1 supersymmetric SU(N) gauge\ntheory: so-called weak-coupling instanton (WCI) calculations give c=1, whereas\nstrong-coupling instanton (SCI) calculations give, instead,\nc=2[(N-1)!(3N-1)]^{-1/N}. By examining correlators of this condensate in\narbitrary multi-instanton sectors, we cast serious doubt on the SCI calculation\nof <{tr\\lambda^2\\over 16\\pi^2}> by showing that an essential step --- namely\ncluster decomposition --- is invalid. We also show that the addition of a\nso-called Kovner-Shifman vacuum (in which <{tr\\lambda^2\\over 16\\pi^2}> = 0)\ncannot straightforwardly resolve this mismatch.", "category": "hep-th" }, { "text": "Causality and classical dispersion relations: We explore the consequences of relativistic causality and covariant stability\nfor short-wavelength dispersion relations in classical systems. For excitations\ndescribed by a finite number of partial differential equations, as is the case\nin relativistic hydrodynamics, we give causality and covariant stability\nconstraints on the excitation's frequency at large momenta.", "category": "hep-th" }, { "text": "Israel--Wilson--Perj\u00e9s Solutions in Heterotic String Theory: We present a simple algorithm to obtain solutions that generalize the\nIsrael--Wilson--Perj\\'es class for the low-energy limit of heterotic string\ntheory toroidally compactified from D=d+3 to three dimensions. A remarkable map\nexisting between the Einstein--Maxwell (EM) theory and the theory under\nconsideration allows us to solve directly the equations of motion making use of\nthe matrix Ernst potentials connected with the coset matrix of heterotic string\ntheory. For the particular case d=1 (if we put n=6, the resulting theory can be\nconsidered as the bosonic part of the action of D=4, N=4 supergravity) we\nobtain explicitly a dyonic solution in terms of one real 2\\times 2--matrix\nharmonic function and 2n real constants (n being the number of Abelian vector\nfields). By studying the asymptotic behaviour of the field configurations we\ndefine the charges of the system. They satisfy the\nBogomol'nyi--Prasad--Sommmerfeld (BPS) bound.", "category": "hep-th" }, { "text": "Correlators of Vertex Operators for Circular Strings with Winding\n Numbers in AdS5xS5: We compute semiclassically the two-point correlator of the marginal vertex\noperators describing the rigid circular spinning string state with one large\nspin and one windining number in AdS_5 and three large spins and three winding\nnumbers in S^5. The marginality condition and the conformal invariant\nexpression for the two-point correlator obtained by using an appropriate vertex\noperator are shown to be associated with the diagonal and off-diagonal Virasoro\nconstraints respectively. We evaluate semiclassically the three-point\ncorrelator of two heavy circular string vertex operators and one zero-momentum\ndilaton vertex operator and discuss its relation with the derivative of the\ndimension of the heavy circular string state with respect to the string\ntension.", "category": "hep-th" }, { "text": "Canonical invariance of spatially covariant scalar-tensor theory: We investigate invariant canonical transformations of a spatially covariant\nscalar-tensor theory of gravity, called the XG theory, by which the action or\nthe Hamiltonian and the primary constraints keep their forms invariant. We\nderive the Hamiltonian in a non perturbative manner and complete the\nHamiltonian analysis for all regions of the theory. We confirm that the theory\nhas at most 3 degrees of freedom in all regions of the theory as long as the\ntheory has the symmetry under the spatial diffeormorphism. Then, we derive the\ninvariant canonical transformation by using the infinitesimal transformation.\nThe invariant metric transformation of the XG theory contains a vector product\nas well as the disformal transformation. The vector product and the disformal\nfactor can depend on the higher order derivative terms of the scalar field and\nthe metric. In addition, we discover the invariant canonical transformation\nwhich transforms the momentum of the metric. Using the invariant\ntransformation, we study the relation between the Horndeski theory and the GLPV\ntheory, and find that we can not obtain the arbitrary GLPV theory from the\nHorndeski theory through the invariant canonical transformation we have found.", "category": "hep-th" }, { "text": "$T\\bar{T}$ deformed partition functions: We demonstrate the presence of modular properties in partition functions of\n$T\\bar{T}$ deformed conformal field theories. These properties are verified\nexplicitly for the deformed free boson. The modular features facilitate a\nderivation of the asymptotic density of states in these theories, which turns\nout to interpolate between Cardy and Hagedorn behaviours. We also point out a\nsub-sector of the spectrum that remains undeformed under the $T\\bar{T}$ flow.\nFinally, we comment on the deformation of the CFT vacuum character and its\nimplications for the holographic dual.", "category": "hep-th" }, { "text": "Statistical mechanics for dilatations in N=4 super Yang--Mills theory: Matrix model describing the anomalous dimensions of composite operators in\n$\\mathcal{N}=4$ super Yang--Mills theory up to one-loop level is considered at\nfinite temperature. We compute the thermal effective action for this model,\nwhich we define as the log of the partition function restricted to the states\nof given fixed length and spin. The result is obtained in the limits of high\nand low temperature.", "category": "hep-th" }, { "text": "A Comment on the Odd Flows for the Supersymmetric KdV equation: In a recent paper Dargis and Mathieu introduced integrodifferential odd flows\nfor the supersymmetric KdV equation. These flows are obtained from the nonlocal\nconservation laws associated with the fourth root of its Lax operator. In this\nnote I show that only half of these flows are of the standard Lax form, while\nthe remaining half provide us with hamiltonians for an SKdV-type reduction of a\nnew supersymmetric hierarchy. This new hierarchy is shown to be closely related\nto the Jacobian supersymmetric KP-hierarchy of Mulase and Rabin. A detailed\nstudy of the algebra of additional symmetries of this new hierarchy reveals\nthat it is isomorphic to the super-W_{1+\\infty} algebra, thus making it a\ncandidate for a possible interrelationship between superintegrability and\ntwo-dimensional supergravity.", "category": "hep-th" }, { "text": "BRST invariant $CP^{1}$ model through improved Dirac quantization: The Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of\nDirac quantization, is applied to the $CP^1$ model, and the compact form of a\nnontrivial first-class Hamiltonian is directly obtained by introducing the BFT\nphysical fields. We also derive a BRST-invariant gauge fixed Lagrangian through\nthe standard path-integral procedure. Furthermore, performing collective\ncoordinate quantization we obtain energy spectrum of rigid rotator in the\n$CP^1$ model. Exploiting the Hopf bundle, we also show that the $CP^1$ model is\nexactly equivalent to the O(3) nonlinear sigma model at the canonical level.", "category": "hep-th" }, { "text": "Fluctuation and Dissipation from a Deformed String/Gauge Duality Model: Using a Lorentz invariant deformed string/gauge duality model at finite\ntemperature we calculate the thermal fluctuation and the corresponding linear\nresponse, verifying the fluctuation-dissipation theorem. The deformed AdS$_5$\nis constructed by the insertion of an exponential factor $\\exp(k/r^2)$ in the\nmetric. We also compute the string energy and the mean square displacement in\norder to investigate the ballistic and diffusive regimes. Furthermore we have\nstudied the dissipation and the linear response in the zero temperature\nscenario.", "category": "hep-th" }, { "text": "Supergravity couplings: a geometric formulation: This report provides a pedagogical introduction to the description of the\ngeneral Poincare supergravity/matter/Yang-Mills couplings using methods of\nKahler superspace geometry. At a more advanced level this approach is\ngeneralized to include tensor field and Chern-Simons couplings in supersymmetry\nand supergravity, relevant in the context of weakly and strongly coupled string\ntheories.", "category": "hep-th" }, { "text": "Discrete Theta Angles, Symmetries and Anomalies: Gauge theories in various dimensions often admit discrete theta angles, that\narise from gauging a global symmetry with an additional symmetry protected\ntopological (SPT) phase. We discuss how the global symmetry and 't Hooft\nanomaly depends on the discrete theta angles by coupling the gauge theory to a\ntopological quantum field theory (TQFT). We observe that gauging an Abelian\nsubgroup symmetry, that participates in symmetry extension, with an additional\nSPT phase leads to a new theory with an emergent Abelian symmetry that also\nparticipates in a symmetry extension. The symmetry extension of the gauge\ntheory is controlled by the discrete theta angle which comes from the SPT\nphase. We find that discrete theta angles can lead to two-group symmetry in 4d\nQCD with $SU(N),SU(N)/\\mathbb{Z}_k$ or $SO(N)$ gauge groups as well as various\n3d and 2d gauge theories.", "category": "hep-th" }, { "text": "Proof of a three-loop relation between the Regge limits of four-point\n amplitudes in N=4 SYM and N=8 supergravity: A previously proposed all-loop-orders relation between the Regge limits of\nfour-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8\nsupergravity is established at the three-loop level. We show that the Regge\nlimit of known expressions for the amplitudes obtained using generalized\nunitarity simplifies in both cases to a (modified) sum over three-loop ladder\nand crossed-ladder scalar diagrams. This in turn is consistent with the result\nobtained using the eikonal representation of the four-point gravity amplitude.\nA possible exact three-loop relation between four-point amplitudes is also\nconsidered.", "category": "hep-th" }, { "text": "On Lie point symmetry of classical Wess-Zumino-Witten model: We perform the group analysis of Witten's equations of motion for a particle\nmoving in the presence of a magnetic monopole, and also when constrained to\nmove on the surface of a sphere, which is the classical Wess-Zumino-Witten\nmodel. We also consider variations of this model. Our analysis gives the\ngenerators of the corresponding Lie point symmetries. The Lie symmetry\ncorresponding to Kepler's third law is obtained in two related examples.", "category": "hep-th" }, { "text": "Complementarity in Wormhole Chromodynamics: The electric charge of a wormhole mouth and the magnetic flux ``linked'' by\nthe wormhole are non-commuting observables, and so cannot be simultaneously\ndiagonalized. We use this observation to resolve some puzzles in wormhole\nelectrodynamics and chromodynamics. Specifically, we analyze the color electric\nfield that results when a colored object traverses a wormhole, and we discuss\nthe measurement of the wormhole charge and flux using Aharonov-Bohm\ninterference effects. We suggest that wormhole mouths may obey conventional\nquantum statistics, contrary to a recent proposal by Strominger.", "category": "hep-th" }, { "text": "Extremal Black Brane Attractors on The Elliptic Curve: Reconsidering the analysis of the moduli space of N=2 eight dimensional\nsupergravity coupled to seven scalars, we propose a new scalar manifold\nfactorization given by \\frac{\\textsc {SO(2,2)}}{{\\textsc{SO(2)}}\\times\n{\\textsc{SO(2)}}}\\times \\frac{\\textsc{SO(2,1)}}{\\textsc{SO(2)}}\\times \\textsc\n{SO(1,1)}. This factorization is supported by the appearance of three solutions\nof Type IIA extremal black p-branes (p=0,1,2) with AdS_{p+2}\\times S^{6-p}\nnear-horizon geometries in eight dimensions. We analyze the corresponding\nattractor mechanism. In particular, we give an interplay between the scalar\nmanifold factors and the extremal black p-brane charges. Then we show that the\ndilaton can be stabilized by the dyonic black 2-brane charges.", "category": "hep-th" }, { "text": "On the renormalisation group for the boundary Truncated Conformal Space\n Approach: In this paper we continue the study of the truncated conformal space approach\nto perturbed boundary conformal field theories. This approach to perturbation\ntheory suffers from a renormalisation of the coupling constant and a\nmultiplicative renormalisation of the Hamiltonian. We show how these two\neffects can be predicted by both physical and mathematical arguments and prove\nthat they are correct to leading order for all states in the TCSA system. We\ncheck these results using the TCSA applied to the tri-critical Ising model and\nthe Yang-Lee model. We also study the TCSA of an irrelevant\n(non-renormalisable) perturbation and find that, while the convergence of the\ncoupling constant and energy scales are problematic, the renormalised and\nrescaled spectrum remain a very good fit to the exact result, and we find a\nnumerical relationship between the IR and UV couplings describing a particular\nflow. Finally we study the large coupling behaviour of TCSA and show that it\naccurately encompasses several different fixed points.", "category": "hep-th" }, { "text": "Comments on Quivers and Fractons: We discuss certain structural analogies between supersymmetric quiver gauge\ntheories and lattice models leading to fracton phases of matter. In particular,\nclasses of quiver models can be viewed as lattice models having sub-system\nsymmetries, dimensions of moduli spaces growing linearly with the size of the\nlattice, and having excitations with limited mobility (with \"excitations\" and\n\"mobility\" properly defined).", "category": "hep-th" }, { "text": "Basic zeta functions and some applications in physics: It is the aim of these lectures to introduce some basic zeta functions and\ntheir uses in the areas of the Casimir effect and Bose-Einstein condensation. A\nbrief introduction into these areas is given in the respective sections. We\nwill consider exclusively spectral zeta functions, that is zeta functions\narising from the eigenvalue spectrum of suitable differential operators. There\nis a set of technical tools that are at the very heart of understanding\nanalytical properties of essentially every spectral zeta function. Those tools\nare introduced using the well-studied examples of the Hurwitz, Epstein and\nBarnes zeta function. It is explained how these different examples of zeta\nfunctions can all be thought of as being generated by the same mechanism,\nnamely they all result from eigenvalues of suitable (partial) differential\noperators. It is this relation with partial differential operators that\nprovides the motivation for analyzing the zeta functions considered in these\nlectures. Motivations come for example from the questions \"Can one hear the\nshape of a drum?\" and \"What does the Casimir effect know about a boundary?\".\nFinally \"What does a Bose gas know about its container?\"", "category": "hep-th" }, { "text": "A Relativistic Quaternionic Wave Equation: We study a one-component quaternionic wave equation which is relativistically\ncovariant. Bi-linear forms include a conserved 4-current and an antisymmetric\nsecond rank tensor. Waves propagate within the light-cone and there is a\nconserved quantity which looks like helicity. The principle of superposition is\nretained in a slightly altered manner. External potentials can be introduced in\na way that allows for gauge invariance. There are some results for scattering\ntheory and for two-particle wavefunctions as well as the beginnings of second\nquantization. However, we are unable to find a suitable Lagrangian or an\nenergy-momentum tensor.", "category": "hep-th" }, { "text": "Exact One-Point Function of N=1 super-Liouville Theory with Boundary: In this paper, exact one-point functions of N=1 super-Liouville field theory\nin two-dimensional space-time with appropriate boundary conditions are\npresented. Exact results are derived both for the theory defined on a\npseudosphere with discrete (NS) boundary conditions and for the theory with\nexplicit boundary actions which preserves super conformal symmetries. We\nprovide various consistency checks. We also show that these one-point functions\ncan be related to a generalized Cardy conditions along with corresponding\nmodular $S$-matrices. Using this result, we conjecture the dependence of the\nboundary two-point functions of the (NS) boundary operators on the boundary\nparameter.", "category": "hep-th" }, { "text": "Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities: The chiral superstring measure constructed in the earlier papers of this\nseries for general gravitino slices is examined in detail for slices supported\nat two points x_\\alpha. In this case, the invariance of the measure under\ninfinitesimal changes of gravitino slices established previously is\nstrengthened to its most powerful form: the measure is shown, point by point on\nmoduli space, to be locally and globally independent from the points x_\\alpha,\nas well as from the superghost insertion points p_a, q_\\alpha introduced\nearlier as computational devices. In particular, the measure is completely\nunambiguous. The limit x_\\alpha = q_\\alpha is then well defined. It is of\nspecial interest, since it elucidates some subtle issues in the construction of\nthe picture-changing operator Y(z) central to the BRST formalism. The formula\nfor the chiral superstring measure in this limit is derived explicitly.", "category": "hep-th" }, { "text": "Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras: We study realizations of the exceptional non-linear (quadratically generated,\nor W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine\nsymmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary\nhighest-weight representations in terms of a single boson and free fermions in\n8 of Spin(7) and 7 of G_2, with the central charges c_8=26/5 and c_7=5,\nrespectively. Furthermore, we show that the general coset Ans\"atze for the N=8\nand N=7 algebras naturally lead to the coset spaces SO(8)xU(1)/SO(7) and\nSO(7)xU(1)/G_2, respectively, as the additional consistent solutions for\ncertain values of the central charge. The coset space SO(8)/SO(7) is the\nseven-sphere S^7, whereas the space SO(7)/G_2 represents the seven-sphere with\ntorsion, S^7_T. The division algebra of octonions and the associated triality\nproperties of SO(8) play an essential role in all these realizations. We also\ncomment on some possible applications of our results to string theory.", "category": "hep-th" }, { "text": "The Search for Zoo-Perparticles: This paper reviews the covariant formalism of N=1, D=10 classical\nsuperparticle models. It discusses the local invariances of a number of\nsuperparticle actions and highlights the problem of finding a covariant\nquantization scenario. Covariant quantization has proved problematic, but it\nhas motivated in seeking alternative approaches that avoids those found in\nearlier models. It also shows new covariant superparticle theories formulated\nin extended spaces that preserve certain canonical form in phase-space, and\neasy to quantize by using the Batalin-Vilkovisky procedure, as the gauge\nalgebra of their constraints only closes on-shell. The mechanics actions\ndescribe particles moving in a superspace consisting of the usual $N=1$\nsuperspace, together with an extra spinor or vector coordinate. A light-cone\nanalysis shows that all these new superparticle models reproduce the physical\nspectrum of the N=1 super-Yang-Mills theory.", "category": "hep-th" }, { "text": "Exact Inner Metric and Microscopic State of AdS$_3$-Schwarzschld BHs: Through full solvability of 2+1 dimensional general relativity we derive out\nexact dynamic inner metric of collapsing stars with inhomogeneous initial mass\ndistribution but joining with outside Anti-deSitt-Schwarzschild black holes\nsmoothly. We prove analytically by standard quantum mechanics that the\nlog-number of such solutions, or microscopic states of the system is\nproportional to the perimeter of the outside black holes. Key formulas for\ngeneralizing to 3+1D Schwarzschild black holes are also presented. Our result\nprovides a bulk space viewpoint to questions on what the microscopic degrees of\nfreedom are and who their carriers are in various holographic and/or asymptotic\nsymmetry methods to black hole entropies. It may also shed light for\nsingularity theorem and cosmic censorship related researches.", "category": "hep-th" }, { "text": "Torsional Regularization of Self-Energy and Bare Mass of Electron: In the presence of spacetime torsion, the momentum components do not commute;\ntherefore, in quantum field theory, summation over the momentum eigenvalues\nwill replace integration over the momentum. In the Einstein--Cartan theory of\ngravity, in which torsion is coupled to spin, the separation between the\neigenvalues increases with the magnitude of the momentum. Consequently, this\nreplacement regularizes divergent integrals in Feynman diagrams with loops by\nturning them into convergent sums. In this article, we apply torsional\nregularization to the self-energy of a charged lepton in quantum\nelectrodynamics. We show that this procedure eliminates the ultraviolet\ndivergence. We also show that torsion gives a photon a small nonzero mass,\nwhich regularizes the infrared divergence. In the end, we calculate the finite\nbare masses of the electron, muon, and tau lepton: $0.4329\\,\\mbox{MeV}$,\n$90.95\\,\\mbox{MeV}$, and $1543\\,\\mbox{MeV}$, respectively. These values\nconstitute about $85\\%$ of the observed, re-normalized masses.", "category": "hep-th" }, { "text": "Astrophysical Violations of the Kerr Bound as a Possible Signature of\n String Theory: In 4D general relativity, the angular momentum of a black hole is limited by\nthe Kerr bound. We suggest that in string theory, this bound can be breached\nand compact black-hole-like objects can spin faster. Near such \"superspinars,\"\nthe efficiency of energy transfer from the accreting matter to radiation can\nreach 100%, compared to the maximum efficiency of 42% of the extremal Kerr (or\n6% of the Schwarzschild) black hole. Finding such superspinning objects as\nactive galactic nuclei, GBHCs, or sources of gamma ray bursts, could be viewed\nas experimental support for string theory.", "category": "hep-th" }, { "text": "Chaos around Holographic Regge Trajectories: Using methods of Hamiltonian dynamical systems, we show analytically that a\ndynamical system connected to the classical spinning string solution\nholographically dual to the principal Regge trajectory is non-integrable. The\nRegge trajectories themselves form an integrable island in the total phase\nspace of the dynamical system. Our argument applies to any gravity background\ndual to confining field theories and we verify it explicitly in various\nsupergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and\nthe AdS soliton. Having established non-integrability for this general class of\nsupergravity backgrounds, we show explicitly by direct computation of the\nPoincare sections and the largest Lyapunov exponent, that such strings have\nchaotic motion.", "category": "hep-th" }, { "text": "Hierarchy problem and the cosmological constant in a five-dimensional\n Brans-Dicke brane world model: We discuss a new solution, admitting the existence of dS_{4} branes, in\nfive-dimensional Brans-Dicke theory. It is shown that, due to a special form of\na bulk scalar field potential, for certain values of the model parameters the\neffective cosmological constant can be made small on the brane, where the\nhierarchy problem of gravitational interaction is solved. We also discuss new\nstabilization mechanism which is based on the use of auxiliary fields.", "category": "hep-th" }, { "text": "Hawking temperature from tunnelling formalism: It has recently been suggested that the attempt to understand Hawking\nradiation as tunnelling across black hole horizons produces a Hawking\ntemperature double the standard value. It is explained here how one can obtain\nthe standard value in the same tunnelling approach.", "category": "hep-th" }, { "text": "2d Index and Surface operators: In this paper we compute the superconformal index of 2d (2,2) supersymmetric\ngauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is\ncomputed by a unitary matrix integral much like the matrix integral that\ncomputes 4d superconformal index. We compute the 2d index explicitly for a\nnumber of examples. In the case of abelian gauge theories we see that the index\nis invariant under flop transition and CY-LG correspondence. The index also\nprovides a powerful check of the Seiberg-type duality for non-abelian gauge\ntheories discovered by Hori and Tong.\n In the later half of the paper, we study half-BPS surface operators in N=2\nsuperconformal gauge theories. They are engineered by coupling the 2d (2,2)\nsupersymmetric gauge theory living on the support of the surface operator to\nthe 4d N=2 theory, so that different realizations of the same surface operator\nwith a given Levi type are related by a 2d analogue of the Seiberg duality. The\nindex of this coupled system is computed by using the tools developed in the\nfirst half of the paper. The superconformal index in the presence of surface\ndefect is expected to be invariant under generalized S-duality. We demonstrate\nthat it is indeed the case. In doing so the Seiberg-type duality of the 2d\ntheory plays an important role.", "category": "hep-th" }, { "text": "New Multicritical Random Matrix Ensembles: In this paper we construct a class of random matrix ensembles labelled by a\nreal parameter $\\alpha \\in (0,1)$, whose eigenvalue density near zero behaves\nlike $|x|^\\alpha$. The eigenvalue spacing near zero scales like\n$1/N^{1/(1+\\alpha)}$ and thus these ensembles are representatives of a {\\em\ncontinous} series of new universality classes. We study these ensembles both in\nthe bulk and on the scale of eigenvalue spacing. In the former case we obtain\nformulas for the eigenvalue density, while in the latter case we obtain\napproximate expressions for the scaling functions in the microscopic limit\nusing a very simple approximate method based on the location of zeroes of\northogonal polynomials.", "category": "hep-th" }, { "text": "Stability of $AdS_p x S^n x S^{q-n}$ Compactifications: We examine the stability of ${\\rm AdS}_p \\times {\\rm S}^n \\times {\\rm\nS}^{q-n}$. The initial data constructed by De Wolfe et al \\cite{Gary} has been\ncarefully analyised and we have confirmed that there is no lower bound for the\ntotal mass for $q< 9$. The effective action on ${\\rm AdS}_p$ has been derived\nfor dilatonic compactification of the system to describe the non-linear\nfluctuation of the background space-time. The stability is discussed applying\nthe positive energy theorem to the effective theory on AdS, which again shows\nthe stability for $q \\geq 9$.", "category": "hep-th" }, { "text": "Integrable XYZ Model with Staggered Anisotropy Parameter: We apply to the XYZ model the technique of construction of integrable models\nwith staggered parameters, presented recently for the XXZ case. The solution of\nmodified Yang-Baxter equations is found and the corresponding integrable\nzig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ\ncase in the appropriate limit.", "category": "hep-th" }, { "text": "Local Fluid Dynamical Entropy from Gravity: Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4\nsuper Yang Mills theory have recently been constructed perturbatively in the\nlong wavelength limit. We demonstrate that these geometries all have regular\nevent horizons, and determine the location of the horizon order by order in a\nboundary derivative expansion. Intriguingly, the derivative expansion allows us\nto determine the location of the event horizon in the bulk as a local function\nof the fluid dynamical variables. We define a natural map from the boundary to\nthe horizon using ingoing null geodesics. The area-form on spatial sections of\nthe horizon can then be pulled back to the boundary to define a local entropy\ncurrent for the dual field theory in the hydrodynamic limit. The area theorem\nof general relativity guarantees the positivity of the divergence of the\nentropy current thus constructed.", "category": "hep-th" }, { "text": "Basic hypergeometry of supersymmetric dualities: We introduce several new identities combining basic hypergeometric sums and\nintegrals. Such identities appear in the context of superconformal index\ncomputations for three-dimensional supersymmetric dual theories. We give both\nanalytic proofs and physical interpretations of the presented identities.", "category": "hep-th" }, { "text": "Symmetries and supersymmetries of the Dirac operators in curved\n spacetimes: It is shown that the main geometrical objects involved in all the symmetries\nor supersymmetries of the Dirac operators in curved manifolds of arbitrary\ndimensions are the Killing vectors and the Killing-Yano tensors of any ranks.\nThe general theory of external symmetry transformations associated to the usual\nisometries is presented, pointing out that these leave the standard Dirac\nequation invariant providing the correct spin parts of the group generators.\nFurthermore, one analyzes the new type of symmetries generated by the\ncovariantly constant Killing-Yano tensors that realize certain square roots of\nthe metric tensor. Such a Killing-Yano tensor produces simultaneously a\nDirac-type operator and the generator of a one-parameter Lie group connecting\nthis operator with the standard Dirac one. In this way the Dirac operators are\nrelated among themselves through continuous transformations associated to\nspecific discrete ones. It is shown that the groups of this continuous symmetry\ncan be only U(1) or SU(2), as those of the (hyper-)Kahler spaces, but arising\neven in cases when the requirements for these special geometries are not\nfulfilled. To exemplify, the Euclidean Taub-NUT space with its Dirac-type\noperators is presented in much details, pointing out that there is an\ninfinite-loop superalgebra playing the role of a closed dynamical algebraic\nstructure. As a final topic, we go to consider the properties of the Dirac-type\noperators of the Minkowski spacetime.", "category": "hep-th" }, { "text": "Topological Gravity as the Early Phase of Our Universe: Motivated by string dualities we propose topological gravity as the early\nphase of our universe. The topological nature of this phase naturally leads to\nthe explanation of many of the puzzles of early universe cosmology. A concrete\nrealization of this scenario using Witten's four dimensional topological\ngravity is considered. This model leads to the power spectrum of CMB\nfluctuations which is controlled by the conformal anomaly coefficients $a,c$.\nIn particular the strength of the fluctuation is controlled by $1/a$ and its\ntilt by $c g^2$ where $g$ is the coupling constant of topological gravity. The\npositivity of $c$, a consequence of unitarity, leads automatically to an IR\ntilt for the power spectrum. In contrast with standard inflationary models,\nthis scenario predicts $\\mathcal{O}(1)$ non-Gaussianities for four- and\nhigher-point correlators and the absence of tensor modes in the CMB\nfluctuations.", "category": "hep-th" }, { "text": "The AdS Virasoro-Shapiro Amplitude: We present a constructive method to compute the AdS Virasoro-Shapiro\namplitude, order by order in AdS curvature corrections. At kth order the answer\ntakes the form of a genus zero world-sheet integral involving weight 3k\nsingle-valued multiple polylogarithms. The coefficients in our ansatz are\nfixed, order by order, by requiring: crossing symmetry; the correct\nsupergravity limit; the correct structure of poles, determined by dispersive\nsum rules; and the dimensions of the first few Konishi-like operators,\navailable from integrability. We explicitly construct the first two curvature\ncorrections. Our final answer then reproduces all localisation results and all\nCFT data available from integrability, to this order, and produces a wealth of\nnew CFT data for planar N=4 SYM at strong coupling.", "category": "hep-th" }, { "text": "Enhanced D-Brane Categories from String Field Theory: We construct D-brane categories in B-type topological string theory as\nsolutions to string field equations of motion. Using the formalism of\nsuperconnections, we show that these solutions form a variant of a construction\nof Bondal and Kapranov. This analysis is an elaboration on recent work of\nLazaroiu. We also comment on the relation between string field theory and the\nderived category approach of Douglas, and Aspinwall and Lawrence.\nNon-holomorphic deformations make a somewhat unexpected appearance in this\nconstruction.", "category": "hep-th" }, { "text": "Holographic entanglement density for spontaneous symmetry breaking: We investigate the properties of the holographic entanglement entropy of the\nsystems in which the $U(1)$ or the translational symmetry is broken\n\\textit{spontaneously}. For this purpose, we define the entanglement density of\nthe strip-subsystems and examine both the first law of entanglement entropy\n(FLEE) and the area theorem. We classify the conditions that FLEE and/or the\narea theorem obey and show that such a classification may be useful for\ncharacterizing the systems. We also find universalities from both FLEE and the\narea theorem. In the spontaneous symmetry breaking case, FLEE is always obeyed\nregardless of the type of symmetry: $U(1)$ or translation. For the\ntranslational symmetry, the area theorem is always violated when the symmetry\nis weakly broken, independent of the symmetry breaking patterns (explicit or\nspontaneous). We also argue that the $\\log$ contribution of the entanglement\nentropy from the Goldstone mode may not appear in the strongly coupled systems.", "category": "hep-th" }, { "text": "A Description of Schwarzschild Black Holes in terms of Intersecting\n M-branes and antibranes: Intersecting M-branes are known to describe multi charged black holes. Using\na configuration of such intersecting branes and antibranes, together with\nmassless excitations living on them, we give a description of Schwarzschild\nblack holes following Danielsson, Guijosa, and Kruczenski. We calculate the\nentropy of these black holes and find that it agrees, upto a numerical factor,\nwith the entropy of the corresponding Schwarzschild black holes in supergravity\napproximation. We give an empirical interpretation of this factor.", "category": "hep-th" }, { "text": "Fermionic Zero Mode and String Creation between D4-Branes at Angles: We study the creation of a fundamental string between D4-branes at angles in\nstring theory. It is shown that $R(-1)^{F}$ part of the one-loop potential of\nopen string changes its sign due to the change of fermionic zero-mode vacua\nwhen the branes cross each other. As a result the effective potential is\nindependent of the angles when supersymmetry is partially unbroken, and leads\nto a consistent picture that a fundamental string is created in the process. We\nalso discuss the s-rule in the configuration. The same result is obtained from\nthe one-loop potential for the orthogonal D4-branes with non-zero field\nstrength. The result is also confirmed from the tension obtained by deforming\nthe Chern-Simons term on one D4-brane, which is induced by another tilted\nD4-brane.", "category": "hep-th" }, { "text": "Supersymmetric K field theories and defect structures: We construct supersymmetric K field theories (i.e., theories with a\nnon-standard kinetic term) in 1+1 and 2+1 dimensions such that the bosonic\nsector just consists of a nonstandard kinetic term plus a potential. Further,\nwe study the possibility of topological defect formation in these\nsupersymmetric models. Finally, we consider more general supersymmetric K field\ntheories where, again, topological defects exist in some cases.", "category": "hep-th" }, { "text": "Renormalized Holographic Subregion Complexity under Relevant\n Perturbations: We construct renormalized holographic entanglement entropy (HEE) and\nsubregion complexity (HSC) in the CV conjecture for asymptotically AdS$_4$ and\nAdS$_5$ geometries under relevant perturbations. Using the holographic\nrenormalization method developed in the gauge/gravity duality, we obtain\ncounter terms which are invariant under coordinate choices. We explicitly\ndefine different forms of renormalized HEE and HSC, according to conformal\ndimensions of relevant operators in the $d=3$ and $d=4$ dual field theories. We\nuse a general embedding for arbitrary entangling subregions and showed that any\nchoice of the coordinate system gives the same form of the counter terms, since\nthey are written in terms of curvature invariants and scalar fields on the\nboundaries. We show an explicit example of our general procedure. Intriguingly,\nwe find that a divergent term of the HSC in the asymptotically AdS$_5$ geometry\nunder relevant perturbations with operators of conformal dimensions in the\nrange $0< \\Delta < \\frac{1}{2}\\,\\, {\\rm and} \\,\\, \\frac{7}{2}< \\Delta < 4$\ncannot be cancelled out by adding any coordinate invariant counter term. This\nimplies that the HSCs in these ranges of the conformal dimensions are not\nrenormalizable covariantly.", "category": "hep-th" }, { "text": "Null Infinity as a Weakly Isolated Horizon: Null infinity (Scri) arises as a boundary of the Penrose conformal completion\nof an asymptotically flat physical space-time. We first note that Scri is a\nweakly isolated horizon (WIH), and then show that its familiar properties can\nbe derived from the general WIH framework. This seems quite surprising because\nphysics associated with black hole (and cosmological) WIHs is very different\nfrom that extracted at Scri. We show that these differences can be directly\ntraced back to the fact that Scri is a WIH in the conformal completion rather\nthan the physical space-time. In particular, the BMS group at Scri stems from\nthe symmetry group of WIHs. We also introduce a unified procedure to arrive at\nfluxes and charges associated with the BMS symmetries at Scri and those\nassociated with black hole (and cosmological) horizons. This procedure differs\nfrom those commonly used in the literature and its novel elements seem\ninteresting in their own right. The fact that is there is a single mathematical\nframework underlying black hole (and cosmological) horizons and Scri paves the\nway to explore the relation between horizon dynamics in the strong field region\nand waveforms at infinity. It should also be useful in the analysis of black\nhole evaporation in quantum gravity.", "category": "hep-th" }, { "text": "Entropy and Black Holes in the Very Early Universe: Model independent arguments following from the Covariant Entropy Principle\nimply that causal diamonds in the very early universe were entirely filled with\na single equilibrated system with finite entropy. A universe where this\ncondition persists forever has no localized excitations. Our own universe\nappears to be headed toward such a state. Within a few hundred times its\ncurrent age it will approach a state where our local group of galaxies sit in\nempty de Sitter space. Eventually, the local group collapse into a black hole,\nwhich evaporates. Localized excitations in de Sitter space are low entropy\nconstrained states of the vacuum ensemble. The origin of these constraints must\nbe in the early universe: the apparent horizon must expand after some initial\nperiod, in a constrained state that is the origin of all localized excitations\nin the universe. We argue that in global FRW coordinates, this corresponds to\nslow roll inflation that ends in a dilute gas of tiny black holes, with mass\ndetermined by the inflationary scale. We then review arguments that these black\nholes can account for the Hot Big Bang, baryogenesis, a distinctive pattern of\nCMB fluctuations, and possibly primordial black hole dark matter consisting of\nlarger black holes that survive until the matter dominated era. The more\ncomplicated question of whether these small black holes can evolve in a way\nthat is consistent with all observational constraints requires computer\nsimulations that have not yet been done.", "category": "hep-th" }, { "text": "Higher-Derivative Chiral Superfield Actions Coupled to N=1 Supergravity: We construct N=1 supergravity extensions of scalar field theories with\nhigher-derivative kinetic terms. Special attention is paid to the auxiliary\nfields, whose elimination leads not only to corrections to the kinetic terms,\nbut to new expressions for the potential energy as well. For example, a\npotential energy can be generated even in the absence of a superpotential. Our\nformalism allows one to write a supergravity extension of any higher-derivative\nscalar field theory and, therefore, has applications to both particle physics\nand cosmological model building. As an illustration, we couple the\nhigher-derivative DBI action describing a 3-brane in 6-dimensions to N=1\nsupergravity. This displays a number of new features-- including the fact that,\nin the regime where the higher-derivative kinetic terms become important, the\npotential tends to be everywhere negative.", "category": "hep-th" }, { "text": "Exact g-function flows from the staircase model: Equations are found for exact g-functions corresponding to integrable bulk\nand boundary flows between successive unitary c<1 minimal conformal field\ntheories in two dimensions, confirming and extending previous perturbative\nresults. These equations are obtained via an embedding of the flows into a\nboundary version of Al. Zamolodchikov's staircase model.", "category": "hep-th" }, { "text": "Asymptotic symmetries of QED and Weinberg's soft photon theorem: Various equivalences between so-called soft theorems which constrain\nscattering amplitudes and Ward identities related to asymptotic symmetries have\nrecently been established in gauge theories and gravity. So far these\nequivalences have been restricted to the case of massless matter fields, the\nreason being that the asymptotic symmetries are defined at null infinity. The\nrestriction is however unnatural from the perspective of soft theorems which\nare insensitive to the masses of the external particles.\n In this work we remove the aforementioned restriction in the context of\nscalar QED. Inspired by the radiative phase space description of massless\nfields at null infinity, we introduce a manifold description of time-like\ninfinity on which the asymptotic phase space for massive fields can be defined.\nThe \"angle dependent\" large gauge transformations are shown to have a well\ndefined action on this phase space, and the resulting Ward identities are found\nto be equivalent to Weinberg's soft photon theorem.", "category": "hep-th" }, { "text": "Entanglement and mutual information in two-dimensional nonrelativistic\n field theories: We carry out a systematic study of entanglement entropy in nonrelativistic\nconformal field theories via holographic techniques. After a discussion of\nrecent results concerning Galilean conformal field theories, we deduce a novel\nexpression for the entanglement entropy of (1+1)-dimensional Lifshitz field\ntheories --- this is done both at zero and finite temperature. Based on these\nresults, we pose a conjecture for the anomaly coefficient of a Lifshitz field\ntheory dual to new massive gravity. It is found that the Lifshitz entanglement\nentropy at finite temperature displays a striking similarity with that\ncorresponding to a flat space cosmology in three dimensions. We claim that this\nstructure is an inherent feature of the entanglement entropy for\nnonrelativistic conformal field theories. We finish by exploring the behavior\nof the mutual information for such theories.", "category": "hep-th" }, { "text": "Domain Wall and de Sitter Solutions of Gauged Supergravity: BPS domain wall solutions of gauged supergravities are found, including those\ntheories which have non-compact gauge groups. These include models that have\nboth an unstable de Sitter solution and stable domain wall solutions.", "category": "hep-th" }, { "text": "A double integral of dlog forms which is not polylogarithmic: Feynman integrals are central to all calculations in perturbative Quantum\nField Theory. They often give rise to iterated integrals of dlog-forms with\nalgebraic arguments, which in many cases can be evaluated in terms of multiple\npolylogarithms. This has led to certain folklore beliefs in the community\nstating that all such integrals evaluate to polylogarithms. Here we discuss a\nconcrete example of a double iterated integral of two dlog-forms that evaluates\nto a period of a cusp form. The motivic versions of these integrals are shown\nto be algebraically independent from all multiple polylogarithms evaluated at\nalgebraic arguments. From a mathematical perspective, we study a mixed elliptic\nHodge structure arising from a simple geometric configuration in\n$\\mathbb{P}^2$, consisting of a modular plane elliptic curve and a set of lines\nwhich meet it at torsion points, which may provide an interesting worked\nexample from the point of view of periods, extensions of motives, and\nL-functions.", "category": "hep-th" }, { "text": "Towards a string representation of infrared SU(2) Yang-Mills theory: We employ a heat kernel expansion to derive an effective action that\ndescribes four dimensional SU(2) Yang-Mills theory in the infrared limit. Our\nresult supports the proposal that at large distances the theory is approximated\nby the dynamics of knotted string-like fluxtubes which appear as solitons in\nthe effective theory.", "category": "hep-th" }, { "text": "The classical dynamics of gauge theories in the deep infrared: Gauge and gravitational theories in asymptotically flat settings possess\ninfinitely many conserved charges associated with large gauge transformations\nor diffeomorphisms that are nontrivial at infinity. To what extent do these\ncharges constrain the scattering in these theories? It has been claimed in the\nliterature that the constraints are trivial, due to a decoupling of hard and\nsoft sectors for which the conserved charges constrain only the dynamics in the\nsoft sector. We show that the argument for this decoupling fails due to the\nfailure in infinite dimensions of a property of symplectic geometry which holds\nin finite dimensions. Specializing to electromagnetism coupled to a massless\ncharged scalar field in four dimensional Minkowski spacetime, we show\nexplicitly that the two sectors are always coupled using a perturbative\nclassical computation of the scattering map. Specifically, while the two\nsectors are uncoupled at low orders, they are coupled at quartic order via the\nelectromagnetic memory effect. This coupling cannot be removed by adjusting the\ndefinitions of the hard and soft sectors (which includes the classical analog\nof dressing the hard degrees of freedom). We conclude that the conserved\ncharges yield nontrivial constraints on the scattering of hard degrees of\nfreedom. This conclusion should also apply to gravitational scattering and to\nblack hole formation and evaporation.\n In developing the classical scattering theory, we show that generic Lorenz\ngauge solutions fail to satisfy the matching condition on the vector potential\nat spatial infinity proposed by Strominger to define the field configuration\nspace, and we suggest a way to remedy this. We also show that when soft degrees\nof freedom are present, the order at which nonlinearities first arise in the\nscattering map is second order in Lorenz gauge, but can be third order in other\ngauges.", "category": "hep-th" }, { "text": "Finite temperature fermionic condensate and currents in topologically\n nontrivial spaces: We investigate the finite temperature fermionic condensate and the\nexpectation values of the charge and current densities for a massive fermion\nfield in a spacetime background with an arbitrary number of toroidally\ncompactified spatial dimensions in the presence of a non-vanishing chemical\npotential. Periodicity conditions along compact dimensions are taken with\narbitrary phases and the presence of a constant gauge field is assumed. The\nlatter gives rise to Aharonov-Bohm-like effects on the expectation values. They\nare periodic functions of magnetic fluxes enclosed by compact dimensions with\nthe period equal to the flux quantum. The current density has nonzero\ncomponents along compact dimensions only. Both low- and high-temperature\nasymptotics of the expectation values are studied. In particular, it has been\nshown that at high temperatures the current density is exponentially\nsuppressed. This behavior is in sharp contrast with the corresponding\nasymptotic in the case of a scalar field, where the current density linearly\ngrows with the temperature. The features for the models in odd dimensional\nspacetimes are discussed. Applications are given to cylindrical and toroidal\nnanotubes described within the framework of effective Dirac theory for the\nelectronic subsystem.", "category": "hep-th" }, { "text": "A non-commuting twist in the partition function: We compute a twisted index for an orbifold theory when the twist generating\ngroup does not commute with the orbifold group. The twisted index requires the\ntheory to be defined on moduli spaces that are compatible with the twist. This\nis carried out for CHL models at special points in the moduli space where they\nadmit dihedral symmetries. The commutator subgroup of the dihedral groups are\ncyclic groups that are used to construct the CHL orbifolds. The residual\nreflection symmetry is chosen to act as a `twist' on the partition function.\nThe reflection symmetries do not commute with the orbifolding group and hence\nwe refer to this as a non-commuting twist. We count the degeneracy of half-BPS\nstates using the twisted partition function and find that the contribution\ncomes mainly from the untwisted sector. We show that the generating function\nfor these twisted BPS states are related to the Mathieu group M_{24}.", "category": "hep-th" }, { "text": "Uses of zeta regularization in QFT with boundary conditions: a\n cosmo-topological Casimir effect: Zeta regularization has proven to be a powerful and reliable tool for the\nregularization of the vacuum energy density in ideal situations. With the\nHadamard complement, it has been shown to provide finite (and meaningful)\nanswers too in more involved cases, as when imposing physical boundary\nconditions (BCs) in two-- and higher--dimensional surfaces (being able to\nmimic, in a very convenient way, other {\\it ad hoc} cut-offs, as non-zero\ndepths). What we have considered is the {\\it additional} contribution to the cc\ncoming from the non-trivial topology of space or from specific boundary\nconditions imposed on braneworld models (kind of cosmological Casimir effects).\nAssuming someone will be able to prove (some day) that the ground value of the\ncc is zero, as many had suspected until very recently, we will then be left\nwith this incremental value coming from the topology or BCs. We show that this\nvalue can have the correct order of magnitude in a number of quite reasonable\nmodels involving small and large compactified scales and/or brane BCs, and\nsupergravitons.", "category": "hep-th" }, { "text": "Thermoelectric Conductivities at Finite Magnetic Field and the Nernst\n Effect: We study the thermoelectric conductivities of a strongly correlated system in\nthe presence of a magnetic field by the gauge/gravity duality. We consider a\nclass of Einstein-Maxwell-Dilaton theories with axion fields imposing momentum\nrelaxation. General analytic formulas for the direct current(DC) conductivities\nand the Nernst signal are derived in terms of the black hole horizon data. For\nan explicit model study, we analyse in detail the dyonic black hole modified by\nmomentum relaxation. In this model, for small momentum relaxation, the Nernst\nsignal shows a bell-shaped dependence on the magnetic field, which is a feature\nof the normal phase of cuprates. We compute all alternating current(AC)\nelectric, thermoelectric, and thermal conductivities by numerical analysis and\nconfirm that their zero frequency limits precisely reproduce our analytic DC\nformulas, which is a non-trivial consistency check of our methods. We discuss\nthe momentum relaxation effects on the conductivities including cyclotron\nresonance poles.", "category": "hep-th" }, { "text": "One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity: We present an ansatz for all one-loop amplitudes in pure Einstein gravity for\nwhich the n external gravitons have the same outgoing helicity. These loop\namplitudes, which are rational functions of the momenta, also arise in the\nquantization of self-dual gravity in four-dimensional Minkowski space. Our\nansatz agrees with explicit computations via D-dimensional unitarity cuts for n\nless than or equal to 6. It also has the expected analytic behavior, for all n,\nas a graviton becomes soft, and as two momenta become collinear. The gravity\nresults are closely related to analogous amplitudes in (self-dual) Yang-Mills\ntheory.", "category": "hep-th" }, { "text": "Time Lumps in Nonlocal Stringy Models and Cosmological Applications: We study lump solutions in nonlocal toy models and their cosmological\napplications. These models are motivated by a description of D-brane decay\nwithin string field theory framework. In order to find cosmological solutions\nwe use the simplest local approximation keeping only second derivative terms in\nnonlocal dynamics. We study a validity of this approximation in flat background\nwhere time lump solutions can be written explicitly. We work out the validity\nof this approximation. We show that our models at large time exhibit the\nphantom behaviour similar to the case of the string kink.", "category": "hep-th" }, { "text": "N=2 Chiral Supergravity in (10 + 2)-Dimensions As Consistent Background\n for Super (2 + 2)-Brane: We present a theory of N=2 chiral supergravity in (10+2)-dimensions. This\nformulation is similar to N=1 supergravity presented recently using\nnull-vectors in 12D. In order to see the consistency of this theory, we perform\na simple dimensional reduction to ten-dimensions, reproducing the type IIB\nchiral supergravity. We also show that our supergravity can be consistent\nbackground for super (2+2)-brane theory, satisfying fermionic invariance of the\ntotal action. Such supergravity theory without manifest Lorentz invariance had\nbeen predicted by the recent F-theory in twelve-dimensions.", "category": "hep-th" }, { "text": "Wilson loops in large N field theories: We propose a method to calculate the expectation values of an operator\nsimilar to the Wilson loop in the large N limit of field theories. We consider\nN=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the\narea of a fundamental string worldsheet in certain supergravity backgrounds. We\nalso consider the case of coincident M-theory fivebranes where one is lead to\ncalculating the area of M-theory two-branes. We briefly discuss the computation\nfor 2+1 dimensional super-Yang-Mills with sixteen supercharges which is\nnon-conformal. In all these cases we calculate the energy of quark-antiquark\npair.", "category": "hep-th" }, { "text": "Generalized Poincare algebras and Lovelock-Cartan gravity theory: We show that the Lagrangian for Lovelock-Cartan gravity theory can be\nre-formulated as an action which leads to General Relativity in a certain\nlimit. In odd dimensions the Lagrangian leads to a Chern-Simons theory\ninvariant under the generalized Poincar\\'{e} algebra $\\mathfrak{B}_{2n+1},$\nwhile in even dimensions the Lagrangian leads to a Born-Infeld theory invariant\nunder a subalgebra of the $\\mathfrak{B}_{2n+1}$ algebra. It is also shown that\ntorsion may occur explicitly in the Lagrangian leading to new torsional\nLagrangians, which are related to the Chern-Pontryagin character for the\n$B_{2n+1}$ group.", "category": "hep-th" }, { "text": "Motivic Amplitudes and Cluster Coordinates: In this paper we study motivic amplitudes--objects which contain all of the\nessential mathematical content of scattering amplitudes in planar SYM theory in\na completely canonical way, free from the ambiguities inherent in any attempt\nto choose particular functional representatives. We find that the cluster\nstructure on the kinematic configuration space Conf_n(P^3) underlies the\nstructure of motivic amplitudes. Specifically, we compute explicitly the\ncoproduct of the two-loop seven-particle MHV motivic amplitude A_{7,2} and find\nthat like the previously known six-particle amplitude, it depends only on\ncertain preferred coordinates known in the mathematics literature as cluster\nX-coordinates on Conf_n(P^3). We also find intriguing relations between motivic\namplitudes and the geometry of generalized associahedrons, to which cluster\ncoordinates have a natural combinatoric connection. For example, the\nobstruction to A_{7,2} being expressible in terms of classical polylogarithms\nis most naturally represented by certain quadrilateral faces of the appropriate\nassociahedron. We also find and prove the first known functional equation for\nthe trilogarithm in which all 40 arguments are cluster X-coordinates of a\nsingle algebra. In this respect it is similar to Abel's 5-term dilogarithm\nidentity.", "category": "hep-th" }, { "text": "Electron-positron pairs production in a macroscopic charged core: Classical and semi-classical energy states of relativistic electrons bounded\nby a massive and charged core with the charge-mass-radio Q/M and macroscopic\nradius R_c are discussed. We show that the energies of semi-classical (bound)\nstates can be much smaller than the negative electron mass-energy (-mc^2), and\nenergy-level crossing to negative energy continuum occurs. Electron-positron\npair production takes place by quantum tunneling, if these bound states are not\noccupied. Electrons fill into these bound states and positrons go to infinity.\nWe explicitly calculate the rate of pair-production, and compare it with the\nrates of electron-positron production by the Sauter-Euler-Heisenberg-Schwinger\nin a constant electric field. In addition, the pair-production rate for the\nelectro-gravitational balance ratio Q/M = 10^{-19} is much larger than the\npair-production rate due to the Hawking processes.", "category": "hep-th" }, { "text": "Topological Conformal Algebra in $2d$ Gravity Coupled to Minimal Matter: An infinite number of topological conformal algebras with varying central\ncharges are explicitly shown to be present in $2d$ gravity (treated both in the\nconformal gauge and in the light-cone gauge) coupled to minimal matter. The\ncentral charges of the underlying $N=2$ theory in two different gauge choices\nare generically found to be different. The physical states in these theories\nare briefly discussed in the light of the $N=2$ superconformal symmetry.", "category": "hep-th" }, { "text": "Managing $\u03b3_5$ in Dimensional Regularization II: the Trace with\n more $\u03b3_5$: In the present paper we evaluate the anomaly for the abelian axial current in\na non abelian chiral gauge theory, by using dimensional regularization. This\namount to formulate a procedure for managing traces with more than one\n$\\gamma_5$. \\par The suggested procedure obeys Lorentz covariance and\ncyclicity, at variance with previous approaches (e.g. the celebrated 't Hooft\nand Veltman's where Lorentz is violated) \\par The result of the present paper\nis a further step forward in the program initiated by a previous work on the\ntraces involving a single $\\gamma_5$. The final goal is an unconstrained\ndefinition of $\\gamma_5$ in dimensional regularization. Here, in the evaluation\nof the anomaly, we profit of the axial current conservation equation, when\nradiative corrections are neglected. This kind of tool is not always exploited\nin field theories with $\\gamma_5$, e.g. in the use of dimensional\nregularization of infrared and collinear divergences.", "category": "hep-th" }, { "text": "Absence of the Gribov ambiguity in a quadratic gauge: The Gribov ambiguity exists in various gauges except algebraic gauges.\nHowever, algebraic gauges are not Lorentz invariant, which is their fundamental\nflaw. In addition, they are not generally compatible with the boundary\nconditions on the gauge fields, which are needed to compactify the space i.e.,\nthe ambiguity continues to exist on a compact manifold. Here we discuss a\nquadratic gauge fixing, which is Lorentz invariant. We consider an example of a\nspherically symmetric gauge field configuration in which we prove that this\nLorentz invariant gauge removes the ambiguity on a compact manifold\n$\\mathbb{S}^3$, when a proper boundary condition on the gauge configuration is\ntaken into account. Thus, providing one example where the ambiguity is absent\non a compact manifold in the algebraic gauge. We also show that the \\tmem{BRST}\ninvariance is preserved in this gauge.", "category": "hep-th" }, { "text": "On the Quantum Origin of Structure in the Inflationary Universe: In this lecture I give a pedagogical introduction to inflationary cosmology\nwith a special focus on the quantum generation of cosmological perturbations.", "category": "hep-th" }, { "text": "Two loop five point integrals: light, heavy and large spin correlators: We evaluated all two loop conformal integrals appearing in five point\ncorrelation functions of protected operators of $\\mathcal{N} = 4$ Super\nYang-Mills in several kinematical regimes. Starting from the correlation\nfunction of the lightest operators of the theory, we were able to extract\nstructure constants of up to two spinning operators for small and large values\nof polarizations and spin. We conjectured an universal all loop behaviour for\nthe large spin small polarization structure constants and comment on the\nsubtleties of analytically continuing it from finite to large spin. We also\nconsider correlation functions of heavier operators that get factorized in the\nmore fundamental object called decagon. We fixed this object at two loops in\ngeneral kinematics and studied its physical properties under OPE and null\nlimits.", "category": "hep-th" }, { "text": "Orientifolds, RR Torsion, and K-theory: We analyze the role of RR fluxes in orientifold backgrounds from the point of\nview of K-theory, and demonstrate some physical implications of describing\nthese fluxes in K-theory rather than cohomology. In particular, we show that\ncertain fractional shifts in RR charge quantization due to discrete RR fluxes\nare naturally explained in K-theory. We also show that some orientifold\nbackgrounds, which are considered distinct in the cohomology classification,\nbecome equivalent in the K-theory description, while others become unphysical.", "category": "hep-th" }, { "text": "Towards a Non-Supersymmetric String Phenomenology: Over the past three decades, considerable effort has been devoted to studying\nthe rich and diverse phenomenologies of heterotic strings exhibiting spacetime\nsupersymmetry. Unfortunately, during this same period, there has been\nrelatively little work studying the phenomenologies associated with their\nnon-supersymmetric counterparts. The primary reason for this relative lack of\nattention is the fact that strings without spacetime supersymmetry are\ngenerally unstable, exhibiting large one-loop dilaton tadpoles. In this paper,\nwe demonstrate that this hurdle can be overcome in a class of tachyon-free\nfour-dimensional string models realized through coordinate-dependent\ncompactifications. Moreover, as we shall see, it is possible to construct\nmodels in this class whose low-lying states resemble the Standard Model (or\neven potential unified extensions thereof) --- all without any light\nsuperpartners, and indeed without supersymmetry at any energy scale. The\nexistence of such models thus opens the door to general studies of\nnon-supersymmetric string phenomenology, and in this paper we proceed to\ndiscuss a variety of theoretical and phenomenological issues associated with\nsuch non-supersymmetric strings. On the theoretical side, we discuss the\nfiniteness properties of such strings, the general characteristics of their\nmass spectra, the magnitude and behavior of their one-loop cosmological\nconstants, and their interpolation properties. By contrast, on the\nphenomenological side, the properties we discuss are more model-specific and\ninclude their construction techniques, their natural energy scales, their\nparticle and charge assignments, and the magnitudes of their associated Yukawa\ncouplings and scalar masses.", "category": "hep-th" }, { "text": "Clock Fields and Logarithmic Decay of Dark Energy: We investigate the physical measurability of the infrared instability of a de\nSitter phase in the formalism recently proposed by Kitamoto et al.. We find\nthat the logarithmic decay of the effective cosmological constant is only\nmeasurable if an additional clock field is introduced.", "category": "hep-th" }, { "text": "All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops: We give a closed-form, prescriptive representation of all-multiplicity\ntwo-loop MHV amplitude integrands in fully-color-dressed (non-planar) maximally\nsupersymmetric Yang-Mills theory.", "category": "hep-th" }, { "text": "Slowly rotating Einstein-Maxwell-dilaton black hole and some aspects of\n its thermodynamics: A slowly rotating black hole solution in Einstein-Maxwell-dilaton gravity was\nconsidered. Having used the obtained solution we investigated thermodynamic\nfunctions such as black hole's temperature, entropy and heat capacity. In\naddition to examine thermodynamic properties of the black hole extended\ntechnique was applied. The equation of state of Van der Waals type was obtained\nand investigated. It has been shown that the given system has phase transitions\nof the first as well as of the zeroth order for the temperatures below a\ncritical one which is notable feature of the black hole. A coexistence relation\nfor two phases was also considered and latent heat was calculated. In the end,\ncritical exponents were calculated.", "category": "hep-th" }, { "text": "Celestial Klein Spaces: We consider the analytic continuation of $(p+q)$-dimensional Minkowski space\n(with $p$ and $q$ even) to $(p,q)$-signature, and study the conformal boundary\nof the resulting \"Klein space\". Unlike the familiar $(-+++..)$ signature, now\nthe null infinity ${\\mathcal I}$ has only one connected component. The spatial\nand timelike infinities ($i^0$ and $i'$) are quotients of generalizations of\nAdS spaces to non-standard signature. Together, ${\\mathcal I}, i^0$ and $i'$\ncombine to produce the topological boundary $S^{p+q-1}$ as an $S^{p-1} \\times\nS^{q-1}$ fibration over a null segment. The highest weight states (the\n$L$-primaries) and descendants of $SO(p,q)$ with integral weights give rise to\nnatural scattering states. One can also define $H$-primaries which are highest\nweight with respect to a signature-mixing version of the Cartan-Weyl generators\nthat leave a point on the celestial $S^{p-1} \\times S^{q-1}$ fixed. These\ncorrespond to massless particles that emerge at that point and are Mellin\ntransforms of plane wave states.", "category": "hep-th" }, { "text": "Twist Quantization of String and B Field Background: In a previous paper, we investigated the Hopf algebra structure in string\ntheory and gave a unified formulation of the quantization of the string and the\nspace-time symmetry. In this paper, this formulation is applied to the case\nwith a nonzero B-field background, and the twist of the Poincare symmetry is\nstudied. The Drinfeld twist accompanied by the B-field background gives an\nalternative quantization scheme, which requires a new normal ordering. In order\nto obtain a physical interpretation of this twisted Hopf algebra structure, we\npropose a method to decompose the twist into two successive twists and we give\ntwo different possibilities of decomposition. The first is a natural\ndecomposition from the viewpoint of the twist quantization, leading to a new\ntype of twisted Poincare symmetry. The second decomposition reveals the\nrelation of our formulation to the twisted Poincare symmetry on the Moyal type\nnoncommutative space.", "category": "hep-th" }, { "text": "On string theory on AdS$_3\\times {M}_7$ in the tensionless limit: We review old and recent results on a special limit of string theory on\nAdS$_3\\times M_7$ with pure NS-NS fluxes: the limit in which the string length\n$\\ell_s=\\sqrt{\\alpha'}$ equals the AdS$_3$ radius $R $. At this point of the\nmoduli space, the theory exhibits special properties, which we discuss. Special\nattention is focused on features of correlation functions that are related to\nthe non-compactness of the boundary CFT target space, and on how these features\nchange when the point $k\\equiv R^2/\\alpha ' =1$ is approached. Also, we briefly\nreview recent proposals for exact realizations of AdS/CFT correspondence at\nthis special point. \\[\\] This is the transcript of the talk delivered by the\nauthor at the 8$^{\\text{th}}$ edition of the Quantum Gravity in the Southern\nCone conference, held in Patagonia, December 16$^{\\text{th}}$ -\n20$^{\\text{th}}$, 2019.", "category": "hep-th" }, { "text": "Release of physical modes from unphysical fields: We present a basic idea and a toy model that physical modes originate from\nunobservable fields. The model is defined on a higher-dimensional space-time\nand has fermionic symmetries that make fields unphysical, and observable modes\ncan appear through a dimensional reduction.", "category": "hep-th" }, { "text": "An Alternative Perturbative Expansion in Quantum Mechanics. Scaling and\n cut-off Resummation: An alternative perturbative expansion in quantum mechanics which allows a\nfull expression of the scaling arbitrariness is introduced. This expansion is\nexamined in the case of the anharmonic oscillator and is conveniently resummed\nusing a method which consists in introducing an energy cut-off that is\ncarefully removed as the order of the expansion is increased. We illustrate\nthis technique numerically by computing the asymptotic behavior of the ground\nstate energy of the anharmonic oscillator for large couplings, and show how the\nexploitation of the scaling arbitrariness substantially improves the\nconvergence of this perturbative expansion.", "category": "hep-th" }, { "text": "Particle scattering and vacuum instability by exponential steps: Particle scattering and vacuum instability in a constant inhomogeneous\nelectric field of particular peak configuration that consists of two\n(exponentially increasing and exponentially decreasing) independent parts are\nstudied. It presents a new kind of external field where exact solutions of the\nDirac and Klein-Gordon equations can be found. We obtain and analyze in- and\nout-solutions of the Dirac and Klein-Gordon equations in this configuration. By\ntheir help we calculate probabilities of particle scattering and\ncharacteristics of the vacuum instability. In particular, we consider in\ndetails three configurations: a smooth peak, a sharp peak, and a strongly\nasymmetric peak configuration. We find asymptotic expressions for total mean\nnumbers of created particles and for vacuum-to-vacuum transition probability.\nWe discuss a new regularization of the Klein step by the sharp peak and compare\nthis regularization with another one given by the Sauter potential.", "category": "hep-th" }, { "text": "On holography for (pseudo-)conformal cosmology: We propose a holographic dual for (pseudo-)conformal cosmological scenario,\nwith a scalar field that forms a moving domain wall in adS_5. The domain wall\nseparates two vacua with unequal energy densities. Unlike in the existing\nconstruction, the 5d solution is regular in the relevant space-time domain.", "category": "hep-th" }, { "text": "Multipolar Expansions for the Relativistic N-Body Problem in the\n Rest-Frame Instant Form: Dixon's multipoles for a system of N relativistic positive-energy scalar\nparticles are evaluated in the rest-frame instant form of dynamics. The Wigner\nhyperplanes (intrinsic rest frame of the isolated system) turn out to be the\nnatural framework for describing multipole kinematics. In particular, concepts\nlike the {\\it barycentric tensor of inertia} can be defined in special\nrelativity only by means of the quadrupole moments of the isolated system.", "category": "hep-th" }, { "text": "The effect of different regulators in the non-local field-antifield\n quantization: Recently it was shown how to regularize the Batalin-Vilkovisky (BV)\nfield-antifield formalism of quantization of gauge theories with the non-local\nregularization (NLR) method. The objective of this work is to make an analysis\nof the behaviour of this NLR formalism, connected to the BV framework, using\ntwo different regulators: a simple second order differential regulator and a\nFujikawa-like regulator. This analysis has been made in the light of the well\nknown fact that different regulators can generate different expressions for\nanomalies that are related by a local couterterm, or that are equivalent after\na reparametrization. This has been done by computing precisely the anomaly of\nthe chiral Schwinger model.", "category": "hep-th" }, { "text": "Some views on monopoles and confinement: Aspects of the monopole condensation picture of confinement are discussed.\nFirst, the nature of the monopole singularities in the abelian projection\napproach is analysed. Their apparent gauge dependence is shown to have a\nnatural interpretation in terms of 't~Hooft-Polyakov-like monopoles in\neuclidean SU(2) gauge theory. Next, the results and predictions of a\nrealization of confinement through condensation of such monopoles are\nsummarized and compared with numerical data.", "category": "hep-th" }, { "text": "The CP(n) Model on Noncommutative Plane: We construct the consistent CP(n) model on noncommutative plane. The\nBogomolny bound on the energy is saturated by (anti-)self-dual solitons with\ninteger topological charge, which is independent of their scaling and\norientation. This integer quantization is satisfied for our general solutions,\nwhich turns out regular everywhere. We discuss the possible implication of our\nresult to the instanton physics in Yang-Mills theories on noncommutative R^4.", "category": "hep-th" }, { "text": "Superpotential of Three Dimensional ${\\cal N}=1$ Heterotic Supergravity: We dimensionally reduce the ten dimensional heterotic action on spacetimes of\nthe form ${\\cal M}_{(2,1)}\\times Y$, where ${\\cal M}_{(2,1)}$ is three\ndimensional maximally symmetric Anti de Sitter or Minkowski space, and $Y$ is a\ncompact seven dimensional manifold with $G_2$ structure. In doing so, we derive\nthe real superpotential functional of the corresponding three dimensional\n${\\cal N}=1$ theory. We confirm that extrema of this functional precisely\ncorrespond to supersymmetric heterotic compactifications on manifolds of $G_2$\nstructure. We make some comments on the role of the superpotential functional\nwith respect to the coupled moduli problem of instanton bundles over $G_2$\nmanifolds.", "category": "hep-th" }, { "text": "Building Quantum Field Theories Out of Neurons: An approach to field theory is studied in which fields are comprised of $N$\nconstituent random neurons. Gaussian theories arise in the infinite-$N$ limit\nwhen neurons are independently distributed, via the Central Limit Theorem,\nwhile interactions arise due to finite-$N$ effects or non-independently\ndistributed neurons. Euclidean-invariant ensembles of neurons are engineered,\nwith tunable two-point function, yielding families of Euclidean-invariant field\ntheories. Some Gaussian, Euclidean invariant theories are reflection positive,\nwhich allows for analytic continuation to a Lorentz-invariant quantum field\ntheory. Examples are presented that yield dual theories at infinite-$N$, but\nhave different symmetries at finite-$N$. Landscapes of classical field\nconfigurations are determined by local maxima of parameter distributions.\nPredictions arise from mixed field-neuron correlators. Near-Gaussianity is\nexhibited at large-$N$, potentially explaining a feature of field theories in\nNature.", "category": "hep-th" }, { "text": "Komar energy and Smarr formula for noncommutative Schwarzschild black\n hole: We calculate the Komar energy $E$ for a noncommutative Schwarzschild black\nhole. A deformation from the conventional identity $E=2ST_H$ is found in the\nnext to leading order computation in the noncommutative parameter $\\theta$\n(i.e. $\\mathcal{O}(\\sqrt{\\theta}e^{-M^2/\\theta})$) which is also consistent\nwith the fact that the area law now breaks down. This deformation yields a\nnonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes.\nWe then work out the Smarr formula, clearly elaborating the differences from\nthe standard result $M=2ST_H$, where the mass ($M$) of the black hole is\nidentified with the asymptotic limit of the Komar energy. Similar conclusions\nare also shown to hold for a deSitter--Schwarzschild geometry.", "category": "hep-th" }, { "text": "Soft Supersymmetry Breaking in Anisotropic LARGE Volume\n Compactifications: We study soft supersymmetry breaking terms for anisotropic LARGE volume\ncompactifications, where the bulk volume is set by a fibration with one small\nfour-cycle and one large two-cycle. We consider scenarios where D7s wrap either\na blow-up cycle or the small fibre cycle. Chiral matter can arise either from\nmodes parallel or perpendicular to the brane. We compute soft terms for this\nmatter and find that for the case where the D7 brane wraps the fibre cycle the\nscalar masses can be parametrically different, allowing a possible splitting of\nthird-generation soft terms.", "category": "hep-th" }, { "text": "On the Lorentz Transformations of Momentum and Energy: Motivated by ultra-high-energy cosmic ray physics, we discuss all the\npossible alternatives to the familiar Lorentz transformations of the momentum\nand the energy of a particle. Starting from natural physical requirements, we\nexclude all the possibilities, apart from the ones which arise from the usual\nfour-vector transformations by means of a change of coordinates in the\nmass-shell. This result confirms the remark, given in a preceding paper, that,\nin a theory without preferred inertial frames, one can always define a linearly\ntransforming energy parameter to which the GZK cutoff argument can be applied.\nWe also discuss the connections between the conservation and the transformation\nproperties of energy-momentum and the relation between energy-momentum and\nvelocity.", "category": "hep-th" }, { "text": "Behavior of Cosmological Perturbations in the Brane-World Mode: In this paper we present a gauge-invariant formalism for perturbations of the\nbrane-world model developed by the author, A. Ishibashi and O. Seto recently,\nand analyze the behavior of cosmological perturbations in a spatially flat\nexpanding universe realized as a boundary 3-brane in AdS$^5$ in terms of this\nformalism. For simplicity we restrict arguments to scalar perturbations. We\nshow that the behavior of cosmological perturbations on superhorizon scales in\nthe brane-world model is the same as that in the standard no-extradimension\nmodel, irrespective of the initial condition for bulk perturbations, in the\nlate stage when the cosmic expansion rate $H$ is smaller than the inverse of\nthe bulk curvature scale $\\ell$. Further, we give rough estimates which\nindicate that in the early universe when $H$ is much larger than $1/\\ell$,\nperturbations in these two models behave quite differently, and the\nconservation of the Bardeen parameter does not hold for superhorizon\nperturbations in the brane-world model.", "category": "hep-th" }, { "text": "$q$-Virasoro/W Algebra at Root of Unity and Parafermions: We demonstrate that the parafermions appear in the $r$-th root of unity limit\nof $q$-Virasoro/$W_n$ algebra. The proper value of the central charge of the\ncoset model $ \\frac{\\widehat{\\mathfrak{sl}}(n)_r \\oplus\n\\widehat{\\mathfrak{sl}}(n)_{m-n}}{\\widehat{\\mathfrak{sl}}(n)_{m-n+r}}$ is given\nfrom the parafermion construction of the block in the limit.", "category": "hep-th" }, { "text": "Ghost wave-function renormalization in Asymptotically Safe Quantum\n Gravity: Motivated by Weinberg's asymptotic safety scenario, we investigate the\ngravitational renormalization group flow in the Einstein-Hilbert truncation\nsupplemented by the wave-function renormalization of the ghost fields. The\nlatter induces non-trivial corrections to the beta-functions for Newton's\nconstant and the cosmological constant. The resulting ghost-improved phase\ndiagram is investigated in detail. In particular, we find a non-trivial\nultraviolet fixed point in agreement with the asymptotic safety conjecture,\nwhich also survives in the presence of extra dimensions. In four dimensions the\nghost anomalous dimension at the fixed point is $\\eta_c^* = -1.8$, supporting\nspace-time being effectively two-dimensional at short distances.", "category": "hep-th" }, { "text": "M-Theory, Torons and Confinement: We study the decompactification limit of M-theory superpotentials for N=1\nfour dimensional supersymmetric gauge theories. These superpotentials can be\ninterpreted as generated by toron configurations. The connection with the\nconfinement picture in the maximal abelian gauge is discussed.", "category": "hep-th" }, { "text": "Recurrent dynamical symmetry breaking and restoration by Wilson lines at\n finite densities on a torus: In this paper we derive the general expression of a one-loop effective\npotential of the nonintegrable phases of Wilson lines for an SU(N) gauge theory\nwith a massless adjoint fermion defined on the spactime manifold\n$R^{1,d-3}\\times T^2$ at finite temperature and fermion density. The Phase\nstructure of the vacuum is presented for the case with $d=4$ and N=2 at zero\ntemperature. It is found that gauge symmetry is broken and restored alternately\nas the fermion density increases, a feature not found in the Higgs mechanism.\nIt is the manifestation of the quantum effects of the nonintegrable phases.", "category": "hep-th" }, { "text": "Higuchi Bound on Slow Roll Inflation and the Swampland: In this paper we study the implications of the generalized Higuchi bound on\nmassive spin-two fields for the derivative of the scalar potential within\nbimetric theory. In contrast to the recent de Sitter swampland conjecture, an\nupper bound on the derivate of the scalar potential follows from the\ngeneralized Higuchi bound. In combination, this leaves a window for the\nderivate of the scalar potential. We discuss this bound in several\nrepresentative bimetric models and parameter regions.", "category": "hep-th" }, { "text": "Classifying BPS bosonic Wilson loops in 3d ${\\cal N}=4$\n Chern-Simons-matter theories: We study the possible BPS Wilson loops in three-dimensional ${\\cal N}=4$\nChern-Simons-matter theory which involve only the gauge field and bilinears of\nthe scalars. Previously known examples are the analogues of the Gaiotto-Yin\nloops preserving four supercharges and \"latitude\" loops preserving two. We\ncarry out a careful classification and find, in addition, loops preserving\nthree supercharges, further inequivalent classes of loops preserving two\nsupercharges and loops preserving a single supercharge. For each of the classes\nof loops, we present a representative example and analyse their full orbit\nunder the broken symmetries.", "category": "hep-th" }, { "text": "Momentum in Single-trace $T\\bar T$ Holography: We extend the study of 2006.13249, 2303.12422 to black strings with general\nmomentum, and discuss their interpretation in single-trace $T\\bar T$ deformed\n$CFT_2$.", "category": "hep-th" }, { "text": "Matrix 3-Lie superalgebras and BRST supersymmetry: Given a matrix Lie algebra one can construct the 3-Lie algebra by means of\nthe trace of a matrix. In the present paper we show that this approach can be\nextended to the infinite-dimensional Lie algebra of vector fields on a manifold\nif instead of the trace of a matrix we consider a differential 1-form which\nsatisfies certain conditions. Then we show that the same approach can be\nextended to matrix Lie superalgebras if instead of the trace of a matrix we\nmake use of the super trace of a matrix. It is proved that a graded triple\ncommutator of matrices constructed with the help of the graded commutator and\nthe super trace satisfies a graded ternary Filippov-Jacobi identity. In two\nparticular cases and we show that the Pauli and Dirac matrices generate the\nmatrix 3-Lie superalgebras, and we find the non-trivial graded triple\ncommutators of these algebras. We propose a Clifford algebra approach to 3-Lie\nsuperalgebras induced by Lie superalgebras. We also discuss an application of\nmatrix 3-Lie superalgebras in BRST-formalism.", "category": "hep-th" }, { "text": "Strong coupling in extended Horava-Lifshitz gravity: An extension of Horava-Lifshitz gravity was recently proposed in order to\naddress the pathological behavior of the scalar mode all previous versions of\nthe theory exhibit. We show that even in this new extension the strong coupling\npersists, casting doubts on whether such a model can constitute an interesting\nalternative to general relativity (GR).", "category": "hep-th" }, { "text": "Fedosov Deformation Quantization as a BRST Theory: The relationship is established between the Fedosov deformation quantization\nof a general symplectic manifold and the BFV-BRST quantization of constrained\ndynamical systems. The original symplectic manifold $\\mathcal M$ is presented\nas a second class constrained surface in the fibre bundle ${{\\mathcal\nT}^*_\\rho}{\\mathcal M}$ which is a certain modification of a usual cotangent\nbundle equipped with a natural symplectic structure. The second class system is\nconverted into the first class one by continuation of the constraints into the\nextended manifold, being a direct sum of ${{\\mathcal T}^*_\\rho}{\\mathcal M}$\nand the tangent bundle $T {\\mathcal M}$. This extended manifold is equipped\nwith a nontrivial Poisson bracket which naturally involves two basic\ningredients of Fedosov geometry: the symplectic structure and the symplectic\nconnection. The constructed first class constrained theory, being equivalent to\nthe original symplectic manifold, is quantized through the BFV-BRST procedure.\nThe existence theorem is proven for the quantum BRST charge and the quantum\nBRST invariant observables. The adjoint action of the quantum BRST charge is\nidentified with the Abelian Fedosov connection while any observable, being\nproven to be a unique BRST invariant continuation for the values defined in the\noriginal symplectic manifold, is identified with the Fedosov flat section of\nthe Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized\nas a conventional product of the quantum BRST invariant observables.", "category": "hep-th" }, { "text": "Kerr-Bolt Black Hole Entropy and Soft Hair: Recently it has been speculated that a set of infinitesimal ${\\rm\nVirasoro_{\\,L}}\\otimes{\\rm Virasoro_{\\,R}}$ diffeomorphisms exist which act\nnon-trivially on the horizon of some black holes such as kerr and Kerr-Newman\nblack hole \\cite{Haco:2018ske,Haco:2019ggi}. Using this symmetry in covariant\nphase space formalism one can obtains Virasoro charges as surface integrals on\nthe horizon. Kerr-Bolt spacetime is well-known for its asymptotically topology\nand has been studied widely in recent years. In this work we are interested to\nfind conserved charge associated to the Virosora symmetry of Kerr-Bolt geometry\nusing covariant phase space formalism. We will show right and left central\ncharge are $c_R=c_L=12 J$ respectively. Our results also show good agreement\nwith Kerr spacetime in the limiting behavior.", "category": "hep-th" }, { "text": "A Smooth Exit from Eternal Inflation?: The usual theory of inflation breaks down in eternal inflation. We derive a\ndual description of eternal inflation in terms of a deformed Euclidean CFT\nlocated at the threshold of eternal inflation. The partition function gives the\namplitude of different geometries of the threshold surface in the no-boundary\nstate. Its local and global behavior in dual toy models shows that the\namplitude is low for surfaces which are not nearly conformal to the round\nthree-sphere and essentially zero for surfaces with negative curvature. Based\non this we conjecture that the exit from eternal inflation does not produce an\ninfinite fractal-like multiverse, but is finite and reasonably smooth.", "category": "hep-th" }, { "text": "Reheating in small-field inflation on the brane: The Swampland Criteria\n and observational constraints in light of the PLANCK 2018 results: We study cosmological inflation and its dynamics in the framework of the\nRandall-Sundrum II brane model. In particular, we analyze in detail four\nrepresentative small-field inflationary potentials, namely Natural inflation,\nHilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each\ncharacterized by two mass scales. We constrain the parameters for which a\nviable inflationary Universe emerges using the latest PLANCK results.\nFurthermore, we investigate whether or not those models in brane cosmology are\nconsistent with the recently proposed Swampland Criteria, and give predictions\nfor the duration of reheating as well as for the reheating temperature after\ninflation. Our results show that (i) the distance conjecture is satisfied, (ii)\nthe de Sitter conjecture and its refined version may be avoided, and (iii) the\nallowed range for the five-dimensional Planck mass, $M_5$, is found to be\nbetween $10^5~\\textrm{TeV}$ and $10^{12}~\\textrm{TeV}$. Our main findings\nindicate that non-thermal leptogenesis cannot work within the framework of\nRS-II brane cosmology, at least for the inflationary potentials considered\nhere.", "category": "hep-th" }, { "text": "On the correspondence between the classical and quantum gravity: The relationship between the classical and quantum theories of gravity is\nreexamined. The value of the gravitational potential defined with the help of\nthe two-particle scattering amplitudes is shown to be in disagreement with the\nclassical result of General Relativity given by the Schwarzschild solution. It\nis shown also that the potential so defined fails to describe whatever\nnon-Newtonian interactions of macroscopic bodies. An alternative interpretation\nof the $\\hbar^0$-order part of the loop corrections is given directly in terms\nof the effective action. Gauge independence of that part of the one-loop\nradiative corrections to the gravitational form factors of the scalar particle\nis proved, justifying the interpretation proposed.", "category": "hep-th" }, { "text": "Cosmology and the Fate of Dilatation Symmetry: We discuss the cosmological constant problem in the light of dilatation\nsymmetry and its possible anomaly. For dilatation symmetric quantum theories\nrealistic asymptotic cosmology is obtained provided the effective potential has\na non-trivial minimum. For theories with dilatation anomaly one needs as a\nnon-trivial \"cosmon condition\" that the energy-momentum tensor in the vacuum is\npurely anomalous. Such a condition is related to the short-distance\nrenormalization group behavior of the fundamental theory. Observable deviations\nfrom the standard hot big bang cosmology are possible.", "category": "hep-th" }, { "text": "The Dirac operator on hypersurfaces: Odd-dimensional Riemannian spaces that are non-orientable, but have a pin\nstructure, require the consideration of the twisted adjoint representation of\nthe corresponding pin group. It is shown here how the Dirac operator should be\nmodified, also on even-dimensional spaces, to make it equivariant with respect\nto the action of that group when the twisted adjoint representation is used in\nthe definition of the pin structure. An explicit description of a pin structure\non a hypersurface, defined by its immersion in a Euclidean space, is used to\nderive a \"Schroedinger\" transform of the Dirac operator in that case. This is\nthen applied to obtain - in a simple manner - the spectrum and eigenfunctions\nof the Dirac operator on spheres and real projective spaces.", "category": "hep-th" }, { "text": "N-vaton: In general there are a large number of light scalar fields in the theories\ngoing beyond standard model, such as string theory, and some of them can be\ntaken as the candidates of curvatons. For simplicity, we assume all of\ncurvatons have the same decay rate and suddenly decay into radiation at the\nsame time. In order to distinguish this scenario from the more general case, we\ncall it \"N-vaton\". We use $\\delta {\\cal N}$ formalism to calculate the\nprimordial power spectrum and bispectrum in N-vaton model and investigate\nvarious bounds on the non-Gaussianity parameter $f_{NL}$. A red tilted\nprimordial power spectrum and a large value of $f_{NL}$ can be naturally\nobtained if the curvature perturbation generated by inflaton also makes a\nsignificant contribution to the primordial power spectrum. As a realistic\nN-vaton model, we suppose that the axions in the KKLT compactifications of Type\nIIB string theory are taken as curvatons and a rich phenomenology is obtained.", "category": "hep-th" }, { "text": "Light-front gauge invariant formulation and electromagnetic duality: The gauge invariant formulation of Maxwell's equations and the\nelectromagnetic duality transformations are given in the light-front (LF)\nvariables. The novel formulation of the LF canonical quantization, which is\nbased on the kinematic translation generator $P^{+}$ rather then on the\nHamiltonian $P^{-}$, is proposed. This canonical quantization is applied for\nthe free electromagnetic fields and for the fields generated by electric and\nmagnetic external currents. The covariant form of photon propagators, which\nagrees with Schwinger's source theory, is achieved when the direct interaction\nof external currents is properly chosen. Applying the path integral formalism,\nthe equivalent LF Lagrangian density, which depends on two Abelian gauge\npotentials, is proposed. Some remarks on the Dirac strings and LF non local\nstructures are presented in the Appendix.", "category": "hep-th" }, { "text": "Stability and fluctuation modes of giant gravitons with NSNS B field: We study the stability of the giant gravitons in the string theory background\nwith NSNS B field. We consider the perturbation of giant gravitons formed by a\nprobe D$(8-p)$ brane in the background generated by D$(p-2)$-D$(p)$ branes for\n$2 \\le p \\le 5$. We use the quadratic approximation to the brane action to find\nthe equations of motion. For $p=5$, giant graviton configurations are stable\nindependent of the size of the brane. For $p \\ne 5$, we calculated the range of\nthe size of the brane where they are stable. We also present the mode\nfrequencies explicitly for some special cases.", "category": "hep-th" }, { "text": "Ground states of holographic superconductors: We investigate the ground states of the Abelian Higgs model in AdS_4 with\nvarious choices of parameters, and with no deformations in the ultraviolet\nother than a chemical potential for the electric charge under the Abelian gauge\nfield. For W-shaped potentials with symmetry-breaking minima, an analysis of\ninfrared asymptotics suggests that the ground state has emergent conformal\nsymmetry in the infrared when the charge of the complex scalar is large enough.\nBut when this charge is too small, the likeliest ground state has Lifshitz-like\nscaling in the infrared. For positive mass quadratic potentials, Lifshitz-like\nscaling is the only possible infrared behavior for constant nonzero values of\nthe scalar. The approach to Lifshitz-like scaling is shown in many cases to be\noscillatory.", "category": "hep-th" }, { "text": "Little IIB Matrix Model: We study the zero-dimensional reduced model of D=6 pure super Yang-Mills\ntheory and argue that the large N limit describes the (2,0) Little String\nTheory. The one-loop effective action shows that the force exerted between two\ndiagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional\nspacetime. We also observe that it is due to non-gravitational interactions. We\nconstruct wave functions and vertex operators which realize the D=6, (2,0)\ntensor representation. We also comment on other \"little\" analogues of the IIB\nmatrix model and Matrix Theory with less supercharges.", "category": "hep-th" }, { "text": "A Coherent State Path Integral for Anyons: We derive an $su(1,1)$ coherent state path integral formula for a system of\ntwo one-dimensional anyons in a harmonic potential. By a change of variables we\ntransform this integral into a coherent states path integral for a harmonic\noscillator with a shifted energy. The shift is the same as the one obtained for\nanyons by other methods. We justify the procedure by showing that the change of\nvariables corresponds to a $su(1,1)$ version of the Holstein-Primakoff\ntransformation.", "category": "hep-th" }, { "text": "Minkowski Conformal Blocks and the Regge Limit for SYK-like Models: We discuss scattering in a CFT via the conformal partial-wave analysis and\nthe Regge limit. The focus of this paper is on understanding an OPE with\nMinkowski conformal blocks. Starting with a t-channel OPE, it leads to an\nexpansion for an s-channel scattering amplitude in terms of t-channel\nexchanges. By contrasting with Euclidean conformal blocks we see a precise\nrelationship between conformal blocks in the two limits without preforming an\nexplicit analytic continuation. We discuss a generic feature for a CFT\ncorrelation function having singular $F^{(M)}(u,v)\\sim {u}^{-\\delta}\\,$,\n$\\delta>0$, in the limit $u \\rightarrow 0$ and $v\\rightarrow 1$. Here,\n$\\delta=(\\ell_{eff}-1)/2$, with $\\ell_{eff}$ serving as an effective spin and\nit can be determined through an OPE. In particular, it is bounded from above,\n$\\ell_{eff} \\leq 2$, for all CFTs with a gravity dual, and it can be associated\nwith string modes interpolating the graviton in AdS. This singularity is\nhistorically referred to as the Pomeron. This bound is nearly saturated by\nSYK-like effective $d=1$ CFT, and its stringy and thermal corrections have\npiqued current interests. Our analysis has been facilitated by dealing with\nWightman functions. We provide a direct treatment in diagonalizing dynamical\nequations via harmonic analysis over physical scattering regions. As an example\nthese methods are applied to the SYK model.", "category": "hep-th" }, { "text": "Eikonal phase matrix, deflection angle and time delay in effective field\n theories of gravity: The eikonal approximation is an ideal tool to extract classical observables\nin gauge theory and gravity directly from scattering amplitudes. Here we\nconsider effective theories of gravity where in addition to the\nEinstein-Hilbert term we include non-minimal couplings of the type $R^3$, $R^4$\nand $FFR$. In particular, we study the scattering of gravitons and photons of\nfrequency $\\omega$ off heavy scalars of mass $m$ in the limit $m\\gg \\omega \\gg\n|\\vec{q}\\,|$, where $\\vec{q}$ is the momentum transfer. The presence of\nnon-minimal couplings induces helicity-flip processes which survive the eikonal\nlimit, thereby promoting the eikonal phase to an eikonal phase matrix. We\nobtain the latter from the relevant two-to-two helicity amplitudes that we\ncompute up to one-loop order, and confirm that the leading-order terms in\n$\\omega$ exponentiate \\`{a} la Amati, Ciafaloni and Veneziano. From the\neigenvalues of the eikonal phase matrix we then extract two physical\nobservables, to 2PM order: the classical deflection angle and Shapiro time\ndelay/advance. Whenever the classical expectation of helicity conservation of\nthe massless scattered particle is violated, i.e. the eigenvalues of the\neikonal matrix are non-degenerate, causality violation due to time advance is a\ngeneric possibility for small impact parameter. We show that for graviton\nscattering in the $R^4$ and $FFR$ theories, time advance is circumvented if the\ncouplings of these interactions satisfy certain positivity conditions, while it\nis unavoidable for graviton scattering in the $R^3$ theory and photon\nscattering in the $FFR$ theory. The scattering processes we consider mimic the\ndeflection of photons and gravitons off spinless heavy objects such as\nblack~holes.", "category": "hep-th" }, { "text": "Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2): In this note we study worldsheet two- and four-point functions at the\none-loop level for the type IIA superstring in AdS(3) x S(3) x M(4) . We first\naddress the regularization ambiguity that appears in the dispersion relation\nderived from integrability. We demonstrate that only the regulator treating all\nfields equally respects worldsheet supersymmetry. This is done in an implicit\nregularization scheme where all divergent terms are collected into master\ntadpole-type integrals. We then investigate one-loop two-body scattering on the\nstring worldsheet and verify that a recent proposal for the dressing phase\nreproduces explicit worldsheet computations. All calculations are done in a\nnear-BMN like expansion of the Green-Schwarz superstring equipped with quartic\nfermions.", "category": "hep-th" }, { "text": "Gauge symmetry of unimodular gravity in Hamiltonian formalism: We work out the description of the gauge symmetry of unimodular gravity in\nthe constrained Hamiltonian formalism. In particular, we demonstrate how the\ntransversality conditions restricting the diffeomorphism parameters emerge from\nthe algebra of the Hamiltonian constraints. The alternative form is long known\nas parametrizing the volume preserving diffeomorphisms by unrestricted\ntwo-forms instead of the transverse vector fields. This gauge symmetry is\nreducible. We work out the Hamiltonian description of this form of unimodular\ngravity (UG) gauge symmetry.\nBecchi-Rouet-Stora-Tyutin--Batalin-Fradkin-Vilkovisky (BFV-BRST) Hamiltonian\nformalism is constructed for both forms of the UG gauge symmetry. These two\nBRST complexes have a subtle inequivalence: Their BRST cohomology groups are\nnot isomorphic. In particular, for the first complex, which is related to the\nrestricted gauge parameters, the cosmological constant does not correspond to\nany nontrivial BRST cocycle, while for the alternative complex it does. In the\nwording of physics, this means $\\Lambda$ is a fixed parameter defined by the\nfield asymptotics rather than the physical observable from the standpoint of\nthe first complex. The second formalism views $\\Lambda$ as the observable with\nunrestricted initial data.", "category": "hep-th" }, { "text": "Neutrino Majorana Masses from String Theory Instanton Effects: Finding a plausible origin for right-handed neutrino Majorana masses in\nsemirealistic compactifications of string theory remains one of the most\ndifficult problems in string phenomenology. We argue that right-handed neutrino\nMajorana masses are induced by non-perturbative instanton effects in certain\nclasses of string compactifications in which the $U(1)_{B-L}$ gauge boson has a\nSt\\\"uckelberg mass. The induced operators are of the form $e^{-U}\\nu_R\\nu_R$\nwhere $U$ is a closed string modulus whose imaginary part transforms\nappropriately under $B-L$. This mass term may be quite large since this is not\na gauge instanton and $Re U$ is not directly related to SM gauge couplings.\nThus the size of the induced right-handed neutrino masses could be a few orders\nof magnitude below the string scale, as phenomenologically required. It is also\nargued that this origin for neutrino masses would predict the existence of\nR-parity in SUSY versions of the SM. Finally we comment on other\nphenomenological applications of similar instanton effects, like the generation\nof a $\\mu$-term, or of Yukawa couplings forbidden in perturbation theory.", "category": "hep-th" }, { "text": "Thirring Model as a Gauge Theory: We reformulate the Thirring model in $D$ $(2 \\le D < 4)$ dimensions as a\ngauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the\ndynamical mass generation of the fermion through the Schwinger-Dyson (SD)\nequation. By virtue of such a gauge symmetry we can greatly simplify the\nanalysis of the SD equation by taking the most appropriate gauge (``nonlocal\ngauge'') for the HLS.\n In the case of even-number of (2-component) fermions, we find the dynamical\nfermion mass generation as the second order phase transition at certain fermion\nnumber, which breaks the chiral symmetry but preserves the parity in (2+1)\ndimensions ($D=3$). In the infinite four-fermion coupling (massless gauge\nboson) limit in (2+1) dimensions, the result coincides with that of the\n(2+1)-dimensional QED, with the critical number of the 4-component fermion\nbeing $N_{\\rm cr} = \\frac{128}{3\\pi^{2}}$. As to the case of odd-number\n(2-component) fermion in (2+1) dimensions, the regularization ambiguity on the\ninduced Chern-Simons term may be resolved by specifying the regularization so\nas to preserve the HLS.\n Our method also applies to the (1+1) dimensions, the result being consistent\nwith the exact solution. The bosonization mechanism in (1+1) dimensional\nThirring model is also reproduced in the context of dual-transformed theory for\nthe HLS.", "category": "hep-th" }, { "text": "Finite Size Scaling in Quantum Hallography: At low temperatures observations of the Hall resistance for Quantum Hall\nsystems at the interface between two Hall plateaux reveal a power-law\nbehaviour, dR_xy/dB ~ T^(-p) (with p = 0.42 +/- 0.01); changing at still\nsmaller temperatures, T < T_s, to a temperature-independent value. Experiments\nalso show that the transition temperature varies with sample size, L, according\nto T_s ~ 1/L. These experiments pose a potential challenge to the holographic\nAdS/QHE model recently proposed in arXiv:1008.1917. This proposal, which was\nmotivated by the natural way AdS/CFT methods capture the emergent duality\nsymmetries exhibited by quantum Hall systems, successfully describes the\nscaling exponent p by relating it to an infrared dynamical exponent z with p =\n2/z. For a broad class of models z is robustly shown to be z = 5 in the regime\nrelevant to the experiments (though becoming z = 1 further in the ultraviolet).\nBy incorporating finite-size effects into these models we show that they\nreproduce a transition to a temperature-independent regime, predicting a\ntransition temperature satisfying T_s ~ 1/L or ~ 1/L^5 in two separate regions\nof parameter space, even though z = 5 governs the temperature dependence of the\nconductivity in both cases. The possibility of a deviation from naive z = 5\nscaling arises because the brane tension introduces a new scale, which alters\nwhere the transition between UV and IR scaling occurs, in an L-dependent way.\nThe AdS/CFT calculation indicates the two regimes of temperature scaling are\nseparated by a first-order transition, suggesting new possibilities for testing\nthe picture experimentally. Remarkably, in this interpretation the gravity dual\nof the transition from temperature scaling to temperature-independent\nresistance is related to the Chandrashekar transition from a star to a black\nhole with increasing mass.", "category": "hep-th" }, { "text": "Is it possible to recover information from the black-hole radiation?: In the framework of communication theory, we analyse the gedanken experiment\nin which beams of quanta bearing information are flashed towards a black hole.\nWe show that stimulated emission at the horizon provides a correlation between\nincoming and outgoing radiations consisting of bosons. For fermions, the\nmechanism responsible for the correlation is the Fermi exclusion principle.\nEach one of these mechanisms is responsible for the a partial transfer of the\ninformation originally coded in the incoming beam to the black--hole radiation.\nWe show that this process is very efficient whenever stimulated emission\noverpowers spontaneous emission (bosons). Thus, black holes are not `ultimate\nwaste baskets of information'.", "category": "hep-th" }, { "text": "Tachyon Perturbation on Two Dimensional Black Hole: We study the geometry of the two dimensional string theoretic black hole\nunder tachyonic perturbations. These perturbations are restricted to affect\nonly the metric and the dilaton, while other string theoretic excitations (like\nthe axion) are ignored. The metric and linearized dilaton perturbations are\ndetermined to lowest non-trivial order of the tachyonic hair in the presence of\nback reaction. We evaluate the Kretschmann scalar and argue that the horizon\ndoes not become singular in the presence of tachyon perturbations (to the order\nof our consideration). A closed-form solution of the allowed tachyon field and\nthat of the allowed tachyon potential emerges as a requirement of\nself-consistency of our solution.", "category": "hep-th" }, { "text": "On the localization of fermions on thick D-branes: Hints on the possible localization of fermions on double thick D-branes\n(Domain Walls) are found by analyzing the moduli space of parameters. Deeper\nanalysis toward this direction might help to select phenomenologically\nplausible models. A new kind of condition for fermion localization is proposed.\nThis might be useful in multi-brane-world scenarios, which are important when\nsymmetry breaking is considered in the AdS/CFT formalism, as well as in curved\nbrane-worlds.", "category": "hep-th" }, { "text": "Conformal Symmetry for Black Holes in Four Dimensions and Irrelevant\n Deformations: It has been argued several times in the past that the structure of the\nentropy formula for general non-extremal asymptotically flat black holes in\nfour dimensions can be understood in terms of an underlying conformal symmetry.\nA recent implementation of this idea, carried out by Cveti\\v{c} and Larsen,\ninvolves the replacement of a conformal factor in the original geometry by an\nalternative conformal factor in such a way that the near-horizon behavior and\nthermodynamic properties of the black hole remain unchanged, while only the\nasymptotics or \"environment\" of the geometry are modified. The solution thus\nobtained, dubbed \"subtracted geometry\", uplifts to an asymptotically\nAdS$_{3}\\times S^{2}$ black hole in five dimensions, and an AdS/CFT\ninterpretation is then possible. Building on this intuition we show that, at\nleast in the static case, the replacement of the conformal factor can be\nimplemented dynamically by means of an interpolating flow which we construct\nexplicitly. Furthermore, we show that this flow can be understood as the effect\nof irrelevant perturbations from the point of view of the dual two-dimensional\nCFT, and we identify the quantum numbers of the operators responsible for the\nflow. This allows us to address quantitatively the validity of CFT computations\nfor these asymptotically flat black holes and provides a framework to\nsystematically compute corrections to the CFT results.", "category": "hep-th" }, { "text": "Comment on \"Relativistic extension of shape-invariant potentials\": This comment directs attention to some fails of the Alhaidari approach to\nsolve relativistic problems. It is shown that his gauge considerations are way\noff the mark and that the class of exactly solvable relativistic problems is\nnot so enlarged as Alhaidari thinks it is.", "category": "hep-th" }, { "text": "D-branes on Calabi-Yau Manifolds and Superpotentials: We show how to compute terms in an expansion of the world-volume\nsuperpotential for fairly general D-branes on the quintic Calabi-Yau using\nlinear sigma model techniques, and show in examples that this superpotential\ncaptures the geometry and obstruction theory of bundles and sheaves on this\nCalabi-Yau.", "category": "hep-th" }, { "text": "Particles creation from JNW quantum perturbed black holes by minimally\n coupled Klein Gordon scalar free fields: In this work, we choose a minimal coupling interaction between massive Klein\nGordon (KG) quantum scalar free fields and Janis-Newman-Winicour (JNW)\nspherically symmetric static black hole, to produce its Hawking temperature and\nluminosity. This is done by calculating asymptotic wave solutions at near and\nfar from the black hole horizon. They are orthogonal mode solutions of local\nHilbert spaces. By using these mode solutions, we calculated Bogolubov\ncoefficients and then, we investigated number density matrix of created\nparticles. Mathematical calculations show that this is not exactly similar to\nthe Planck`s black body radiation energy density distribution but, it is \"gray\"\nbody radiation distribution depended to the emitted Hawking particles\nfrequency. Their difference is a non-vanishing absorptivity factor of\nbackscattered particles after to form horizon of a collapsing body. Our\nmotivation is determination of position of Hawking created pairs in which, two\ndifferent proposals are proposed, so called as \"fairwall\" and \"quantum\natmosphere\".", "category": "hep-th" }, { "text": "Supersymmetric WZW $\u03c3$ Model on Full and Half Plane: We study classical integrability of the supersymmetric U(N) $\\sigma$ model\nwith the Wess-Zumino-Witten term on full and half plane. We demonstrate the\nexistence of nonlocal conserved currents of the model and derive general\nrecursion relations for the infinite number of the corresponding charges in a\nsuperfield framework. The explicit form of the first few supersymmetric charges\nare constructed. We show that the considered model is integrable on full plane\nas a concequence of the conservation of the supersymmetric charges. Also, we\nstudy the model on half plane with free boundary, and examine the conservation\nof the supersymmetric charges on half plane and find that they are conserved as\na result of the equations of motion and the free boundary condition. As a\nresult, the model on half plane with free boundary is integrable. Finally, we\nconclude the paper and some features and comments are presented.", "category": "hep-th" }, { "text": "Classical W-symmetry and Grassmannian Manifold: Classical W-symmetry is globally parametrized by the Grassmannian Manifold\nwhich is associated with the non-relativistic fermions. We give the\nbosonization rule which defines the natural higher coordinates system to\ndescribe the W-geometry. Generators of the W-algebra can be obtained from a\nsingle tau-function by using vertex operators.", "category": "hep-th" }, { "text": "Fields in nonaffine bundles. III. Effective symmetries and conserved\n currents in strings and higher branes: The principles of a previously developed formalism for the covariant\ntreatment of multi-scalar fields for which (as in a nonlinear sigma model) the\nrelevant target space is not of affine type -- but curved -- are recapitulated.\nTheir application is extended from ordinary harmonic models to a more general\ncategory of \"harmonious\" field models, with emphasis on cases in which the\nfield is confined to a string or higher brane worldsheet, and for which the\nrelevant internal symmetry group is non Abelian, so that the conditions for\nconservation of the corresponding charge currents become rather delicate,\nparticularly when the symmetry is gauged. Attention is also given to the\nconditions for conservation of currents of a different kind -- representing\nsurface fluxes of generalised momentum or energy -- associated with symmetries\nnot of the internal target space but of the underlying spacetime background\nstructure, including the metric and any relevant gauge field. For the\ncorresponding current to be conserved the latter need not be manifestly\ninvariant: preservation modulo a gauge adjustment will suffice. The simplest\ncase is that of \"strong\" symmetry, meaning invariance under the action of an\neffective Lie derivative (an appropriately gauge adjusted modification of an\nordinary Lie derivative). When the effective symmetry is of the more general\n\"weak\" kind, the kinetic part of the current is not conserved by itself but\nonly after being supplemented by a suitable contribution from the background.", "category": "hep-th" }, { "text": "Deformation Theory of Holomorphic Vector Bundles, Extended Conformal\n Symmetry and Extensions of 2D Gravity: Developing on the ideas of R. Stora and coworkers, a formulation of two\ndimensional field theory endowed with extended conformal symmetry is given,\nwhich is based on deformation theory of holomorphic and Hermitian spaces. The\ngeometric background consists of a vector bundle $E$ over a closed surface\n$\\Sigma$ endowed with a holomorphic structure and a Hermitian structure\nsubordinated to it. The symmetry group is the semidirect product of the\nautomorphism group ${\\rm Aut}(E)$ of $E$ and the extended Weyl group ${\\rm\nWeyl}(E)$ of $E$ and acts on the holomorphic and Hermitian structures. The\nextended Weyl anomaly can be shifted into an automorphism chirally split\nanomaly by adding to the action a local counterterm, as in ordinary conformal\nfield theory. The dependence on the scale of the metric on the fiber of $E$ is\nencoded in the Donaldson action, a vector bundle generalization of the\nLiouville action. The Weyl and automorphism anomaly split into two\ncontributions corresponding respectively to the determinant and\nprojectivization of $E$. The determinant part induces an effective ordinary\nWeyl or diffeomorphism anomaly and the induced central charge can be computed.", "category": "hep-th" }, { "text": "Super-renormalizable or Finite Lee-Wick Quantum Gravity: We propose a class of multidimensional higher derivative theories of gravity\nwithout extra real degrees of freedom besides the graviton field. The\npropagator shows up the usual real graviton pole and extra complex conjugates\npoles that do not contribute to the absorptive part of the physical scattering\namplitudes. Indeed, they may consistently be excluded from the asymptotic\nobservable states of the theory making use of the Lee-Wick and Cutkoski,\nLandshoff, Olive and Polkinghorne prescription for the construction of a\nunitary S-matrix. Therefore, the spectrum consists on the graviton and short\nlived elementary unstable particles that we named \"anti-gravitons\" because of\ntheir repulsive contribution to the gravitational potential at short distance.\nHowever, another interpretation of the complex conjugate pairs is proposed\nbased on the Calmet's suggestion, i.e. they could be understood as black hole\nprecursors long established in the classical theory. Since the theory is CPT\ninvariant, the complex conjugate of the micro black hole precursor has received\nas a white hole precursor consistently with the t'Hooft complementary\nprinciple. It is proved that the quantum theory is super-renormalizable in even\ndimension, i.e. only a finite number of divergent diagrams survive, and finite\nin odd dimension. Furthermore, turning on a local potential of the Riemann\ntensor we can make the theory finite in any dimension. The singularity-free\nNewtonian gravitational potential is explicitly computed for a range of higher\nderivative theories. Finally, we propose a new super-reneromalizable or finite\nLee-Wick standard model of particle physics.", "category": "hep-th" }, { "text": "Bulk and brane radiative effects in gauge theories on orbifolds: We have computed one-loop bulk and brane mass renormalization effects in a\nfive-dimensional gauge theory compactified on the M_4 \\times S^1/Z_2 orbifold,\nwhere an arbitrary gauge group G is broken by the orbifold action to its\nsubgroup H. The space-time components of the gauge boson zero modes along the H\ngenerators span the gauge theory on the orbifold fixed point branes while the\nzero modes of the higher-dimensional components of the gauge bosons along the\nG/H generators play the role of Higgs fields with respect to the gauge group H.\nNo quadratic divergences in the mass renormalization of the gauge and Higgs\nfields are found either in the bulk or on the branes. All brane effects for the\nHiggs field masses vanish (only wave function renormalization effects survive)\nwhile bulk effects are finite and can trigger, depending on the fermionic\ncontent of the theory, spontaneous Hosotani breaking of the brane gauge group\nH. For the gauge fields we do find logarithmic divergences corresponding to\nmass renormalization of their heavy Kaluza-Klein modes. Two-loop brane effects\nfor Higgs field masses are expected from wave function renormalization brane\neffects inserted into finite bulk mass corrections.", "category": "hep-th" }, { "text": "Non-Higgsable clusters for 4D F-theory models: We analyze non-Higgsable clusters of gauge groups and matter that can arise\nat the level of geometry in 4D F-theory models. Non-Higgsable clusters seem to\nbe generic features of F-theory compactifications, and give rise naturally to\nstructures that include the nonabelian part of the standard model gauge group\nand certain specific types of potential dark matter candidates. In particular,\nthere are nine distinct single nonabelian gauge group factors, and only five\ndistinct products of two nonabelian gauge group factors with matter, including\n$SU(3) \\times SU(2)$, that can be realized through 4D non-Higgsable clusters.\nThere are also more complicated configurations involving more than two gauge\nfactors; in particular, the collection of gauge group factors with jointly\ncharged matter can exhibit branchings, loops, and long linear chains.", "category": "hep-th" }, { "text": "Critical Phenomena, Strings, and Interfaces: Some points concerning the relation of strings to interfaces in statistical\nsystems are discussed.", "category": "hep-th" }, { "text": "Superfield approach to symmetry invariance in QED with complex scalar\n fields: We show that the Grassmannian independence of the super Lagrangian density,\nexpressed in terms of the superfields defined on a (4, 2)-dimensional\nsupermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST)\nand anti-BRST invariance of the corresoponding four (3 + 1)-dimensional (4D)\nLagrangian density that describes the interaction between the U(1) gauge field\nand the charged complex scalar fields. The above 4D field theoretical model is\nconsidered on a (4, 2)-dimensional supermanifold parametrized by the ordinary\nfour spacetime variables x^\\mu (with \\mu = 0, 1, 2, 3) and a pair of\nGrassmannian variables \\theta and \\bar\\theta (with \\theta^2 = \\bar\\theta^2 = 0,\n\\theta \\bar\\theta + \\bar\\theta \\theta = 0). Geometrically, the (anti-)BRST\ninvariance is encoded in the translation of the super Lagrangian density along\nthe Grassmannian directions of the above supermanifold such that the outcome of\nthis shift operation is zero.", "category": "hep-th" }, { "text": "Gauged D=7 Supergravity on the S**1/Z_2 Orbifold: We construct the most general couplings of a bulk seven-dimensional\nYang-Mills-Einstein N=2 supergravity with a boundary six-dimensional chiral\nN=(0,1) theory of vectors and charged hypermultiplets. The boundary consists of\ntwo brane worlds sitting at the fixed points of an S^1/Z_2 compactification of\nthe seven-dimensional bulk supergravity. The resulting 6D massless spectrum\nsurviving the orbifold projection is anomalous. By introducing boundary fields\nat the orbifold fixed points, we show that all anomalies are cancelled by a\nGreen-Schwarz mechanism. In addition, all couplings of the boundary fields to\nthe bulk are completely specified by supersymmetry. We emphasize that there is\nno bulk Chern-Simons term to cancel the anomalies. The latter is traded for a\nGreen-Schwarz term which emerges in the boundary theory after a duality\ntransformation implemented to construct the bulk supergravity.", "category": "hep-th" }, { "text": "Anomalies on Orbifolds: We discuss the form of the chiral anomaly on an S1/Z2 orbifold with chiral\nboundary conditions. We find that the 4-divergence of the higher-dimensional\ncurrent evaluated at a given point in the extra dimension is proportional to\nthe probability of finding the chiral zero mode there. Nevertheless the\nanomaly, appropriately defined as the five dimensional divergence of the\ncurrent, lives entirely on the orbifold fixed planes and is independent of the\nshape of the zero mode. Therefore long distance four dimensional anomaly\ncancellation ensures the consistency of the higher dimensional orbifold theory.", "category": "hep-th" }, { "text": "Disc partition function of 2d $R^2$ gravity from DWG matrix model: We compute the sum over flat surfaces of disc topology with arbitrary number\nof conical singularities. To that end, we explore and generalize a specific\ncase of the matrix model of dually weighted graphs (DWG) proposed and solved by\none of the authors, M. Staudacher and Th. Wynter. Namely, we compute the sum\nover quadrangulations of the disc with certain boundary conditions, with\nparameters controlling the number of squares (area), the length of the boundary\nand the coordination numbers of vertices. The vertices introduce conical\ndefects with angle deficit given by a multiple of $\\pi$, corresponding to\npositive, zero or negative curvature. Our results interpolate between the\nwell-known 2d quantum gravity solution for the disc with fluctuating 2d metric\nand the regime of 'almost flat' surfaces with all the negative curvature\nconcentrated on the boundary. We also speculate on possible ways to study the\nfluctuating 2d geometry with $AdS_2$ background instead of the flat one.", "category": "hep-th" }, { "text": "Multi-Regge kinematics and the scattering equations: We study the solutions to the scattering equations in various\nquasi-multi-Regge regimes where the produced particles are ordered in rapidity.\nWe observe that in all cases the solutions to the scattering equations admit\nthe same hierarchy as the rapidity ordering, and we conjecture that this\nbehaviour holds independently of the number of external particles. In\nmulti-Regge limit, where the produced particles are strongly ordered in\nrapidity, we determine exactly all solutions to the scattering equations that\ncontribute to the Cachazo-He-Yuan (CHY) formula for gluon scattering in this\nlimit. When the CHY formula is localised on these solutions, it reproduces the\nexpected factorisation of tree-level amplitudes in terms of impact factors and\nLipatov vertices. We also investigate amplitudes in various quasi-MRK. While in\nthese cases we cannot determine the solutions to the scattering equations\nexactly, we show that again our conjecture combined with the CHY formula\nimplies the factorisation of the amplitude into universal buildings blocks for\nwhich we obtain a CHY-type representation.", "category": "hep-th" }, { "text": "Ultraviolet Behavior of N=8 Supergravity: In these lectures I describe the remarkable ultraviolet behavior of N=8\nsupergravity, which through four loops is no worse than that of N=4\nsuper-Yang-Mills theory (a finite theory). I also explain the computational\ntools that allow multi-loop amplitudes to be evaluated in this theory - the KLT\nrelations and the unitarity method - and sketch how ultraviolet divergences are\nextracted from the amplitudes.", "category": "hep-th" }, { "text": "Running Shear Viscosities in Anisotropic Holographic Superfluids: We have examined holographic renormalization group($RG$) flows of the shear\nviscosities in anisotropic holographic superfluids via their gravity duals,\nEinstein-SU(2) Yang-Mills system. In anisotropic phase, below the critical\ntemperature $T_c$, the SO(3) isometry(spatial rotation) in the dual gravity\nsystem is broken down to the residual SO(2). The shear viscosities in the\nsymmetry broken directions of the conformal fluids defined on $AdS$ boundary\npresent non-universal values which depend on the chemical potential $\\mu$ and\ntemperature $T$ of the system and also satisfy non-trivial holographic\n$RG$-flow equations. The shear viscosities flow down to the specific values in\n$IR$ region, in fact which are given by the ratios of the metric components in\nthe symmetry unbroken direction to those in the broken directions, evaluated at\nthe black brane horizon in the dual gravity system.", "category": "hep-th" }, { "text": "Inequivalent Quantization in the Skyrme Model: Quantum mechanics on manifolds is not unique and in general infinite number\nof inequivalent quantizations can be considered. They are specified by the\ninduced spin and the induced gauge structures on the manifold. The\nconfiguration space of collective mode in the Skyrme model can be identified\nwith $S^{3}$ and thus the quantization is not unique. This leads to the\ndifferent predictions for the physical observables.", "category": "hep-th" }, { "text": "Inflation, Gravity Mediated Supersymmetry Breaking, and de Sitter Vacua\n in Supergravity with a K\u00e4hler-Invariant FI Term: We use a new mechanism for generating a Fayet-Iliopoulos term in\nsupergravity, which is not associated to an R symmetry, to construct a\nsemi-realistic theory of slow-roll inflation for a theory with the same\nK\\\"ahler potential and superpotential as the KKLT string background (without\nanti-D3 branes). In our model, supersymmetry must be broken at a high scale in\na hidden sector to ensure that the cutoff of the effective field theory is\nabove the Hubble scale of inflation. The gravitino has a super-EeV mass and\nsupersymmetry breaking is communicated to the observable sector through gravity\nmediation. Some mass scales of the supersymmetry-breaking soft terms in the\nobservable sector can be parametrically smaller than the SUSY breaking scale.\nIf a string realization of the new FI term were found, our model could be the\nbasis for a low energy effective supergravity description of realistic\nsuperstring models of inflation.", "category": "hep-th" }, { "text": "Derived Categories and Zero-Brane Stability: We define a particular class of topological field theories associated to open\nstrings and prove the resulting D-branes and open strings form the bounded\nderived category of coherent sheaves. This derivation is a variant of some\nideas proposed recently by Douglas. We then argue that any 0-brane on any\nCalabi-Yau threefold must become unstable along some path in the Kahler moduli\nspace. As a byproduct of this analysis we see how the derived category can be\ninvariant under a birational transformation between Calabi-Yaus.", "category": "hep-th" }, { "text": "Magnetized Type I Orbifolds in Four Dimensions: I review the basic features of four dimensional Z_2 x Z_2 (shift)\norientifolds with internal magnetic fields, describing two examples with N=1\nsupersymmetry. As in the corresponding six-dimensional examples, D9-branes\nmagnetized along four internal directions can mimic D5-branes, even in presence\nof multiplets of image branes localized on different fixed tori. Chiral\nlow-energy spectra can be obtained if the model also contains D5-branes\nparallel to the magnetized directions.", "category": "hep-th" }, { "text": "On duality of the noncommutative extension of the Maxwell-Chern-Simons\n model: We study issues of duality in 3D field theory models over a canonical\nnoncommutative spacetime and obtain the noncommutative extension of the\nSelf-Dual model induced by the Seiberg-Witten map. We apply the dual projection\ntechnique to uncover some properties of the noncommutative Maxwell-Chern-Simons\ntheory up to first-order in the noncommutative parameter. A duality between\nthis theory and a model similar to the ordinary self-dual model is\nestabilished. The correspondence of the basic fields is obtained and the\nequivalence of algebras and equations of motion are directly verified. We also\ncomment on previous results in this subject.", "category": "hep-th" }, { "text": "Living on the walls of super-QCD: We study BPS domain walls in four-dimensional $\\mathcal{N}=1$ massive SQCD\nwith gauge group $SU(N)$ and $F N=1 Breaking in Supergravity: We discuss some issues related to spontaneous N=2-> N=1 supersymmetry\nbreaking. In particular, we state a set of geometrical conditions which are\nnecessary that such a breaking occurs. Furthermore, we discuss the low energy\nN=1 effective Lagrangian and show that it satisfies non-trivial consistency\nconditions which can also be viewed as conditions on the geometry of the scalar\nmanifold.", "category": "hep-th" }, { "text": "Flat deformations of type IIB S-folds: Type IIB S-folds of the form $\\textrm{AdS}_{4} \\times \\textrm{S}^1 \\times\n\\textrm{S}^5$ have been shown to contain axion-like deformations parameterising\nflat directions in the 4D scalar potential and corresponding to marginal\ndeformations of the dual S-fold CFT's. In this note we present a\ngroup-theoretical characterisation of such flat deformations and provide a 5D\ninterpretation thereof in terms of $\\mathfrak{so}(6)$-valued duality twists\ninducing a class of Cremmer--Scherk--Schwarz flat gaugings in a reduction from\n5D to 4D. In this manner we establish the existence of two flat deformations\nfor the $\\mathcal{N}=4$ and $\\textrm{SO}(4)$ symmetric S-fold causing a\nsymmetry breaking down to its $\\textrm{U}(1)^2$ Cartan subgroup. The result is\na new two-parameter family of non-supersymmetric S-folds which are\nperturbatively stable at the lower-dimensional supergravity level, thus\nproviding the first examples of such type IIB backgrounds.", "category": "hep-th" }, { "text": "The central charge in three dimensional anti-de Sitter space: This paper collects the various ways of computing the central charge\n$c=3l/2G$ arising in 3d asymptotically anti-de Sitter spaces, in the\nChern-Simons formulation. Their similarities and differences are displayed.", "category": "hep-th" }, { "text": "Non-Unitary Holography: We propose gauge theory/gravity duality involving conformal theories based on\nU(N+k|k) gauge groups. We show that to all orders in 1/N these non-unitary\ntheories based on supergroups are indistinguishable from the corresponding\nunitary theories where the gauge group is replaced by U(N). This leads to\nnon-unitary gravity duals which to all orders in 1/N are indistinguishable from\ntheir unitary cousins. They are distinguished by operators whose correlation\nfunctions differ by O(exp(-aN)). The celebrated type IIB on AdS^5 x S^5 and\nM-theory on AdS^4 x S^7 fall in this class and thus seem to also admit\nnon-unitary non-perturbative completions. It is tempting to conjecture that\nthis setup may provide a non-unitary model for black hole evaporation.", "category": "hep-th" }, { "text": "The web of swampland conjectures and the TCC bound: We consider the swampland distance and de Sitter conjectures, of respective\norder one parameters $\\lambda$ and $c$. Inspired by the recent Trans-Planckian\nCensorship conjecture (TCC), we propose a generalization of the distance\nconjecture, which bounds $\\lambda$ to be a half of the TCC bound for $c$, i.e.\n$\\lambda \\geq \\frac{1}{2}\\sqrt{\\frac{2}{3}}$ in 4d. In addition, we propose a\ncorrespondence between the two conjectures, relating the tower mass $m$ on the\none side to the scalar potential $V$ on the other side schematically as $m\\sim\n|V|^{\\frac{1}{2}}$, in the large distance limit. These proposals suggest a\ngeneralization of the scalar weak gravity conjecture, and are supported by a\nvariety of examples. The lower bound on $\\lambda$ is verified explicitly in\nmany cases in the literature. The TCC bound on $c$ is checked as well on ten\ndifferent no-go theorems, which are worked-out in detail, and $V$ is analysed\nin the asymptotic limit. In particular, new results on 4d scalar potentials\nfrom type II compactifications are obtained.", "category": "hep-th" }, { "text": "Problems and Progress in Covariant High Spin Description: A universal description of particles with spins j greater or equal one ,\ntransforming in (j,0)+(0,j), is developed by means of representation specific\nsecond order differential wave equations without auxiliary conditions and in\ncovariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac\nspinor components for fermions, or, within the basis of the more fundamental\nWeyl-Van-der-Waerden sl(2,C) spinor-tensors. At the root of the method, which\nis free from the pathologies suffered by the traditional approaches, are\nprojectors constructed from the Casimir invariants of the spin-Lorentz group,\nand the group of translations in the Minkowski space time.", "category": "hep-th" }, { "text": "Proper treatment of scalar and vector exponential potentials in the\n Klein-Gordon equation: Scattering and bound states: We point out a misleading treatment in the literature regarding to\nbound-state solutions for the $s$-wave Klein-Gordon equation with exponential\nscalar and vector potentials. Following the appropriate procedure for an\narbitrary mixing of scalar and vector couplings, we generalize earlier works\nand present the correct solution to bound states and additionally we address\nthe issue of scattering states. Moreover, we present a new effect related to\nthe polarization of the charge density in the presence of weak short-range\nexponential scalar and vector potentials.", "category": "hep-th" }, { "text": "Primordial perturbations and non-Gaussianities in DBI and general\n multi-field inflation: We study cosmological perturbations in general inflation models with multiple\nscalar fields and arbitrary kinetic terms, with special emphasis on the\nmulti-field extension of Dirac-Born-Infeld (DBI) inflation. We compute the\nsecond-order action governing the dynamics of linear perturbations in the most\ngeneral case. Specializing to DBI, we show that the adiabatic and entropy modes\npropagate with a {\\it common} effective sound speed and are thus amplified at\nsound horizon crossing. In the small sound speed limit, we find that the\namplitude of the entropy modes is much higher than that of the adiabatic modes.\nWe also derive, in the general case, the third-order action which is useful for\nstudying primordial non-Gaussianities generated during inflation. In the DBI\ncase, we compute the dominant contributions to non-Gaussianities, which depend\non both the adiabatic and entropy modes.", "category": "hep-th" }, { "text": "Energy functionals from Conformal Gravity: We provide a new derivation of the Hawking mass and Willmore energy\nfunctionals for asymptotically AdS spacetimes, by embedding Einstein-AdS\ngravity in Conformal Gravity. By construction, the evaluation of the\nfour-dimensional Conformal Gravity action in a manifold with a conical defect\nproduces a codimension-2 conformal invariant functional $L_{\\Sigma}$. The\nenergy functionals are then particular cases of $L_{\\Sigma}$ for Einstein-AdS\nand pure AdS ambient spaces, respectively. The bulk action is finite for AdS\nasymptotics and both Hawking mass and Willmore energy are finite as well. The\nresult suggests a generic relation between conformal invariance and\nrenormalization, where the codimension-2 properties are inherited from the bulk\ngravity action.", "category": "hep-th" }, { "text": "Classical BRST charge for nonlinear algebras: We study the construction of the classical nilpotent canonical BRST charge\nfor the nonlinear gauge algebras where a commutator (in terms of Poisson\nbrackets) of the constraints is a finite order polynomial of the constraints.\nSuch a polynomial is characterized by the coefficients forming a set of higher\norder structure constraints. Assuming the set of constraints to be linearly\nindependent, we find the restrictions on the structure constraints when the\nnilpotent BRST charge can be written in a simple and universal form. In the\ncase of quadratically nonlinear algebras we find the expression for third order\ncontribution in the ghost fields to the BRST charge without the use of any\nadditional restrictions on the structure constants.", "category": "hep-th" }, { "text": "Superstring Perturbation Theory Revisited: Perturbative superstring theory is revisited, with the goal of giving a\nsimpler and more direct demonstration that multi-loop amplitudes are\ngauge-invariant (apart from known anomalies), satisfy space-time supersymmetry\nwhen expected, and have the expected infrared behavior. The main technical tool\nis to make the whole analysis, including especially those arguments that\ninvolve integration by parts, on supermoduli space, rather than after\ndescending to ordinary moduli space.", "category": "hep-th" }, { "text": "The large $N$ phase diagram of ${\\cal N}=2$ $SU(N)$ Chern-Simons theory\n with one fundamental chiral multiplet: We study the theory of a single fundamental fermion and boson coupled to\nChern-Simons theory at leading order in the large $N$ limit. Utilizing recent\nprogress in understanding the Higgsed phase in Chern-Simons-Matter theories, we\ncompute the quantum effective potential that is exact to all orders in the 't\nHooft coupling for the lightest scalar operator of this theory at finite\ntemperature. Specializing to the zero temperature limit we use this potential\nto determine the phase diagram of the large $N$ ${\\cal N}=2$ supersymmetric\ntheory with this field content. This intricate two dimensional phase diagram\nhas four topological phases that are separated by lines of first and second\norder phase transitions and includes special conformal points at which the\ninfrared dynamics is governed by Chern-Simons theory coupled respectively to\nfree bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus\nfree fermions. We also describe the vacuum structure of the most general ${\\cal\nN} = 1$ supersymmetric theory with one fundamental boson and one fundamental\nfermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of\nthe 't Hooft coupling.", "category": "hep-th" }, { "text": "Landau quantization for a neutral particle in presence of topological\n defects: In this paper we study the Landau levels in the non-relativistic dynamics of\na neutral particle which possesses a permanent magnetic dipole moment\ninteracting with an external electric field in the curved spacetime background\nwith the presence or absence of a torsion field. The eigenfunction and\neigenvalues of Hamiltonian are obtained. We show that the presence of the\ntopological defect breaks the infinite degeneracy of the Landau levels arising\nin this system. We also apply a duality transformation to discuss this same\nquantization for a dynamics of a neutral particle with a permanent electric\ndipole moment.", "category": "hep-th" }, { "text": "Massive Type IIA Theory on K3: In this paper we study K3 compactification of ten-dimensional massive type\nIIA theory with all possible Ramond-Ramond background fluxes turned on. The\nresulting six-dimensional theory is a new massive (gauged) supergravity with an\naction that is manifestly invariant under an O(4,20) / (O(4) times O(20))\nduality symmetry. We discover that this six-dimensional theory interpolates\nbetween vacua of ten-dimensional massive IIA supergravity and vacua of massless\nIIA supergravity with appropriate background fluxes turned on. This in turn\nsuggests a new 11-dimensional interpretation for the massive type IIA theory.", "category": "hep-th" }, { "text": "A new method for probing the late-time dynamics in the Lorentzian type\n IIB matrix model: The type IIB matrix model has been investigated as a possible nonperturbative\nformulation of superstring theory. In particular, it was found by Monte Carlo\nsimulation of the Lorentzian version that the 9-dimensional rotational symmetry\nof the spatial matrices is broken spontaneously to the 3-dimensional one after\nsome \"critical time\". In this paper we develop a new simulation method based on\nthe effective theory for the submatrices corresponding to the late time. Using\nthis method, one can obtain the results for $N\\times N$ matrices by simulating\nmatrices typically of the size $O(\\sqrt{N})$. We confirm the validity of this\nmethod and demonstrate its usefulness in simplified models.", "category": "hep-th" }, { "text": "Super Landau-Ginzburg mirrors and algebraic cycles: We investigate the super Landau-Ginzburg mirrors of gauged linear sigma\nmodels which, in an appropriate low energy limit, reduce to nonlinear sigma\nmodels with Kaehler supermanifold target spaces of nonnegative super-first\nChern class.", "category": "hep-th" }, { "text": "The extension of the massless fermion in the cosmic string spacetime: In this work, we have obtained the solutions of a massless fermion which is\nunder the external magnetic field around a cosmic string for specific three\npotential models using supersymmetric quantum mechanics. The constant magnetic\nfield, energy dependent potentials and position dependent mass models are\ninvestigated for the Dirac Hamiltonians and an extension of these three\npotential models and their solutions are also obtained. The energy spectrum and\npotential graphs for each case are discussed for the $\\alpha$ deficit angle.", "category": "hep-th" }, { "text": "Radiative Corrections in Nonrelativistic Chern-Simons Theory: We present the one-loop scalar field effective potential for the $N=2$\nsupersymmetric nonrelativistic self-interacting matter fields coupled to an\nAbelian Chern-Simons gauge field and for its generalization when bosonic matter\nfields are coupled to non-Abelian Chern-Simons field. In both models, Gauss's\nlaw linearly relates the magnetic field to the matter field densities; hence,\nwe also include radiative effects from the background gauge field. We compute\nthe scalar field effective potentials in two gauge families, a gauge\nreminiscent of the $R_\\xi$-gauge in the limit $\\xi\\rightarrow 0$ and in the\nCoulomb family gauges. We regularize the theory with operator regularization\nand a cutoff to demonstrate that the results are independent of the\nregularization scheme.", "category": "hep-th" }, { "text": "Abelian Chern-Simons field theory and anyon equation on a cylinder: We present the anyon equation on a cylinder and in an infinite potential wall\nfrom the abelian Chern-Simons theory coupled to non-relativistic matter field\nby obtaining the effective hamiltonian through the canonical transformation\nmethod used for the theory on a plane and on a torus. We also give the periodic\nproperty of the theory on the cylinder.", "category": "hep-th" }, { "text": "DeWitt-Virasoro construction in tensor representations: We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987\n[hep-th] to tensor representations of higher ranks. A rank-$n$ tensor state,\nwhich is by itself coordinate invariant, is expanded in terms of position\neigenstates that transform as tensors of the same rank. The representation of\nthe momentum operator in these basis states is then obtained by generalizing\nDeWitt's argument in Phys.Rev.85:653-661,1952. Such a representation is written\nin terms of certain bi-vector of parallel displacement and its covariant\nderivatives. With this machinery at hand we find tensor representations of the\nDWV generators defined in the previous work. The results differ from those in\nspin-zero representation by additional terms involving the spin connection.\nHowever, we show that the DWV algebra found earlier as a scalar expectation\nvalue remains the same, as required by consistency, as all the additional\ncontributions conspire to cancel in various ways. In particular, vanishing of\nthe anomaly term requires the same condition of Ricci-flatness for the\nbackground.", "category": "hep-th" }, { "text": "A Note About Localized Photons on the Brane: A first order formulation for the Maxwell field in five dimensions is\ndimensionally reduced using the Randall-Sundrum mechanism. We will see that\nmassive photons can not be localized on the brane.", "category": "hep-th" }, { "text": "Quantum Field, Thermodynamics and Black Hole on Coherent State\n Representation of Fuzzy Space: We first use the coherent state formalism of fuzzy space to show that the\nfuzziness will eliminate point-like structure of a particle in favor of smeared\nobject, which is an exponential decay function in contrast to the Gaussian type\nin the Moyal noncommutative space. The exponential decay function implies that,\nin the UV region, the fuzziness provides an extra power-decay factor in the\nFeynman propagator, contrasts to the exponential-decay factor in the Moyal\nspace. We also calculate the particle heat capacity and see that it approaches\nto zero at high temperature. Next, we use the found smeared source to study the\nSchwarzschild-like geometry and see that the black hole can reach a finite\nmaximum temperature before cooling down to absolute zero and leave a stable\nremnant, as that in the noncommutative case. The properties of fuzzy 3D BTZ and\nthe fuzzy Kaluza-Klein black holes are also discussed. Finally, we present a\ncriterion for existence a regular black hole with a general smeared source\nfunction.", "category": "hep-th" }, { "text": "Conformal Anomaly and Off-Shell Extensions of Gravity: The gauge dependence of the conformal anomaly for spin 3/2 and spin 2 fields\nin non-conformal supergravities has been a long standing puzzle. In this Letter\nwe argue that the `correct' gauge choice is the one that follows from requiring\nall terms that would imply a violation of the Wess-Zumino consistency condition\nto be absent in the counterterm, because otherwise the usual link between the\nanomaly and the one-loop divergence becomes invalid. Remarkably, the `good'\nchoice of gauge is the one that confirms our previous result that a complete\ncancellation of conformal anomalies in D=4 can only be achieved for N-extended\n(Poincar\\'e) supergravities with $N\\geq 5$.", "category": "hep-th" }, { "text": "Non-Hermitian Lagrangian for quasi-relativistic fermions: We present a Lorentz-symmetry violating Lagrangian for free fermions, which\nis local but not Hermitian, whereas the corresponding Hamiltonian is Hermitian\nbut not local. A specific feature of the model is that the dispersion relation\nis relativistic in both the IR and in the UV, but not in an intermediate\nregime, set by a given mass scale. The consistency of the model is shown by the\nstudy of properties expected in analogy with the Dirac Lagrangian.", "category": "hep-th" }, { "text": "Wedge-Local Quantum Fields and Noncommutative Minkowski Space: Within the setting of a recently proposed model of quantum fields on\nnoncommutative Minkowski spacetime, the consequences of the consistent\napplication of the proper, untwisted Poincare group as the symmetry group are\ninvestigated. The emergent model contains an infinite family of fields which\nare labelled by different noncommutativity parameters, and related to each\nother by Lorentz transformations. The relative localization properties of these\nfields are investigated, and it is shown that to each field one can assign a\nwedge-shaped localization region of Minkowski space. This assignment is\nconsistent with the principles of covariance and locality, i.e. fields\nlocalized in spacelike separated wedges commute.\n Regarding the model as a non-local, but wedge-local, quantum field theory on\nordinary (commutative) Minkowski spacetime, it is possible to determine\ntwo-particle S-matrix elements, which turn out to be non-trivial. Some partial\nnegative results concerning the existence of observables with sharper\nlocalization properties are also obtained.", "category": "hep-th" }, { "text": "Large N and double scaling limits in two dimensions: Recently, the author has constructed a series of four dimensional\nnon-critical string theories with eight supercharges, dual to theories of light\nelectric and magnetic charges, for which exact formulas for the central charge\nof the space-time supersymmetry algebra as a function of the world-sheet\ncouplings were obtained. The basic idea was to generalize the old matrix model\napproach, replacing the simple matrix integrals by the four dimensional matrix\npath integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov\ncritical points by the Argyres-Douglas critical points. In the present paper,\nwe study qualitatively similar toy path integrals corresponding to the two\ndimensional N=2 supersymmetric non-linear sigma model with target space CP^n\nand twisted mass terms. This theory has some very strong similarities with N=2\nsuper Yang-Mills, including the presence of critical points in the vicinity of\nwhich the large n expansion is IR divergent. The model being exactly solvable\nat large n, we can study non-BPS observables and give full proofs that double\nscaling limits exist and correspond to universal continuum limits. A complete\ncharacterization of the double scaled theories is given. We find evidence for\ndimensional transmutation of the string coupling in some non-critical string\ntheories. We also identify en passant some non-BPS particles that become\nmassless at the singularities in addition to the usual BPS states.", "category": "hep-th" }, { "text": "The Algebra of Chern-Simons Classes and the Poisson Bracket on it: Developing ideas based on combinatorial formulas for characteristic classes\nwe introduce the algebra modeling secondary characteristic classes associated\nto $N$ connections. Certain elements of the algebra correspond to the ordinary\nand secondary characteristic classes.That construction allows us to give easily\nthe explicit formulas for some known secondary classes and to construct the new\nones. We write how $i$-th differential and $i$-th homotopy operator in the\nalgebra are connected with the Poisson bracket defined in this algebra. There\nis an analogy between this algebra and the noncommutative symplectic geometry\nof Kontsevich. We consider then an algebraic model of the action of the gauge\ngroup. We describe how elements in the algebra corresponding to the secondary\ncharacteristic classes change under this action.", "category": "hep-th" }, { "text": "Non supersymmetric femion boson symmetry: In this work we present symmetry transformations relating bosons to fermions\nwhich cannot be represented as a supersymmetric algebra. We present a symmetry\ntransformation relating a complex scalar and a fermion in four dimensions and\nconstruct a theory defined by an action that respects the symmetry quantum\nmechanically. We next invoke gauge symmetry by adding a gauge field and a\ncorresponding fermion and construct two different symmetry transformations with\ncorresponding actions such that the corresponding theories respect the fermion\nboson symmetry transformations quantum mechanically. Unlike in a supersymmetric\ntheory, the vacuum energy in the above theories could be negative.\nPhenomenological implications of the theories are open to research.", "category": "hep-th" }, { "text": "Noncommutative hamiltonian formalism for noncommutative gravity: We present a covariant canonical formalism for noncommutative gravity, and in\ngeneral for noncommutative geometric theories defined via a twisted\n$\\star$-wedge product between forms. Noether theorems are generalized to the\nnoncommutative setting, and gauge generators are constructed in a twisted phase\nspace with $\\star$-deformed Poisson bracket. This formalism is applied to\nnoncommutative $d=4$ vierbein gravity, and allows to find the canonical\ngenerators of the tangent space $\\star$-gauge group.", "category": "hep-th" }, { "text": "Curiosities on Free Fock Spaces: We consider some curious aspects of single-species free Fock spaces, such as\nnovel bosonization and fermionization formulae and relations to various\nphysical properties of bosonic particles. We comment on generalizations of\nthese properties to physically more interesting many-species free Fock spaces.", "category": "hep-th" }, { "text": "One-loop analysis with nonlocal boundary conditions: In the eighties, Schroder studied a quantum mechanical model where the\nstationary states of Schrodinger's equation obey nonlocal boundary conditions\non a circle in the plane. For such a problem, we perform a detailed one-loop\ncalculation for three choices of the kernel characterizing the nonlocal\nboundary conditions. In such cases, the zeta(0) value is found to coincide with\nthe one resulting from Robin boundary conditions. The detailed technique here\ndeveloped may be useful for studying one-loop properties of quantum field\ntheory and quantum gravity if nonlocal boundary conditions are imposed.", "category": "hep-th" }, { "text": "Massless Thirring fermion fields in the boson field representation: We show that the boson field representation of the massless fermion fields,\nsuggested by Morchio, Pierotti and Strocchi in J. Math. Phys. 33, 777 (1992)\nfor the operator solution of the massless Thirring model, agrees completely\nwith the existence of the chirally broken phase in the massless Thirring model\nrevealed in EPJC 20, 723 (2001) and hep-th/0112183, when the free massless\nboson fields are described by the quantum field theory, free of infrared\ndivergences in 1+1-dimensional space-time, formulated in hep-th/0112184 and\nhep-th/0204237.", "category": "hep-th" }, { "text": "Supergravity EFTs and swampland constraints: In these proceedings, we review recent progress in analyzing the behavior of\nlower-dimensional supergravity theories when combined with swampland\nconjectures. We show that within supergravity the effectiveness and usefulness\nof swampland conjectures gets amplified, existing criteria can be intertwined\nand also new ones can be uncovered. Furthermore, we elaborate on some\npreviously unpublished work. This includes evidence for the possible existence\nof a novel conjecture on Yukawa couplings and an argument to constrain large\nclasses of D-term inflationary models using known conjectures.", "category": "hep-th" }, { "text": "The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM: We give an explicit recursive formula for the all L-loop integrand for\nscattering amplitudes in N=4 SYM in the planar limit, manifesting the full\nYangian symmetry of the theory. This generalizes the BCFW recursion relation\nfor tree amplitudes to all loop orders, and extends the Grassmannian duality\nfor leading singularities to the full amplitude. It also provides a new\nphysical picture for the meaning of loops, associated with canonical operations\nfor removing particles in a Yangian-invariant way. Loop amplitudes arise from\nthe \"entangled\" removal of pairs of particles, and are naturally presented as\nan integral over lines in momentum-twistor space. As expected from manifest\nYangian-invariance, the integrand is given as a sum over non-local terms,\nrather than the familiar decomposition in terms of local scalar integrals with\nrational coefficients. Knowing the integrands explicitly, it is straightforward\nto express them in local forms if desired; this turns out to be done most\nnaturally using a novel basis of chiral, tensor integrals written in\nmomentum-twistor space, each of which has unit leading singularities. As simple\nillustrative examples, we present a number of new multi-loop results written in\nlocal form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise\nexpressions are presented for all 2-loop MHV amplitudes, as well as the 5-point\n3-loop MHV amplitude. The structure of the loop integrand strongly suggests\nthat the integrals yielding the physical amplitudes are \"simple\", and\ndetermined by IR-anomalies. We briefly comment on extending these ideas to more\ngeneral planar theories.", "category": "hep-th" }, { "text": "The Quantum Effective Action, Wave Functions and Yang-Mills (2+1): We explore the relationship between the quantum effective action and the\nground state (and excited state) wave functions of a field theory. Applied to\nthe Yang-Mills theory in 2+1 dimensions, we find the leading terms of the\neffective action from the ground state wave function previously obtained in the\nHamiltonian formalism by solving the Schrodinger equation.", "category": "hep-th" }, { "text": "A modification of the 10d superparticle action inspired by the\n Gupta-Bleuler quantization scheme method: We reconsider the issue of the existence of a complex structure in the\nGupta-Bleuler quantization scheme. We prove an existence theorem for the\ncomplex structure associated with the $d=10$ Casalbuoni-Brink-Schwarz\nsuperparticle, based on an explicitly constructed Lagrangian that allows a\nholomorphic-antiholomorphic splitting of the fermionic constraints consistent\nwith the vanishing of all first class constraints on the physical states.", "category": "hep-th" }, { "text": "An analytic study on the excited states of holographic superconductors: Based on the Sturm-Liouville eigenvalue problem, we develop a general\nanalytic technique to investigate the excited states of the holographic\nsuperconductors. By including more higher order terms in the expansion of the\ntrial function, we observe that the analytic results agree well with the\nnumeric data, which indicates that the Sturm-Liouville method is very powerful\nto study the holographic superconductors even if we consider the excited\nstates. For both the holographic s-wave and p-wave models, we find that the\nexcited state has a lower critical temperature than the corresponding ground\nstate and the difference of the dimensionless critical chemical potential\nbetween the consecutive states is around 5. Moreover, we analytically confirm\nthat the holographic superconductor phase transition with the excited states\nbelongs to the second order, which can be used to back up the numerical\nfindings for both s-wave and p-wave superconductors.", "category": "hep-th" }, { "text": "Including four-gluon interactions into Landau and maximally-Abelian\n gauge Dyson-Schwinger studies: In Dyson-Schwinger studies of the Yang-Mills propagators the four-gluon\ninteraction has been usually neglected due to the related technical\ndifficulties with the associated two-loop terms and especially their\nrenormalization. A possible scenario to renormalize these fully-dressed\ntwo-loop terms is presented. Preliminary results for the Landau gauge gluon\npropagator are shown. Implications for the gluon propagators in maximally\nAbelian gauge are discussed.", "category": "hep-th" }, { "text": "String solutions in Chern-Simons-Higgs model coupled to an axion: We study a d=2+1 dimensional Chern-Simons gauge theory coupled to a Higgs\nscalar and an axion field, finding the form of the potential that allows the\nexistence of selfdual equations and the corresponding Bogomolny bound for the\nenergy of static configurations. We show that the same conditions allow for the\nN=2 supersymmetric extension of the model, reobtaining the BPS equations from\nthe supersymmetry requirement. Explicit electrically charged vortex-like\nsolutions to these equations are presented.", "category": "hep-th" }, { "text": "The B-field soft theorem and its unification with the graviton and\n dilaton: In theories of Einstein gravity coupled with a dilaton and a two-form, a soft\ntheorem for the two-form, known as the Kalb-Ramond B-field, has so far been\nmissing. In this work we fill the gap, and in turn formulate a unified soft\ntheorem valid for gravitons, dilatons and B-fields in any tree-level scattering\namplitude involving the three massless states. The new soft theorem is fixed by\nmeans of on-shell gauge invariance and enters at the subleading order of the\ngraviton's soft theorem. In contrast to the subsubleading soft behavior of\ngravitons and dilatons, we show that the soft behavior of B-fields at this\norder cannot be fully fixed by gauge invariance. Nevertheless, we show that it\nis possible to establish a gauge invariant decomposition of the amplitudes to\nany order in the soft expansion. We check explicitly the new soft theorem in\nthe bosonic string and in Type II superstring theories, and furthermore\ndemonstrate that, at the next order in the soft expansion, totally gauge\ninvariant terms appear in both string theories which cannot be factorized into\na soft theorem.", "category": "hep-th" }, { "text": "Particle astrophysics in nonlinear supersymmetric general relativity: An explanation of relations between the large scale structure of the universe\nand the tiny scale structure of the particle physics, e.g. the observed\nmysterious relation between the (dark) energy density and the dark matter of\nthe universe and the neutrino mass and the SUSY breaking mass scale of the\nparticle physics may be given by the nonlinear supersymmmetric general\nrelativity (NLSUSY GR). NLSUSY GR shows that studying the physics before/of the\nBig Bang of the universe may be significant and may give new insight to\nunsolved problems of the low energy particle physics, cosmology and their\nrelations.", "category": "hep-th" }, { "text": "Infinite statistics, symmetry breaking and combinatorial hierarchy: The physics of symmetry breaking in theories with strongly interacting quanta\nobeying infinite (quantum Boltzmann) statistics known as quons is discussed.\nThe picture of Bose/Fermi particles as low energy excitations over nontrivial\nquon condensate is advocated. Using induced gravity arguments it is\ndemonstrated that the Planck mass in such low energy effective theory can be\nfactorially (in number of degrees of freedom) larger than its true ultraviolet\ncutoff. Thus, the assumption that statistics of relevant high energy\nexcitations is neither Bose nor Fermi but infinite can remove the hierarchy\nproblem without necessity to introduce any artificially large numbers. Quantum\nmechanical model illustrating this scenario is presented.", "category": "hep-th" }, { "text": "Quantization of Fayet-Iliopoulos Parameters in Supergravity: In this short note we discuss quantization of the Fayet-Iliopoulos parameter\nin supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos\nparameter determines a lift of the group action to a line bundle, and such\nlifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted\nin terms of moment maps and symplectic reductions, we argue that in\nsupergravity the quantization of the Fayet-Iliopoulos parameter has a natural\nunderstanding in terms of linearizations in geometric invariant theory (GIT)\nquotients, the algebro-geometric version of symplectic quotients.", "category": "hep-th" }, { "text": "The Casimir effect for pistons with transmittal boundary conditions: This work focuses on the analysis of the Casimir effect for pistons subject\nto transmittal boundary conditions. In particular we consider, as piston\nconfiguration, a direct product manifold of the type $I\\times N$ where $I$ is a\nclosed interval of the real line and $N$ is a smooth compact Riemannian\nmanifold. By utilizing the spectral zeta function regularization technique, we\ncompute the Casimir energy of the system and the Casimir force acting on the\npiston. Explicit results for the force are provided when the manifold $N$ is a\n$d$-dimensional ball.", "category": "hep-th" }, { "text": "High Temperature Effects on Compactlike Structures: In this work we investigate the transition from kinks to compactons at high\ntemperatures. We deal with a family of models, described by a real scalar field\nwith standard kinematics, controlled by a single parameter, real and positive.\nThe family of models supports kinklike solutions, and the solutions tend to\nbecome compact when the parameter increases to larger and larger values. We\nstudy the one-loop corrections at finite temperature, to see how the thermal\neffects add to the effective potential. The results suggest that the symmetry\nis restored at very high temperatures.", "category": "hep-th" }, { "text": "Arbitrary Superspin Massive Superparticles: We propose the action for a massive $N$-extended superparticle with a pure\n(half)integer superspin $Y,~Y = 0, 1/2, 1, 3/2, \\ldots$. Regardless of the\nsuperspin value, the configuration space is ${\\Bbb R}^{4|4N} \\times S^2$, where\n$S^2$ corresponds to spinning degrees of freedom. Being explicitly\nsuper-Poincar\\'e invariant, the model possesses two gauge symmetries implying\nstrong conservation of the squared momentum and superspin. Hamilton constrained\ndynamics is developed and canonical quantization is studied. For $N$ = 1 we\nshow that the physical super wave-functions are to be on-shell massive chiral\nsuperfields. Central-charges generalizations of the model are given.", "category": "hep-th" }, { "text": "Supersymmetric Yang-Mills Theories in $D\\ge 12$: We present supersymmetric Yang-Mills theories in arbitrary even dimensions\nwith the signature (9+m,1+m) where $m=0,1,2,...$ beyond ten-dimensions up to\ninfinity. This formulation utilizes null-vectors and is a generalization of our\nprevious work in 10+2 dimensions to arbitrary even dimensions with the above\nsignature. We have overcome the previously-observed obstruction beyond 11+3\ndimensions, by the aid of projection operators. Both component and superspace\nformulations are presented. This also suggests the possibility of consistent\nsupergravity theories in any even dimensions beyond 10+1 dimensions.", "category": "hep-th" }, { "text": "Charged Open Membrane Solutions On A Manifold With Boundary: Explicit open single and multi-membrane solutions of the low energy limit of\nM-theory on the orbifold $R^{10}\\times S^1/Z_2$ are presented. This low energy\naction is described by an 11-dimensional supergravity action coupled to two\n$E_8$ super Yang-Mills fields, which propagate only on the 10-dimensional\nboundaries of the target space. The membrane solutions we construct preserve\nhalf the supersymmetries. They carry electric charge and current with respect\nto the gauge fields, whose generators are in the Cartan subalgebra of the two\n$E_8$ gauge groups present at the boundaries.", "category": "hep-th" }, { "text": "Quantum gravity on a torus: Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach\nto quantum gravity where one assumes space-time foliation into spatial\nhyper-surfaces of fixed topology. Most of the CDT results were obtained for the\nspatial topology of the 3-sphere. It was shown that CDT has rich phase\nstructure, including the semiclassical phase consistent with Einstein's general\nrelativity. Some of the phase transitions were found to be second (or higher)\norder which makes a possibility of taking continuum limit viable. Here we\npresent new results of changing the spatial topology to that of the 3-torus. We\nargue that the topology change does not change the phase structure nor the\norder of the phase transitions. Therefore CDT results seem to be universal\nindependent of the topology chosen.", "category": "hep-th" }, { "text": "Non-geometric heterotic backgrounds and 6D SCFTs/LSTs: We study ${\\mathcal N}=(1,0)$ six-dimensional theories living on defects of\nnon-geometric backgrounds of the $E_8\\times E_8$ and the\n$\\text{Spin}(32)/{\\mathbb Z}_2$ heterotic strings. Such configurations can be\nanalyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau\nthreefolds. The majority of the resulting dual threefolds turn out to contain\nsingularities which do not admit a crepant resolution. When the singularities\ncan be resolved crepantly, the theories living on the defect are explicitly\ndetermined and reveal a form of duality in which distinct defects are described\nby the same IR fixed point. In particular, a subclass of non-geometric defects\ncorresponds to SCFTs/LSTs arising from small heterotic instantons on ADE\nsingularities.", "category": "hep-th" }, { "text": "Dyson's Classification And Real Division Superalgebras: It is well-known that unitary irreducible representations of groups can be\nusefully classified in a 3-fold classification scheme: Real, Complex,\nQuaternionic. In 1962 Freeman Dyson pointed out that there is an analogous\n10-fold classification of irreducible representations of groups involving both\nunitary and antiunitary operators. More recently it was realized that there is\nalso a 10-fold classification scheme involving superdivision algebras. Here we\ngive a careful proof of the equivalence of these two 10-fold ways.", "category": "hep-th" }, { "text": "Exact conditions for Quasi-normal modes of extremal M5-branes and Exact\n WKB analysis: We study the quasi-normal modes (QNMs) of a massless scalar perturbation to\nthe extremal M5-branes metric by using the exact WKB analysis. The exact WKB\nanalysis provides two exact QNMs conditions depending on the argument of the\ncomplex frequency of the perturbation. The exact conditions show that the\ndiscontinuity of the perturbative part of the QNMs leads the non-perturbative\npart of themselves. We also find a new example of the Seiberg-Witten/gravity\ncorrespondence, which helps us to compute the QNMs from our conditions.", "category": "hep-th" }, { "text": "On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli\n Black Holes and Their Holographic Pictures: In this paper, the curvature structure of a (2+1)-dimensional black hole in\nthe massive-charged-Born-Infeld gravity is investigated. The metric that we\nconsider is characterized by four degrees of freedom which are the mass and\nelectric charge of the black hole, the mass of the graviton field, and a\ncosmological constant. For the charged and neutral cases separately, we present\nvarious constraints among scalar polynomial curvature invariants which could\ninvariantly characterize our desired spacetimes. Specially, an appropriate\nscalar polynomial curvature invariant and a Cartan curvature invariant which\ntogether could detect the black hole horizon would be explicitly constructed.\nUsing algorithms related to the focusing properties of a bundle of light rays\non the horizon which are accounted for by the Raychaudhuri equation, a\nprocedure for isolating the black hole parameters, as the algebraic\ncombinations involving the curvature invariants, would be presented. It will be\nshown that this technique could specially be applied for black holes with zero\nelectric charge, contrary to the cases of solutions of lower-dimensional\nnon-massive gravity. In addition, for the case of massive (2+1)-dimensional\nblack hole, the irreducible mass, which quantifies the maximum amount of energy\nwhich could be extracted from a black hole would be derived. Therefore, we show\nthat the Hawking temperatures of these black holes could be reduced to the pure\ncurvature properties of the spacetimes. Finally, we comment on the relationship\nbetween our analysis and the novel roles it could play in numerical quark-gluon\nplasma simulations and other QCD models and also black hole information paradox\nwhere the holographic correspondence could be exploited.", "category": "hep-th" }, { "text": "Standard Model Vacua in Heterotic M-Theory: We present a class of N=1 supersymmetric ``standard'' models of particle\nphysics, derived directly from heterotic M-theory, that contain three families\nof chiral quarks and leptons coupled to the gauge group SU(3)_C X SU(2)_L X\nU(1)_Y. These models are a fundamental form of ``brane world'' theories, with\nan observable and hidden sector each confined, after compactification on a\nCalabi--Yau threefold, to a BPS three-brane separated by a higher dimensional\nbulk space with size of the order of the intermediate scale. The requirement of\nthree families, coupled to the fundamental conditions of anomaly freedom and\nsupersymmetry, constrains these models to contain additional five-branes\nlocated in the bulk space and wrapped around holomorphic curves in the\nCalabi--Yau threefold.", "category": "hep-th" }, { "text": "Dynamical supersymmetry analysis of conformal invariance for\n superstrings in type IIB R-R plane-wave: In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet\nconformal invariance for superstrings in type IIB R-R plane-wave in\nsemi-light-cone gauge. Here we give further justification to the results found\nin that work through alternative arguments using dynamical supersymmetries. We\nshow that by using the susy algebra the same quantum definition of the\nenergy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi\nidentities we indirectly compute the Virasoro anomaly terms by calculating\nsecond order susy variation of the EM tensor. Certain integrated form of all\nsuch terms are shown to vanish. In order to deal with various divergences that\nappear in such computations we take a point-split definition of the same EM\ntensor. The final results are shown not to suffer from the ordering ambiguity\nas noticed in the previous work provided the coincidence limit is taken before\nsending the regularization parameter to zero at the end of the computation.", "category": "hep-th" }, { "text": "The Bubble of Nothing under T-duality: The bubble of nothing is a solution to Einstein's equations where a circle\nshrinks and pinches off smoothly. As such, it is one of the simplest examples\nof a dynamical cobordism to nothing. We take a first step in studying how this\nsolution transforms under T-duality in bosonic string theory. Applying\nBuscher's rules reveals that the dual solution features a singular, strongly\ncoupled core, with a circle blowing-up rather than pinching off. This naive\napproach to T-duality solely accounts for the zero-modes of the fields after\ndimensional reduction on the circle. For this reason, we argue that this is not\nthe full picture that the T-dual solution should depend non-trivially on the\ndual circle. We point out evidence to this effect both in the gravity\ndescription and on the worldsheet. A more complete description of the T-dual\nobject would require a full-fledged sigma model for the bubble of nothing.\nNevertheless, inspired by similar examples in the literature, we detail one\npossible scenario where the stringy bubble of nothing is mediated by closed\nstring tachyon condensation and we discuss its T-duality.", "category": "hep-th" }, { "text": "Continuous Spin Representations of the Poincar\u00e9 and Super-Poincar\u00e9\n Groups: We construct Wigner's continuous spin representations of the Poincar\\'e\nalgebra for massless particles in higher dimensions. The states are labeled\nboth by the length of a space-like translation vector and the Dynkin indices of\nthe {\\it short little group} $SO(d-3)$, where $d$ is the space-time dimension.\nContinuous spin representations are in one-to-one correspondence with\nrepresentations of the short little group. We also demonstrate how combinations\nof the bosonic and fermionic representations form supermultiplets of the\nsuper-Poincar\\'e algebra. If the light-cone translations are nilpotent, these\nrepresentations become finite dimensional, but contain zero or negative norm\nstates, and their supersymmetry algebra contains a central charge in four\ndimensions.", "category": "hep-th" }, { "text": "Closed String Tachyon Condensation in Supercritical Strings and RG Flows: We show an explicit relation between an RG flow of a two-dimensional gravity\nand an on-shell tachyon condensation in the corresponding string theory, in the\ncase when the string theory is supercritical. The shape of the tachyon\npotential in this case can, in principle, be obtained by examining various RG\nflows. We also argue that the shape of tachyon potential for a (sub)critical\nstring can be obtained by analyzing a supercritical string which is obtained\nfrom the (sub)critical string.", "category": "hep-th" }, { "text": "Kinklike structures in models of the Dirac-Born-Infeld type: The present work investigates several models of a single real scalar field,\nengendering kinetic term of the Dirac-Born-Infeld type. Such theories introduce\nnonlinearities to the kinetic part of the Lagrangian, which presents a square\nroot restricting the field evolution and including additional powers in\nderivatives of the scalar field, controlled by a real parameter. In order to\nobtain topological solutions analytically, we propose a first-order framework\nthat simplifies the equation of motion ensuring solutions that are linearly\nstable. This is implemented using the deformation method, and we introduce\nexamples presenting two categories of potentials, one having polynomial\ninteractions and the other with nonpolynomial interactions. We also explore how\nthe Dirac-Born-Infeld kinetic term affects the properties of the solutions. In\nparticular, we note that the kinklike solutions are similar to the ones\nobtained through models with standard kinetic term and canonical potential, but\ntheir energy densities and stability potentials vary according to the parameter\nintroduced to control the new models.", "category": "hep-th" }, { "text": "Hamiltonian reduction and supersymmetric mechanics with Dirac monopole: We apply the technique of Hamiltonian reduction for the construction of\nthree-dimensional ${\\cal N}=4$ supersymmetric mechanics specified by the\npresence of a Dirac monopole. For this purpose we take the conventional ${\\cal\nN}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces\nand perform its Hamiltonian reduction to three-dimensional system. We formulate\nthe final system in the canonical coordinates, and present, in these terms, the\nexplicit expressions of the Hamiltonian and supercharges. We show that, besides\na magnetic monopole field, the resulting system is specified by the presence of\na spin-orbit coupling term. A comparison with previous work is also carried\nout.", "category": "hep-th" }, { "text": "A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds: We explore a ``fertile patch'' of the heterotic landscape based on a Z_6-II\norbifold with SO(10) and E_6 local GUT structures. We search for models\nallowing for the exact MSSM spectrum. Our result is that of order 100 out of a\ntotal 3\\times 10^4 inequivalent models satisfy this requirement.", "category": "hep-th" }, { "text": "Quantum group gauge theory on quantum spaces: We construct quantum group-valued canonical connections on quantum\nhomogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere\nof Podles quantum differential coming from the 3-D calculus of Woronowicz on\n$SU_q(2)$ . The construction is presented within the setting of a general\ntheory of quantum principal bundles with quantum group (Hopf algebra) fiber,\nassociated quantum vector bundles and connection one-forms. Both the base space\n(spacetime) and the total space are non-commutative algebras (quantum spaces).", "category": "hep-th" }, { "text": "Lagrange Brackets and U(1) fields: The idea of a companion Lagrangian associated with $p$-Branes is extended to\ninclude the presence of U(1) fields. The Brane Lagrangians are constructed with\n$F_{ij}$ represented in terms of Lagrange Brackets, which make manifest the\nreparametrisation invariance of the theory; these are replaced by Poisson\nBrackets in the companion Lagrangian, which is now covariant under field\nredefinition. The ensuing Lagrangians possess a similar formal structure to\nthose in the absence of an anti-symmetric field tensor.", "category": "hep-th" }, { "text": "Quantum Einstein Gravity as a Topological Field Theory: General covariance in quantum gravity is seen once one integrates over all\npossible metrics. In recent years topological field theories have given us a\ndifferent route to general covariance without integrating over all possible\nmetrics. Here we argue that Einstein quantum gravity may be viewed as a\ntopological field theory provided a certain constrant from the path integral\nmeasure is satisfied.", "category": "hep-th" }, { "text": "Critical exponents of the Gross-Neveu model from the effective average\n action: The phase transition of the Gross-Neveu model with N fermions is investigated\nby means of a non-perturbative evolution equation for the scale dependence of\nthe effective average action. The critical exponents and scaling amplitudes are\ncalculated for various values of N in d=3. It is also explicitely verified that\nthe Neveu-Yukawa model belongs to the same universality class as the\nGross-Neveu model.", "category": "hep-th" }, { "text": "Super Gluon Five-Point Amplitudes in AdS Space: We present the tree-level five-point amplitude of the lowest KK mode of SYM\non AdS$_5$$\\times$S$^3$, dual to the correlator of the flavor current multiplet\nin the dual 4d ${\\cal N}=2$ SCFT. Its color and kinematical structure is\nparticularly simple and resembles that of the flat-space gluon amplitude.", "category": "hep-th" }, { "text": "Comparing Double String Theory Actions: Aimed to a deeper comprehension of a manifestly T-dual invariant formulation\nof string theory, in this paper a detailed comparison between the non-covariant\naction proposed by Tseytlin and the covariant one proposed by Hull is done.\nThese are obtained by making both the string coordinates and their duals\nexplicitly appear, on the same foot, in the world-sheet action, so \"doubling\"\nthe string coordinates along the compact dimensions. After a discussion of the\nnature of the constraints in both the models and the relative quantization, it\nresults that the string coordinates and their duals behave like \"non-commuting\"\nphase space type coordinates but their expressions in terms of Fourier modes\ngenerate the oscillator algebra of the standard bosonic string formulation. A\nproof of the equivalence of the two formulations is given. Furthermore,\nopen-string solutions are also discussed.", "category": "hep-th" }, { "text": "Superpotential de-sequestering in string models: Non-perturbative superpotential cross-couplings between visible sector matter\nand K\\\"ahler moduli can lead to significant flavour-changing neutral currents\nin compactifications of type IIB string theory. Here, we compute corrections to\nYukawa couplings in orbifold models with chiral matter localised on D3-branes\nand non-perturbative effects on distant D7-branes. By evaluating a threshold\ncorrection to the D7-brane gauge coupling, we determine conditions under which\nthe non-perturbative corrections to the Yukawa couplings appear. The flavour\nstructure of the induced Yukawa coupling generically fails to be aligned with\nthe tree-flavour structure. We check our results by also evaluating a\ncorrelation function of two D7-brane gauginos and a D3-brane Yukawa coupling.\nFinally, by calculating a string amplitude between n hidden scalars and visible\nmatter we show how non-vanishing vacuum expectation values of distant D7-brane\nscalars, if present, may correct visible Yukawa couplings with a flavour\nstructure that differs from the tree-level flavour structure.", "category": "hep-th" }, { "text": "On General BCJ Relation at One-loop Level in Yang-Mills Theory: BCJ relation reveals a dual between color structures and kinematic structure\nand can be used to reduce the number of independent color-ordered amplitudes at\ntree level. Refer to the loop-level in Yang-Mills theory, we investigate the\nsimilar BCJ relation in this paper. Four-point 1-loop example in N = 4 SYM can\nhint about the relation of integrands. Five-point example implies that the\ngeneral formula can be proven by unitary- cut method. We will then prove a\n'general' BCJ relation for 1-loop integrands by D-dimension unitary cut, which\ncan be regarded as a non-trivial generalization of the (fundamental)BCJ\nrelation given by Boels and Isermann in [arXiv:1109.5888 [hep-th]] and\n[arXiv:1110.4462 [hep-th]].", "category": "hep-th" }, { "text": "Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on\n Confining Strings: Recently we observed a crossover transition (in the Fayet-Iliopoulos\nparameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N)\ngauge group and N_f > N quark flavors. At strong coupling this theory can be\ndescribed by a dual non-Abelian weakly coupled SQCD with the dual gauge group\nU(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings.\nWe continue the study of confinement dynamics in these theories, in particular,\nmetamorphoses of excitation spectra, from a different side. A number of results\nobtained previously are explained, enhanced and supplemented by analyzing the\nworld-sheet dynamics on the non-Abelian confining strings. The world-sheet\ntheory is the two-dimensional N=(2,2) supersymmetric weighted CP(N_f-1) model.\nWe explore the vacuum structure and kinks on the world sheet, corresponding to\nconfined monopoles in the bulk theory. We show that (in the equal quark mass\nlimit) these kinks fall into the fundamental representation of the unbroken\nglobal SU(N)\\times SU(N_f-N)\\timesU(1) group. This result confirms the presence\nof \"extra\" stringy meson states in the adjoint representation of the global\ngroup in the bulk theory. The non-Abelian bulk duality is in one-to-one\ncorrespondence with a duality taking place in the N=(2,2) supersymmetric\nweighted CP(N_f-1) model.", "category": "hep-th" }, { "text": "String theory and the 4D/3D reduction of Seiberg duality. A Review: We review the reduction of four-dimensional N=1 Seiberg duality to three\ndimensions focusing on the D brane engineering approach. We start with an\noverview of four-dimensional Seiberg duality for theories with various types of\ngauge groups and matter content both from a field-theoretic and a brane\nengineering point of view. Then we describe two families of N=2\nthree-dimensional dualities, namely Giveon-Kutasov-like and Aharony-like\ndualities. The last part of our discussion is devoted to the 4D/3D reduction of\nthe dualities studied above. We discuss both the analysis at finite radius,\ncrucial for preserving the duality in the dimensional reduction, and the\nzero-size limit that must be supported by a real mass flow and a Higgsing,\nwhich can differ case by case. We show that this mechanism is reproduced in the\nbrane description by T-duality, supplying a unified picture for all the\ndifferent cases. As a bonus we show that this analysis provides a brane\ndescription for Aharony-like dualities.", "category": "hep-th" }, { "text": "Combinatorial $B_n$-analogues of Schubert polynomials: Combinatorial $B_n$-analogues of Schubert polynomials and corresponding\nsymmetric functions are constructed from an exponential solution of the\n$B_n$-Yang-Baxter equation that involves the nilCoxeter algebra of the\nhyperoctahedral group.", "category": "hep-th" }, { "text": "Singularity-free model of electric charge in physical vacuum: Non-zero\n spatial extent and mass generation: We propose a model of a spinless electrical charge as a self-consistent field\nconfiguration of the electromagnetic (EM) field interacting with a physical\nvacuum effectively described by the logarithmic quantum Bose liquid. We show\nthat, in contrast to the EM field propagating in a trivial vacuum, a regular\nsolution does exist, and both its mass and spatial extent emerge naturally from\ndynamics. It is demonstrated that the charge and energy density distribution\nacquire Gaussian-like form. The solution in the logarithmic model is stable and\nenergetically favourable, unlike that obtained in a model with a quartic\n(Higgs-like) potential.", "category": "hep-th" }, { "text": "Entanglement Entropy at Finite Density from Extremal Black Holes: I compute the entanglement entropy of a strongly coupled 2+1d quantum field\ntheory containing fermions at finite density using gauge/gravity duality. The\ndual geometry is an extremal black hole in 3+1d Einstein-Maxwell theory. This\nsystem was recently shown to exhibit non-Fermi liquid behavior, but the leading\ngeometrical contribution to the entanglement entropy does not produce an\nexpected violation of the boundary law. I discuss this negative result in the\ncontext of attempts to find highly entangled states of quantum matter.", "category": "hep-th" }, { "text": "Forces from Connes' geometry: We try to give a pedagogical introduction to Connes' derivation of the\nstandard model of electro-magnetic, weak and strong forces from gravity.", "category": "hep-th" }, { "text": "Quantum Null Energy Condition and its (non)saturation in 2d CFTs: We consider the Quantum Null Energy Condition (QNEC) for holographic\nconformal field theories in two spacetime dimensions (CFT$_2$). We show that\nQNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein\ngravity, including systems that are far from thermal equilibrium. If the\nRyu-Takayanagi surface encounters bulk matter QNEC does not need to be\nsaturated, whereby we give both analytical and numerical examples. In\nparticular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries\nwe find a curious half-saturation of QNEC for large entangling regions. We also\naddress order one corrections from quantum backreactions of a scalar field in\nAdS$_3$ dual to a primary operator of dimension $h$ in a large central charge\nexpansion and explicitly compute both, the backreacted Ryu--Takayanagi surface\npart and the bulk entanglement contribution to EE and QNEC. At leading order\nfor small entangling regions the contribution from bulk EE exactly cancels the\ncontribution from the back-reacted Ryu-Takayanagi surface, but at higher orders\nin the size of the region the contributions are almost equal while QNEC is not\nsaturated. For a half-space entangling region we find that QNEC is gapped by\n$h/4$ in the large $h$ expansion.", "category": "hep-th" }, { "text": "Einstein gravity from the ${\\N=4}$ spinning particle: We obtain a manifestly background independent BRST quantization of the $\\N=4$\nsupersymmetric spinning particle. We show that nilpotency of the BRST charge\n$Q$ implies the Einstein equations admitting a cosmological constant of\nindefinite sign. The physical graviton states are given by the vertex operator,\nobtained by an infinitesimal variation of $Q$, acting on diffeomorphism ghost\nstates. In addition, the tree-point graviton scattering vertex is correctly\nreproduced by the worldline computation with these vertex operators.", "category": "hep-th" }, { "text": "Natural inflation with multiple sub-Planckian axions: We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural\ninflation to models with $N>2$ axions, which obtains a super-Planckian\neffective axion decay constant $f_{\\textrm{eff}}\\gg M_{Pl}$ through an\nalignment of the anomaly coefficients of multiple axions having sub-Planckian\nfundamental decay constants $f_0\\ll M_{Pl}$. The original version of the KNP\nmechanism realized with two axions requires that some of the anomaly\ncoefficients should be of the order of $f_{\\textrm{eff}}/f_0$, which would be\nuncomfortably large if $f_{\\rm eff}/f_0 \\gtrsim {\\cal O}(100)$ as suggested by\nthe recent BICEP2 results. We note that the KNP mechanism can be realized with\nthe anomaly coefficients of $\\mathcal{O}(1)$ if the number of axions $N$ is\nlarge as $N\\ln N\\gtrsim 2\\ln (f_{\\textrm{eff}}/f_0)$, in which case the\neffective decay constant can be enhanced as $f_{\\rm eff}/f_0 \\sim \\sqrt{N\n!}\\,n^{N-1}$ for $n$ denoting the typical size of the integer-valued anomaly\ncoefficients. Comparing to the other multiple axion scenario, the N-flation\nscenario which requires $N \\sim f_{\\textrm{eff}}^2/f_0^2$, the KNP mechanism\nhas a virtue of not invoking to a too large number of axions, although it\nrequires a specific alignment of the anomaly coefficients, which can be\nachieved with a probability of ${\\cal O}(f_0/f_{\\rm eff})$ under a random\nchoice of the anomaly coefficients. We also present a simple model realizing a\nmultiple axion monodromy along the inflaton direction.", "category": "hep-th" }, { "text": "Closed Universe in Mirage Cosmology: We study the cosmological evolution of the closed universe on a spherical\nprobe brane moving in the AdS$_m\\times S^n$ background and the near-horizon\nbackground of the dilatonic D-branes. The Friedmann equations describing the\nevolution of the brane universe, and the effective energy density and pressure\nsimulated on the probe brane due to its motion in the curved background\nspacetime are obtained and analyzed. We also comment on the relevance of the\nspherical probe brane to the giant graviton for the special value of the probe\nenergy.", "category": "hep-th" }, { "text": "Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions: The task of calculating operator dimensions in the planar limit of N=4 super\nYang-Mills theory can be vastly simplified by mapping the dilatation generator\nto the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used\nin this context to compute the spectra of spin chains associated with various\nsectors of the theory which are known to decouple in the planar (large-N_c)\nlimit. These techniques are powerful at leading order in perturbation theory\nbut become increasingly complicated beyond one loop in the 't Hooft parameter\nlambda=g_YM^2 N_c, where spin chains typically acquire long-range\n(non-nearest-neighbor) interactions. In certain sectors of the theory,\nmoreover, higher-loop Bethe ansaetze do not even exist. We develop a virial\nexpansion of the spin chain Hamiltonian as an alternative to the Bethe ansatz\nmethodology, a method which simplifies the computation of dimensions of\nmulti-impurity operators at higher loops in lambda. We use these methods to\nextract previously reported numerical gauge theory predictions near the BMN\nlimit for comparison with corresponding results on the string theory side of\nthe AdS/CFT correspondence. For completeness, we compare our virial results\nwith predictions that can be derived from current Bethe ansatz technology.", "category": "hep-th" }, { "text": "The $L_{\\infty}$ structure of gauge theories with matter: In this work we present an algebraic approach to the dynamics and\nperturbation theory at tree-level for gauge theories coupled to matter. The\nfield theories we will consider are: Chern-Simons-Matter, Quantum\nChromodynamics, and scalar Quantum Chromodynamics. Starting with the\nconstruction of the master action in the classical Batalin-Vilkovisky\nformalism, we will extract the $L_{\\infty}$-algebra that allow us to\nrecursively calculate the perturbiner expansion from its minimal model. The\nMaurer-Cartan action obtained in this procedure will then motivate a generating\nfunction for all the tree-level scattering amplitudes. There are two\ninteresting outcomes of this construction: a generator for fully-flavoured\namplitudes via a localisation on Dyck words; and closed expressions for fermion\nand scalar lines attached to $n$-gluons with arbitrary polarisations.", "category": "hep-th" }, { "text": "Quenched mesonic spectrum at large N: We compute the masses of the $\\pi$ and of the $\\rho$ mesons in the quenched\napproximation on a lattice with fixed lattice spacing $a \\simeq 0.145 \\\n\\mathrm{fm}$ for SU($N$) gauge theory with $N = 2,3,4,6$. We find that a simple\nlinear expression in $1/N^2$ correctly captures the features of the\nlowest-lying meson states at those values of $N$. This enables us to\nextrapolate to $N = \\infty$ the behaviour of $m_{\\pi}$ as a function of the\nquark mass and of $m_{\\rho}$ as a function of $m_{\\pi}$. Our results for the\nlatter agree within 5% with recent predictions obtained in the AdS/CFT\nframework.", "category": "hep-th" }, { "text": "Hamiltonian formalism for Bose excitations in a plasma with a\n non-Abelian interaction I: plasmon -- hard particle scattering: The Hamiltonian theory for the collective longitudinally polarized gluon\nexcitations (plasmons) coupling with classical high-energy test color-charged\nparticle propagating through a high-temperature gluon plasma is developed. A\ngeneralization of the Lie-Poisson bracket to the case of a continuous medium\ninvolving bosonic normal field variable\n$a^{\\phantom{\\ast}\\!\\!a}_{\\hspace{0.03cm}{\\bf k}}$ and a non-Abelian color\ncharge $Q^{\\hspace{0.03cm}a}$ is performed and the corresponding Hamilton\nequations are presented. The canonical transformations including simultaneously\nboth bosonic degrees of freedom of the soft collective excitations and degree\nof freedom of hard test particle connecting with its color charge in the hot\ngluon plasma are written out. A complete system of the canonicity conditions\nfor these transformations is derived. The notion of the plasmon number density\n${\\mathcal N}^{a\\hspace{0.03cm}a^{\\prime}_{\\phantom{1}}\\!}_{{\\bf k}}$, which is\na nontrivial matrix in the color space, is introduced. An explicit form of the\neffective fourth-order Hamiltonian describing elastic scattering of plasmon off\na hard color particle is found and the self-consistent system of Boltzmann type\nkinetic equations taking into account the time evolution of the mean value of\nthe color charge of the hard particle is obtained. On the basis of these\nequations, a model problem of interaction of two infinitly narrow wave packets\nis considered. A system of nonlinear first-order ordinary differential\nequations defining the dynamics of the interaction of the colorless $N^{l}_{\\bf\nk}$ and color $W^{l}_{\\bf k}$ components of the plasmon number density is\nderived. The problem of determining the third- and fourth-order coefficient\nfunctions entering into the canonical transformations of the original bosonic\nvariable $a^{\\phantom{\\ast}\\!\\!a}_{{\\bf k}}$ and color charge\n$Q^{\\hspace{0.03cm}a}$ is discussed.", "category": "hep-th" }, { "text": "Comment on ``On spin-1 massive particles coupled to a Chern-Simons\n field'': In this comment we discuss some serious inconsistencies presented by Gomes,\nMalacarne and da Silva in their paper, Phys.Rev. D60 (1999) 125016\n(hep-th/9908181).", "category": "hep-th" }, { "text": "The Monodromic Axion-Photon Coupling: We consider the general form of the axion coupling to photons in the\naxion-Maxwell theory. On general grounds this coupling takes the form of a\nmonodromic function of the axion, which we call $g(a)$, multiplying the\nChern-Pontryagin density $F \\widetilde{F}$ of the photon. We show that the\nnon-linearity of $g(a)$ is a spurion for the shift symmetry of the axion. In\nthis context, when $g(a) \\neq \\mathbb{Z}a$, the linearized coupling of the\naxion $g'(a)$ is not quantized and there is a correlated mass term for the\naxion. Singularities in $g(a)$ due to the fast rearrangement of degrees of\nfreedom are shown to have corresponding cusps and singularities in the axion\npotential. We derive the general form of $g(a)$ for the QCD axion, axions with\nperturbatively broken shift symmetries and axions descending from extra\ndimensions. In all cases, we show that there is a uniform general form of the\nmonodromic function $g(a)$ and it is connected to the axion potential.", "category": "hep-th" }, { "text": "Application of the canonical quantization of systems with curved phase\n space to the EMDA theory: The canonical quantization of dynamical systems with curved phase space\nintroduced by I.A. Batalin, E.S. Fradkin and T.E. Fradkina is applied to the\nfour-dimensional Einstein-Maxwell Dilaton-Axion theory. The spherically\nsymmetric case with radial fields is considered. The Lagrangian density of the\ntheory in the Einstein frame is written as an expression with first order in\ntime derivatives of the fields. The phase space is curved due to the nontrivial\ninteraction of the dilaton with the axion and the electromagnetic fields.", "category": "hep-th" }, { "text": "Generalized Uncertainty Principle: Implications for Black Hole\n Complementarity: At the heart of the black hole information loss paradox and the firewall\ncontroversy lies the conflict between quantum mechanics and general relativity.\nMuch has been said about quantum corrections to general relativity, but much\nless in the opposite direction. It is therefore crucial to examine possible\ncorrections to quantum mechanics due to gravity. Indeed, the Heisenberg\nUncertainty Principle is one profound feature of quantum mechanics, which\nnevertheless may receive correction when gravitational effects become\nimportant. Such generalized uncertainty principle [GUP] has been motivated from\nnot only quite general considerations of quantum mechanics and gravity, but\nalso string theoretic arguments. We examine the role of GUP in the context of\nblack hole complementarity. We find that while complementarity can be violated\nby large N rescaling if one assumes only the Heisenberg's Uncertainty\nPrinciple, the application of GUP may save complementarity, but only if certain\nN-dependence is also assumed. This raises two important questions beyond the\nscope of this work, i.e., whether GUP really has the proposed form of\nN-dependence, and whether black hole complementarity is indeed correct.", "category": "hep-th" }, { "text": "The Number Operator for Generalized Quons: We construct the number operator for particles obeying infinite statistics,\ndefined by a generalized q-deformation of the Heisenberg algebra, and prove the\npositivity of the norm of linearly independent state vectors.", "category": "hep-th" }, { "text": "Curiosities above c = 24: Two-dimensional rational CFT are characterised by an integer $\\ell$, related\nto the number of zeroes of the Wronskian of the characters. For two-character\nRCFT's with $\\ell<6$ there is a finite number of theories and most of these are\nclassified. Recently it has been shown that for $\\ell \\ge 6$ there are\ninfinitely many admissible characters that could potentially describe CFT's. In\nthis note we examine the $\\ell=6$ case, whose central charges lie between 24\nand 32, and propose a classification method based on cosets of meromorphic\nCFT's. We illustrate the method using theories on Kervaire lattices with\ncomplete root systems. In the process we construct the first known\ntwo-character RCFT's beyond $\\ell=2$.", "category": "hep-th" }, { "text": "Coupled Inflation and Brane Gases: We study an effective four-dimensional theory with an action with two scalar\nfields minimally coupled to gravity, and with a matter action which couples to\nthe two scalar fields via an overall field-dependent coefficient in the action.\nSuch a theory could arise from a dimensional reduction of supergravity coupled\nto a gas of branes winding the compactified dimensions. We show the existence\nof solutions corresponding to power-law inflation. The graceful exit from\ninflation can be obtained by postulating the decay of the branes, as would\noccur if the branes are unstable in the vacuum and stabilized at high densities\nby plasma effects. This construction provides an avenue for connecting string\ngas cosmology and the late-time universe.", "category": "hep-th" }, { "text": "Remarks on a $B \\wedge F$ model with topological mass from gauging spin: Aspects of screening and confinement are reassessed for a $B \\wedge F$ model\nwith topological mass with the gauging of spin. Our discussion is carried out\nusing the gauge-invariant, but path-dependent, variables formalism. We\nexplicitly show that the static potential profile is the sum of a Yukawa and a\nlinear potential, leading to the confinement of static external charges.\nInterestingly enough, similar results are obtained in a theory of antisymmetric\ntensor fields that results from the condensation of topological defects as a\nconsequence of the Julia-Toulouse mechanism.", "category": "hep-th" }, { "text": "Practicalities of renormalizing quantum field theories: We review the techniques used to renormalize quantum field theories at\nseveral loop orders. This includes the techniques to systematically extract the\ninfinities in a Feynman integral and the implementation of the algorithm within\ncomputer algebra. To illustrate the method we discuss the renormalization of\nphi^4 theory and QCD including the application of the critical point large $N$\ntechnique as a check on the anomalous dimensions. The renormalization of\nnon-local operators in QCD is also discussed including the derivation of the\ntwo loop correction to the Gribov mass gap equation in the Landau gauge.", "category": "hep-th" }, { "text": "On the Two-Point Correlation Function in Dynamical Scaling and\n SCHR\u00d6dinger Invariance: The extension of dynamical scaling to local, space-time dependent rescaling\nfactors is investigated. For a dynamical exponent $z=2$, the corresponding\ninvariance group is the Schr\\\"odinger group. Schr\\\"odinger invariance is shown\nto determine completely the two-point correlation function. The result is\nchecked in two exactly solvable models.", "category": "hep-th" }, { "text": "The large Nc limit of N=2 super Yang-Mills, fractional instantons and\n infrared divergences: We investigate the large Nc limit of pure N=2 supersymmetric gauge theory\nwith gauge group SU(Nc) by using the exact low energy effective action. Typical\none-complex dimensional sections of the moduli space parametrized by a global\ncomplex mass scale v display three qualitatively different regions depending on\nthe ratio between |v| and the dynamically generated scale Lambda. At large\n|v|/Lambda, instantons are exponentially suppressed as N goes to infinity. When\n|v| is of order Lambda, singularities due to massless dyons occur. They are\ndensely distributed in rings of calculable thicknesses in the v-plane. At small\n|v|/Lambda, instantons disintegrate into fractional instantons of charge\n1/(2N). These fractional instantons give non-trivial contributions to all\norders of 1/N, unlike a planar diagrams expansion which generates a series in\n1/N^2, implying the presence of open strings. We have explicitly calculated the\nfractional instantons series in two representative examples, including the 1/N\nand 1/N^2 corrections. Our most interesting finding is that the 1/N expansion\nbreaks down at singularities on the moduli space due to severe infrared\ndivergencies, a fact that has remarkable consequences.", "category": "hep-th" }, { "text": "Mobility edge and Black Hole Horizon: We conjecture that the mobility edge in the 4D Euclidean Dirac operator\nspectrum in QCD in the deconfined phase found in the lattice studies\ncorresponds to the near black hole (BH) horizon region in the holographic dual.\nWe present some evidences both from the field theory side and from the\nworldsheet theory of long open string.", "category": "hep-th" }, { "text": "Universal Bounds in Even-Spin CFTs: We prove using invariance under the modular $S$- and $ST$-transformations\nthat every unitary two-dimensional conformal field theory (CFT) of only\neven-spin operators (with no extended chiral algebra and with central charges\n$c,\\tilde{c}>1$) contains a primary operator with dimension $\\Delta_1$\nsatisfying $0 < \\Delta_1 < (c+\\tilde{c})/24 + 0.09280...$ After deriving both\nanalytical and numerical bounds, we discuss how to extend our methods to bound\nhigher conformal dimensions before deriving lower and upper bounds on the\nnumber of primary operators in a given energy range. Using the AdS$_3$/CFT$_2$\ndictionary, the bound on $\\Delta_1$ proves the lightest massive excitation in\nappropriate theories of 3D matter and gravity with cosmological constant\n$\\Lambda < 0$ can be no heavier than $1/(8G_N)+O(\\sqrt{-\\Lambda})$; the bounds\non the number operators are related via AdS/CFT to the entropy of states in the\ndual gravitational theory. In the flat-space approximation, the limiting mass\nis exactly that of the lightest BTZ black hole.", "category": "hep-th" }, { "text": "Thermal Operator Representation of Finite Temperature Graphs II: Using the mixed space representation, we extend our earlier analysis to the\ncase of Dirac and gauge fields and show that in the absence of a chemical\npotential, the finite temperature Feynman diagrams can be related to the\ncorresponding zero temperature graphs through a thermal operator. At non-zero\nchemical potential we show explicitly in the case of the fermion self-energy\nthat such a factorization is violated because of the presence of a singular\ncontact term. Such a temperature dependent term which arises only at finite\ndensity and has a quadratic mass singularity cannot be related, through a\nregular thermal operator, to the fermion self-energy at zero temperature which\nis infrared finite. Furthermore, we show that the thermal radiative corrections\nat finite density have a screening effect for the chemical potential leading to\na finite renormalization of the potential.", "category": "hep-th" }, { "text": "Tachyonic Instability and Darboux Transformation: Using Darboux transformation one can construct infinite family of potentials\nwhich lead to the flat spectrum of scalar field fluctuations with arbitrary\nmultiple precision, and, at the same time, with \"essentially blue\" spectrum of\nperturbations of metric. Besides, we describe reconstruction problem: find\nclassical potential V(phi) starting from the known \"one-loop potential\" u(t) =\nd^2V(phi(t))/d phi(t)^2.", "category": "hep-th" }, { "text": "Fusion Algebras Induced by Representations of the Modular Group: Using the representation theory of the subgroups SL_2(Z_p) of the modular\ngroup we investigate the induced fusion algebras in some simple examples. Only\nsome of these representations lead to 'good' fusion algebras. Furthermore, the\nconformal dimensions and the central charge of the corresponding rational\nconformal field theories are calculated. Two series of representations which\ncan be realized by unitary theories are presented. We show that most of the\nfusion algebras induced by admissible representations are realized in well\nknown rational models.", "category": "hep-th" }, { "text": "BPS Supermultiplets in Five Dimensions: BPS representations of 5-dimensional supersymmetry algebras are classified.\nFor BPS states preserving 1/2 the supersymmetry, there are two distinct classes\nof multiplets for N=4 supersymmetry and three classes for N=8 supersymmetry.\nFor N=4 matter theories, the two 1/2 supersymmetric BPS multiplets are the\nmassive vector multiplet and the massive self-dual 2-form multiplet. Some\napplications to super-Yang-Mills, supergravity and little string theories are\nconsidered.", "category": "hep-th" }, { "text": "Quantization and the Issue of Time for Various Two-Dimensional Models of\n Gravity: It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and\n$R^2$-Gravity are {\\em embedded} in the Katanaev-Volovich model of\n 2D NonEinsteinian Gravity. Different approaches to the formulation of a\nquantum theory for the above systems are then presented: The Dirac constraints\ncan be solved exactly in the momentum representation, the path integral can be\nintegrated out, and the constraint algebra can be {\\em explicitely} canonically\nabelianized, thus allowing also for a (superficial) reduced phase space\nquantization. Non--trivial dynamics are obtained by means of time dependent\ngauges. All of these approaches lead to the {\\em same} finite dimensional\nquantum mechanical system.", "category": "hep-th" }, { "text": "Criticality and Transport in Magnetized Holographic Systems: In this master's thesis the Einstein-Maxwell-Dilaton theory is used to model\nthe dynamics of 2+1-dimensional, strongly coupled, large-$N$ quantum field\ntheories with intrinsic T-violation, at finite density and temperature, in the\npresence of a magnetic field. We include axion fields in order to introduce\nmomentum relaxation. We find analytic expressions for the DC conductivity and\npresent numerical results for the AC conductivity. We also classify the\nIR-asymptotic hyperscaling violating solutions of the theory.", "category": "hep-th" }, { "text": "Quantum Black Hole Formation in the BFSS Matrix Model: We study the various head-on collisions of two bunches of D0-branes and their\nreal-time evolution in the BFSS matrix model in classical limit. For a various\nmatrix size N respecting the 't Hooft scaling, we find quantitative evidence\nfor the formation of a single bound state of D0-branes at late time, which is\nmatrix model thermalization and dual to the formation of a larger black hole.", "category": "hep-th" }, { "text": "Metal or Insulator? Dirac operator spectrum in holographic QCD: The lattice studies in QCD demonstrate the nontrivial localization behavior\nof the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian\nof $4+1$ dimensional disordered system. We use the holographic viewpoint to\nprovide the conjectural explanation of these properties. The delocalization of\nall modes in the confined phase is related to the $\\theta=\\pi$ - like phenomena\nwhen the domain walls between degenerated vacua are possible. It is conjectured\nthat the localized modes separated by mobility edge from the rest of the\nspectrum in deconfined QCD correspond to the near-horizon region in the\nholographic dual.", "category": "hep-th" }, { "text": "Gauss-Bonnet black holes supported by a nonlinear electromagnetic field: We study $D$-dimensional charged static spherically symmetric black hole\nsolutions in Gauss-Bonnet theory coupled to nonlinear electrodynamics defined\nas arbitrary functions of the field invariant and constrained by several\nphysical conditions. These solutions are characterized in terms of the mass\nparameter $m$, the electromagnetic energy $\\varepsilon$ and the Gauss-Bonnet\nparameter $l_{\\alpha}^2$. We find that a general feature of these solutions is\nthat the metric behaves in a different way in $D=5$ and $D>5$ space-time\ndimensions. Moreover, such solutions split into two classes, according to\nwhether they are defined everywhere or show branch singularities, depending on\n($m, \\varepsilon, l_{\\alpha}^2$). We describe qualitatively the structures\ncomprised within this scenario, which largely extends the results obtained in\nthe literature for several particular families of nonlinear electrodynamics. An\nexplicit new example, illustrative of our results, is introduced. Finally we\nallow non-vanishing values of the cosmological constant length $l_{\\Lambda}^2$,\nand study the existence of new structures, in both asymptotically Anti-de\nSitter and de Sitter spaces.", "category": "hep-th" }, { "text": "Microscopics of Extremal Kerr from Spinning M5 Branes: We show that the spinning magnetic one-brane in minimal five-dimensional\nsupergravity admits a decoupling limit that interpolates smoothly between a\nself-dual null orbifold of AdS_3 \\times S^2 and the near-horizon limit of the\nextremal Kerr black hole times a circle. We use this interpolating solution to\nunderstand the field theory dual to spinning M5 branes as a deformation of the\nDiscrete Light Cone Quantized (DLCQ) Maldacena-Stominger-Witten (MSW) CFT. In\nparticular, the conformal weights of the operators dual to the deformation\naround AdS_3 \\times S^2 are calculated. We present pieces of evidence showing\nthat a CFT dual to the four-dimensional extremal Kerr can be obtained from the\ndeformed MSW CFT.", "category": "hep-th" }, { "text": "Why Comparable? A Multiverse Explanation of the Dark Matter-Baryon\n Coincidence: The densities of dark and baryonic matter are comparable: \\zeta = \\rho_D /\n\\rho_B ~ O(1). This is surprising because they are controlled by different\ncombinations of low-energy physics parameters. Here we consider the probability\ndistribution over \\zeta in the landscape. We argue that the Why Comparable\nproblem can be solved without detailed anthropic assumptions, and independently\nof the nature of dark matter. Overproduction of dark matter suppresses the\nprobability like 1/(1+\\zeta), if the causal patch is used to regulate\ninfinities. This suppression can counteract a prior distribution favoring large\n\\zeta, selecting \\zeta ~ O(1).\n This effect not only explains the Why Comparable coincidence but also renders\notherwise implausible models of dark matter viable. For the special case of\naxion dark matter, Wilczek and independently Freivogel have already noted that\na 1/(1+\\zeta) suppression prevents overproduction of a GUT-scale QCD axion. If\nthe dark matter is the LSP, the effect can explain the moderate fine-tuning of\nthe weak scale in simple supersymmetric models.", "category": "hep-th" }, { "text": "DBI Galileon inflation in background SUGRA: We introduce a model of potential driven DBI Galileon inflation in background\nN=1,D=4 SUGRA. Starting from D4-$\\bar{D4}$ brane-antibrane in the bulk N=2,D=5\nSUGRA including quadratic Gauss-Bonnet corrections, we derive an effective\nN=1,D=4 SUGRA by dimensional reduction, that results in a Coleman-Weinberg type\nGalileon potential. We employ this potential in modeling inflation and in\nsubsequent study of primordial quantum fluctuations for scalar and tensor\nmodes. Further, we estimate the major observable parameters in both de Sitter\n(DS) and beyond de Sitter (BDS) limits and confront them with recent\nobservational data from WMAP7 by using the publicly available code CAMB.", "category": "hep-th" }, { "text": "PT symmetric fermionic field theories with axions: Renormalization and\n dynamical mass generation: We consider the renormalisation properties of non-Hermitian Yukawa theories\ninvolving a pseudoscalar (axion) field at or near $4$ dimensions. The\nnon-Hermiticity is \\cPT-symmetric where $\\mathcal P$ is a linear idempotent\noperator (such as parity) and $\\mathcal T$ is an anti-linear idempotent\noperator (such as time-reversal). The coupling constants of the Yukawa and\nquartic scalar coupling terms reflect this non-Hermiticity. The path integral\nrepresenting the field theory is used to discuss the Feynman rules associated\nwith the field theory. The fixed point structure associated with the\nrenormalisation group has \\cPT- symmetric and Hermitian fixed points. At two\nloops in the massless theory, we demonstrate the flow from Hermitian to\nnon-Hermitian fixed points. From the one-loop renormalisation of a massive\nYukawa theory, a self-consistent Nambu-Jona Lasinio gap equation is established\nand its real solutions are discussed.", "category": "hep-th" }, { "text": "Clarifying perturbations in the ekpyrotic universe: In this note I try to clarify the problem of perturbations in the ekpyrotic\nuniverse. I write down the most general matching conditions and specify the\nchoices taken by the two debating sides. I also bring up the problem of surface\nstresses which always have to be present when a transition from a collapsing to\nan expanding phase is made.", "category": "hep-th" }, { "text": "Dualities in the classical supergravity limits: Duality symmetries of supergravity theories are powerful tools to restrict\nthe number of possible actions, to link different dimensions and number of\nsupersymmetries and might help to control quantisation.\n(Hodge-Dirac-)Dualisation of gauge potentials exchanges Noether and topological\ncharges, equations of motion and Bianchi identities, internal rigid symmetries\nand gauge symmetries, local transformations with nonlocal ones and most\nexciting particles and waves. We compare the actions of maximally dualised\nsupergravities (ie with gauge potential forms of lowest possible degree) to the\nnon-dualised actions coming from 11 (or 10) dimensions by plain dimensional\nreduction as well as to other theories with partial dualisations. The effect on\nthe rigid duality group is a kind of contraction resulting from the elimination\nof the unfaithful generators associated to the (inversely) dualised scalar\nfields. New gauge symmetries are introduced by these (un)dualisations and it is\nclear that a complete picture of duality (F(ull)-duality) should include all\ngauge symmetries at the same time as the rigid symmetries and the spacetime\nsymmetries. We may read off some properties of F-duality on the internal rigid\nDynkin diagram: field content, possible dualisations, increase of the rank\naccording to the decrease of space dimension... Some recent results are\nincluded to suggest the way towards unification via a universal twisted\nself-duality (TS) structure. The analysis of this structure had revealed\nseveral profound differences according to the parity mod 4 of the dimension of\nspacetime (to be contrasted with the (Bott) period 8 of spinor properties).", "category": "hep-th" }, { "text": "Thick Domain Walls and Charged Dilaton Black Holes: We study a black hole domain wall system in dilaton gravity which is the\nlow-energy limit of the superstring theory. We solve numerically equations of\nmotion for real self-interacting scalar field and justify the existence of\nstatic axisymmetric field configuration representing the thick domain wall in\nthe background of a charged dilaton black hole. It was also confirmed that the\nextreme dilaton black hole always expelled the domain wall.", "category": "hep-th" }, { "text": "Supergravity p-branes revisited: extra parameters, uniqueness, and\n topological censorship: We perform a complete integration of the Einstein-dilaton-antisymmetric form\naction describing black p-branes in arbitrary dimensions assuming the\ntransverse space to be homogeneous and possessing spherical, toroidal or\nhyperbolic topology. The generic solution contains eight parameters satisfying\none constraint. Asymptotically flat solutions form a five-parametric subspace,\nwhile conditions of regularity of the non-degenerate event horizon further\nrestrict this number to three, which can be related to the mass and the charge\ndensities and the asymptotic value of the dilaton. In the case of a degenerate\nhorizon, this number is reduced by one. Our derivation constitutes a\nconstructive proof of the uniqueness theorem for $p$-branes with the\nhomogeneous transverse space. No asymptotically flat solutions with toroidal or\nhyperbolic transverse space within the considered class are shown to exist,\nwhich result can be viewed as a demonstration of the topological censorship for\np-branes. From our considerations it follows, in particular, that some\npreviously discussed p-brane-like solutions with extra parameters do not\nsatisfy the standard conditions of asymptotic flatness and absence of naked\nsingularities. We also explore the same system in presence of a cosmological\nconstant, and derive a complete analytic solution for higher-dimensional\ncharged topological black holes, thus proving their uniqueness.", "category": "hep-th" }, { "text": "An Alternative to Compactification: Conventional wisdom states that Newton's force law implies only four\nnon-compact dimensions. We demonstrate that this is not necessarily true in the\npresence of a non-factorizable background geometry. The specific example we\nstudy is a single 3-brane embedded in five dimensions. We show that even\nwithout a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and\ngeneral relativistic gravity is reproduced to more than adequate precision.", "category": "hep-th" }, { "text": "Born-Infeld Black-Body Radiation: The problem of black-body radiation is considered in the Born-Infeld theory\nof electrodynamics. In particular, at 2-loop order the deviation from the\nPlanck expression due to the self-interaction of photons is calculated. It is\nseen that the system of interacting photons of the theory, opposed to its\nnon-Abelian counterpart, has higher internal energy at this order of\nperturbation. Possible implications of the result on the evolution of very\nhight temperature systems, including various stellar media and the early\nuniverse, are briefly discussed.", "category": "hep-th" }, { "text": "Gravitational lensing and shadow of charged black holes in the\n low-energy limit of string theory: In this work, we investigate the shadow cast and strong field gravitational\nlensing of a new class of black hole solutions in dilaton gravity where dilaton\nfield is coupled with nonlinear Maxwell invariant [Younesizadeh et al. in Int J\nMod Phys A 34(35):1950239]. The space-time is a stationary axisymmetric\ngeometry. The key part in our investigations is finding the effect of dilaton\nparameter N on the size of shadows and the energy emission rate. As the N\nparameter increases, the size of black hole shadow increases. Also, the energy\nemission rate increases with increase in the dilaton parameter N. By supposing\nthe gravitational field of the supermassive object at the heart of Milky Way\ngalaxy described by this metric, we estimated the numerical values of the\nobservables for gravitational lensing in the strong field limit.", "category": "hep-th" }, { "text": "Scaling Behaviors of Branched Polymers: We study the thermodynamic behavior of branched polymers. We first study\nrandom walks in order to clarify the thermodynamic relation between the\ncanonical ensemble and the grand canonical ensemble. We then show that\ncorrelation functions for branched polymers are given by those for $\\phi^3$\ntheory with a single mass insertion, not those for the $\\phi^3$ theory\nthemselves. In particular, the two-point function behaves as $1/p^4$, not as\n$1/p^2$, in the scaling region. This behavior is consistent with the fact that\nthe Hausdorff dimension of the branched polymer is four.", "category": "hep-th" }, { "text": "T-Duality Group for Open String Theory: We study T-duality for open strings on tori $\\T^d$. The general boundary\nconditions for the open strings are constructed, and it is shown that T-duality\ngroup, which preserves the mass spectrum of closed strings, preserves also the\nmass spectrum of the open strings. The open strings are transformed to those\nwith different boundary conditions by T-duality. We also discuss the T-duality\nfor D-brane mass spectrum, and show that the D-branes and the open strings with\nboth ends on them are transformed together consistently.", "category": "hep-th" }, { "text": "Agujeros negros clasicos y cuanticos en teoria de cuerdas: Introductory lectures on classical and quantum string black holes\n(supergravity, branes and dualities) given at the VII School \"La Hechicera\" of\nRelativity, Fields and Astrophysics, held in the University of Los Andes,\nMerida (Venezuela) 2001. Fully in Spanish.", "category": "hep-th" }, { "text": "Celestial Feynman Rules for Scalars: Off-shell celestial amplitudes with both time-like and space-like external\nlegs are defined. The Feynman rules for scalar amplitudes, viewed as a set of\nrecursion relations for off-shell momentum space amplitudes, are transformed to\nthe celestial sphere using the split representation. For four-point celestial\namplitudes, the Feynman expansion is shown to be equivalent to a conformal\npartial wave decomposition, providing an interpretation of conformal partial\nwave expansion coefficients as integrals over off-shell three-point structures.\nA conformal partial wave decomposition for a simple four-point $s$-channel\nmassless scalar celestial amplitude is derived.", "category": "hep-th" }, { "text": "The supersymmetric extension of the replica model: We perform a $\\mathcal{N}=1$ supersymmetric extension of the replica model\nquantized in the Landau gauge and compute the gluon and gluino propagators at\ntree-level, such results display a supersymmetric confined model very similar\nto the supersymmetric version of the Gribov-Zwanziger approach.", "category": "hep-th" }, { "text": "Squeezing as a probe of the universality hypothesis: We compute analytically the radiative quantum corrections, up to\nnext-to-leading loop order, to the universal critical exponents for both\nmassless and massive O($N$) $\\lambda\\phi^{4}$ scalar squeezed field theories\nfor probing the universality hypothesis. For that, we employ six distinct and\nindependent methods. The outcomes for the universal squeezed critical exponents\nobtained through these methods are identical among them and reduce to the\nconventional ones where squeezing is absent. Although the squeezing mechanism\nmodifies the internal properties of the field, the squeezed critical indices\nare not affected by the squeezing effect, thus implying the validity of the\nuniversality hypothesis, at least at the loop level considered. At the end, we\npresent the corresponding physical interpretation for the results in terms of\nthe geometric symmetry properties of the squeezed field.", "category": "hep-th" }, { "text": "Four-modulus \"Swiss Cheese\" chiral models: We study the 'Large Volume Scenario' on explicit, new, compact, four-modulus\nCalabi-Yau manifolds. We pay special attention to the chirality problem pointed\nout by Blumenhagen, Moster and Plauschinn. Namely, we thoroughly analyze the\npossibility of generating neutral, non-perturbative superpotentials from\nEuclidean D3-branes in the presence of chirally intersecting D7-branes. We find\nthat taking proper account of the Freed-Witten anomaly on non-spin cycles and\nof the Kaehler cone conditions imposes severe constraints on the models.\nNevertheless, we are able to create setups where the constraints are solved,\nand up to three moduli are stabilized.", "category": "hep-th" }, { "text": "Holography in Lovelock Chern-Simons AdS Gravity: We analyse holographic field theory dual to Lovelock Chern-Simons AdS Gravity\nin higher dimensions using first order formalism. We first find asymptotic\nsymmetries in the AdS sector showing that they consist of local translations,\nlocal Lorentz rotations, dilatations and non-Abelian gauge transformations.\nThen, we compute $1$-point functions of energy-momentum and spin currents in a\ndual conformal field theory and write Ward identities. We find that the\nholographic theory possesses Weyl anomaly and also breaks non-Abelian gauge\nsymmetry at the quantum level.", "category": "hep-th" }, { "text": "Local BRST cohomology in minimal D=4, N=1 supergravity: The local BRST cohomology is computed in old and new minimal supergravity,\nincluding the coupling to Yang-Mills gauge multiplets. This covers the\ndetermination of all gauge invariant local actions for these models, the\nclassification of all the possible counterterms that are invariant on-shell, of\nall candidate gauge anomalies, and of the possible nontrivial (continuous)\ndeformations of the standard actions and gauge transformations. Among others it\nis proved that in old minimal supergravity the most general gauge invariant\naction can indeed be constructed from well-known superspace integrals, whereas\nin new minimal supergravity there are only a few additional (but important)\ncontributions which cannot be constructed in this way without further ado.\nFurthermore the results indicate that supersymmetry itself is not anomalous in\nminimal supergravity and show that the gauge transformations are extremely\nstable under consistent deformations of the models. There is however an unusual\ndeformation converting new into old minimal supergravity with local\nR-invariance which is reminiscent of a duality transformation.", "category": "hep-th" }, { "text": "Conformal Bootstrap Analysis for Yang-Lee Edge Singularity: The Yang-Lee edge singularity is investigated by the determinant method of\nthe conformal field theory. The critical dimension Dc, for which the scale\ndimension of scalar Delta_phi is vanishing, is discussed by this determinant\nmethod. The result is incorporated in the Pade analysis of epsilon expansion,\nwhich leads to an estimation of the value Delta_phi between three and six\ndimensions. The structure of the minors is viewed from the fixed points.", "category": "hep-th" }, { "text": "The microscopic spectrum of the QCD Dirac operator with finite quark\n masses: We compute the microscopic spectrum of the QCD Dirac operator in the presence\nof dynamical fermions in the framework of random-matrix theory for the chiral\nGaussian unitary ensemble. We obtain results for the microscopic spectral\ncorrelators, the microscopic spectral density, and the distribution of the\nsmallest eigenvalue for an arbitrary number of flavors, arbitrary quark masses,\nand arbitrary topological charge.", "category": "hep-th" }, { "text": "An Origin Story for Amplitudes: We classify origin limits of maximally helicity violating multi-gluon\nscattering amplitudes in planar $\\mathcal{N}=4$ super-Yang-Mills theory, where\na large number of cross ratios approach zero, with the help of cluster\nalgebras. By analyzing existing perturbative data, and bootstrapping new data,\nwe provide evidence that the amplitudes become the exponential of a quadratic\npolynomial in the large logarithms. With additional input from the\nthermodynamic Bethe ansatz at strong coupling, we conjecture exact expressions\nfor amplitudes with up to 8 gluons in all origin limits. Our expressions are\ngoverned by the tilted cusp anomalous dimension evaluated at various values of\nthe tilt angle.", "category": "hep-th" }, { "text": "Non-perturbative topological string theory on compact Calabi-Yau 3-folds: We obtain analytic and numerical results for the non-perturbative amplitudes\nof topological string theory on arbitrary, compact Calabi-Yau manifolds. Our\napproach is based on the theory of resurgence and extends previous special\nresults to the more general case. In particular, we obtain explicit\ntrans-series solutions of the holomorphic anomaly equations. Our results\npredict the all orders, large genus asymptotics of the topological string free\nenergies, which we test in detail against high genus perturbative series\nobtained recently in the compact case. We also provide additional evidence that\nthe Stokes constants appearing in the resurgent structure are closely related\nto integer BPS invariants.", "category": "hep-th" }, { "text": "Covariance of WDVV equations: The (generalized) WDVV equations for the prepotentials in $2d$ topological\nand $4,5d$ Seiberg-Witten models are covariant with respect to non-linear\ntransformations, described in terms of solutions of associated linear problem.\nBoth time-variables and the prepotential change non-trivially, but period\nmatrix (prepotential's second derivatives) remains intact.", "category": "hep-th" }, { "text": "Fermion states on domain wall junctions and the flavor number: In this paper we address the problem of localizing fermion states on stable\ndomain walls junctions. The study focus on the consequences of intersecting six\nindependent 8d domain walls to form 4d junctions in a ten-dimensional\nspacetime. This is related to the mechanism of relaxing to three space\ndimensions through the formation of domain wall junctions. The model is based\non six bulk real scalar fields, the phi-4 model in its broken phase, the\nprototype of the Higgs field, and is such that the fermion and scalar modes\nbound to the domain walls are the zero mode and a single massive bound state,\nwhich can be regarded as a two level system, at least at sufficiently low\nenergy. Inside the junction, we use the fact that some states are statistically\nmore favored to address the possibility of constraining the flavor number of\nthe elementary fermions.", "category": "hep-th" }, { "text": "Quark mass correction to the string potential: A consistent method for calculating the interquark potential generated by the\nrelativistic string with massive ends is proposed. In this approach the\ninterquark potential in the model of the Nambu--Goto string with point--like\nmasses at its ends is calculated. At first the calculation is done in the\none--loop approximation and then the variational estimation is performed. The\nquark mass correction results in decreasing the critical distance\n(deconfinement radius). When quark mass decreases the critical distance also\ndecreases. For obtaining a finite result under summation over eigenfrequencies\nof the Nambu--Goto string with massive ends a suitable mode--by--mode\nsubtraction is proposed. This renormalization procedure proves to be completely\nunique. In the framework of the developed approach the one--loop interquark\npotential in the model of the relativistic string with rigidity is also\ncalculated.", "category": "hep-th" }, { "text": "The Energy Loss of a Heavy Quark Moving Through a General Fluid\n Dynamical Flow: We determine the most general form of the covariant drag force exerted on a\nquark moving through a fluid dynamical flow. Up to first order in derivative\nexpansion, our general formula requires the specification of seven coefficient\nfunctions. We use the perturbative method introduced in arXiv:1202.2737 and\nfind all these coefficients in the hydrodynamic regime of a $\\mathcal{N}=4$ SYM\nplasma. Having this general formula, we can obtain the rate of the energy and\nmomentum loss of a quark, namely the drag force, in a general flow. This result\nmakes it possible to perturbatively study the motion of heavy quarks moving\nthrough the Bjorken flow up to first order in derivative expansion.", "category": "hep-th" }, { "text": "On the BRST approach to the description of a Regge trajectory: The free field theory for Regge trajectory is described in the framework of\nthe BRST - quantization method. The physical spectrum includes daugther\ntrajectories along with parent one. The applicability of the BRST approach to\nthe description of a single Regge trajectory without its daughter trajectories\nis discussed. The simple example illustrates the appropriately modified BRST\nconstruction for the needed second class constraints.", "category": "hep-th" }, { "text": "A new symmetry of the colored Alexander polynomial: We present a new conjectural symmetry of the colored Alexander polynomial,\nthat is the specialization of the quantum $\\mathfrak{sl}_N$ invariant widely\nknown as the colored HOMFLY-PT polynomial. We provide arguments in support of\nthe existence of the symmetry by studying the loop expansion and the character\nexpansion of the colored HOMFLY-PT polynomial. We study the constraints this\nsymmetry imposes on the group theoretic structure of the loop expansion and\nprovide solutions to those constraints. The symmetry is a powerful tool for\nresearch on polynomial knot invariants and in the end we suggest several\npossible applications of the symmetry.", "category": "hep-th" }, { "text": "Thermal AdS(3), BTZ and competing winding modes condensation: We study the thermal physics of AdS(3) and the BTZ black hole when embedded\nin String theory. The exact calculation of the Hagedorn temperature in TAdS(3)\nis reinterpreted as the appearance of a winding tachyon both in AdS(3) and BTZ.\nWe construct a dual framework for analyzing the phases of the system. In this\ndual framework, tachyon condensation and geometric capping appear on the same\nfooting, bridging the usual gap of connecting tachyon condensation to\nmodifications of geometry. This allows us to construct in a natural way a\ncandidate for the unstable phase, analogous to a small black hole in higher\ndimensions. Additional peculiar effects associated with the Hagedorn\ntemperature and the Hawking-Page transition, some to do with the asymptotic\nstructure of AdS(3) and some with strong curvature effects, are analyzed and\nexplained.", "category": "hep-th" }, { "text": "Invariance of Unruh and Hawking radiation under matter-induced\n supertranslations: Matter fields are supertranslated upon crossing a shock wave, which leads to\nentanglement of the quantum vacuum between the two regions on either side of\nthe shock wave. We probe this entanglement for a scalar field in a planar shock\nwave background by computing the Bogoliubov transformation between the inertial\nand uniformly accelerated observer. The resulting Bogoliubov coefficients are\nshown to reproduce the standard Unruh effect without dependence on the form\nfactor of the shock wave. In contrast, excited states lead to observables that\ndepend upon the form factor. In the context of nonspherical gravitational\ncollapse, we comment that the angular dependence of the limiting advanced time\nleads to similar supertranslation effects that do not affect the Hawking\nspectrum but do affect scattering amplitudes.", "category": "hep-th" }, { "text": "Dirac versus reduced phase space quantization for systems admitting no\n gauge conditions: The constrained Hamiltonian systems admitting no gauge conditions are\nconsidered. The methods to deal with such systems are discussed and developed.\nAs a concrete application, the relationship between the Dirac and reduced phase\nspace quantizations is investigated for spin models belonging to the class of\nsystems under consideration. It is traced out that the two quantization methods\nmay give similar, or essentially different physical results, and, moreover, a\nclass of constrained systems, which can be quantized only by the Dirac method,\nis discussed. A possible interpretation of the gauge degrees of freedom is\ngiven.", "category": "hep-th" }, { "text": "Gluonic fields of a static particle to all orders in 1/N: We determine the expectation value of the gauge invariant operator Tr\n[F^2+... ] for N=4 SU(N) SYM, in the presence of an infinitely heavy static\nparticle in the symmetric representation of SU(N). We carry out the computation\nin the context of the AdS/CFT correspondence, by considering the perturbation\nof the dilaton field caused by the presence of a D3 brane dual to such an\nexternal probe. We find that the effective chromo-electric charge of the probe\nhas exactly the same expression as the one recently found in the computation of\nenergy loss by radiation.", "category": "hep-th" }, { "text": "Anomalous U(1)'s in Type I and Type IIB D=4, N=1 string vacua: We study the cancellation of U(1) anomalies in Type I and Type IIB D=4, N=1\nstring vacua. We first consider the case of compact toroidal $Z_N$ Type IIB\norientifolds and then proceed to the non-compact case of Type IIB D3 branes at\norbifold and orientifold singularities. Unlike the case of the heterotic string\nwe find that for each given vacuum one has generically more than one U(1) with\nnon-vanishing triangle anomalies. There is a generalized Green-Schwarz\nmechanism by which these anomalies are cancelled. This involves only the\nRamond-Ramond scalars coming from the twisted closed string spectrum but not\nthose coming from the untwisted sector. Associated to the anomalous U(1)'s\nthere are field-dependent Fayet-Illiopoulos terms whose mass scale is fixed by\nundetermined vev's of the NS-NS partners of the relevant twisted RR fields.\nThus, unlike what happens in heterotic vacua, the masses of the anomalous\nU(1)'s gauge bosons may be arbitrarily light. In the case of D3 branes at\nsingularities, appropriate factorization of the U(1)'s constrains the\nChan-Paton matrices beyond the restrictions from cancellation of non-abelian\nanomalies. These conditions can be translated to constraints on the T-dual Type\nIIB brane box configurations. We also construct a new large family of N=1\nchiral gauge field theories from D3 branes at orientifold singularities, and\ncheck its non-abelian and U(1) anomalies cancel.", "category": "hep-th" }, { "text": "Determination of critical exponents and equation of state by field\n theory method: Path integrals have played a fundamental role in emphasizing the profound\nanalogies between Quantum Field Theory (QFT), and Classical as well as Quantum\nStatistical Physics. Ideas coming from Statistical Physics have then led to a\ndeeper understanding of Quantum Field Theory and open the way for a wealth of\nnon-perturbative methods. Conversely QFT methods are become essential for the\ndescription of the phase transitions and critical phenomena beyond mean field\ntheory. This is the point we want to illustrate here. We therefore review the\nmethods, based on renormalized phi^4_3 quantum field theory and renormalization\ngroup, which have led to an accurate determination of critical exponents of the\nN-vector model, and more recently of the equation of state of the 3D Ising\nmodel. The starting point is the perturbative expansion for RG functions or the\neffective potential to the order presently available. Perturbation theory is\nknown to be divergent and its divergence has been related to instanton\ncontributions. This has allowed to characterize the large order behaviour of\nperturbation series, an information that can be used to efficiently \"sum\" them.\nPractical summation methods based on Borel transformation and conformal mapping\nhave been developed, leading to the most accurate results available probing\nfield theory in a non perturbative regime. We illustrate the methods with a\nshort discussion of the scaling equation of state of the 3D Ising model.\nCompared to exponents its determination involves a few additional (non-trivial)\ntechnical steps, like the use of the parametric representation, and the\norder-dependent mapping.", "category": "hep-th" }, { "text": "Field-enlarging transformations and chiral theories: A field-enlarging transformation in the chiral electrodynamics is performed.\nThis introduces an additional gauge symmetry to the model that is unitary and\nanomaly-free and allows for comparison of different models discussed in the\nliterature. The problem of superfluous degrees of freedom and their influence\non quantization is discussed. Several \"mysteries\" are explained from this point\nof view.", "category": "hep-th" }, { "text": "Looking at the Gregory-Laflamme instability through quasi-normal modes: We study evolution of gravitational perturbations of black strings. It is\nwell known that for all wavenumber less than some threshold value, the black\nstring is unstable against scalar type of gravitational perturbations, which is\nnamed the Gregory-Laflamme instability. Using numerical methods, we find the\nquasinormal modes and time-domain profiles of the black string perturbations in\nthe stable sector and also show the appearance of the Gregory-Laflamme\ninstability in the time domain. The dependence of the black string quasinormal\nspectrum and late time tails on such parameters as the wave vector and the\nnumber of extra dimensions is discussed. There is a numerical evidence that in\nthe threshold point of instability the static solution of the wave equation is\ndominant. For wavenumbers slightly larger than the threshold value, in the\nregion of stability, we see tiny oscillations with very small damping rate.\nWhile, for wavenumbers slightly smaller than the threshold value, in the region\nof the Gregory-Laflamme instability, we observe tiny oscillations with very\nsmall growth rate. We also find the level crossing of imaginary part of\nquasinormal modes between the fundamental mode and the first overtone mode,\nwhich accounts for the peculiar time domain profiles.", "category": "hep-th" }, { "text": "Non-Local Effects of Multi-Trace Deformations in the AdS/CFT\n Correspondence: The AdS/CFT correspondence relates deformations of the CFT by \"multi-trace\noperators\" to \"non-local string theories\". The deformed theories seem to have\nnon-local interactions in the compact directions of space-time; in the gravity\napproximation the deformed theories involve modified boundary conditions on the\nfields which are explicitly non-local in the compact directions. In this note\nwe exhibit a particular non-local property of the resulting space-time theory.\nWe show that in the usual backgrounds appearing in the AdS/CFT correspondence,\nthe commutator of two bulk scalar fields at points with a large enough distance\nbetween them in the compact directions and a small enough time-like distance\nbetween them in AdS vanishes, but this is not always true in the deformed\ntheories. We discuss how this is consistent with causality.", "category": "hep-th" }, { "text": "Casimir Energies for Spherically Symmetric Cavities: A general calculation of Casimir energies --in an arbitrary number of\ndimensions-- for massless quantized fields in spherically symmetric cavities is\ncarried out. All the most common situations, including scalar and spinor\nfields, the electromagnetic field, and various boundary conditions are treated\nwith care. The final results are given as analytical (closed) expressions in\nterms of Barnes zeta functions. A direct, straightforward numerical evaluation\nof the formulas is then performed, which yields highly accurate numbers of, in\nprinciple, arbitrarily good precision.", "category": "hep-th" }, { "text": "Holography for Einstein-Maxwell-dilaton theories from generalized\n dimensional reduction: We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related\nto higher dimensional AdS-Maxwell gravity via a dimensional reduction over\ncompact Einstein spaces combined with continuation in the dimension of the\ncompact space to non-integral values (`generalized dimensional reduction').\nThis relates (fairly complicated) black hole solutions of EMD theories to\nsimple black hole/brane solutions of AdS-Maxwell gravity and explains their\nproperties. The generalized dimensional reduction is used to infer the\nholographic dictionary and the hydrodynamic behavior for this class of theories\nfrom those of AdS. As a specific example, we analyze the case of a black brane\ncarrying a wave whose universal sector is described by gravity coupled to a\nMaxwell field and two neutral scalars. At thermal equilibrium and finite\nchemical potential the two operators dual to the bulk scalar fields acquire\nexpectation values characterizing the breaking of conformal and generalized\nconformal invariance. We compute holographically the first order transport\ncoefficients (conductivity, shear and bulk viscosity) for this system.", "category": "hep-th" }, { "text": "Quasi-instantons in QCD with chiral symmetry restoration: We show, without using semiclassical approximations, that, in\nhigh-temperature QCD with chiral symmetry restoration and U(1) axial symmetry\nbreaking, the partition function for sufficiently light quarks can be expressed\nas an ensemble of noninteracting objects with topological charge that obey the\nPoisson statistics. We argue that the topological objects are\n\"quasi-instantons\" (rather than bare instantons) taking into account quantum\neffects. Our result is valid even close to the (pseudo)critical temperature of\nthe chiral phase transition.", "category": "hep-th" }, { "text": "Entropy Function for Heterotic Black Holes: We use the entropy function formalism to study the effect of the Gauss-Bonnet\nterm on the entropy of spherically symmetric extremal black holes in heterotic\nstring theory in four dimensions. Surprisingly the resulting entropy and the\nnear horizon metric, gauge field strengths and the axion-dilaton field are\nidentical to those obtained by Cardoso et. al. for a supersymmetric version of\nthe theory that contains Weyl tensor squared term instead of the Gauss-Bonnet\nterm. We also study the effect of holomorphic anomaly on the entropy using our\nformalism. Again the resulting attractor equations for the axion-dilaton field\nand the black hole entropy agree with the corresponding equations for the\nsupersymmetric version of the theory. These results suggest that there might be\na simpler description of supergravity with curvature squared terms in which we\nsupersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.", "category": "hep-th" }, { "text": "$\\mathcal{N} = (2,2)$ extended $\\mathfrak{sl}(3|2)$ Chern-Simons $AdS_3$\n supergravity with new boundaries: We present the first example of $\\mathcal{N}=(2,2)$ formulation for the\nextended higher-spin $AdS_3$ supergravity with the most general boundary\nconditions as an extension of the $\\mathcal{N} =\\,(1,1)$ work, discovered\nrecently by us [1]. Using the method proposed by Grumiller and Riegler, we\nconstruct a consistent class of the most general boundary conditions to extend\nit. An important consequence of our method is that, for the loosest set of\nboundary conditions it ensures that their asymptotic symmetry algebras consist\nof two copies of the $\\mathfrak{sl}(3|2)_k$. Moreover, we enjoin some certain\nrestrictions on the gauge fields for the most general boundary conditions,\nleading to the supersymmetric extensions of the Brown and Henneaux boundary\nconditions. Based on these results, we finally find out that the asymptotic\nsymmetry algebras are two copies of the super $\\mathcal{W}_3$ algebra for\n$\\mathcal{N} = (2,2)$ extended higher-spin supergravity theory in $AdS_3$.", "category": "hep-th" }, { "text": "Exactly Marginal Deformations of N=4 SYM and of its Supersymmetric\n Orbifold Descendants: In this paper we study exactly marginal deformations of field theories living\non D3-branes at low energies. These theories include N=4 supersymmetric\nYang-Mills theory and theories obtained from it via the orbifolding procedure.\nWe restrict ourselves only to orbifolds and deformations which leave some\nsupersymmetry unbroken. A number of new families of N=1 superconformal field\ntheories are found. We analyze the deformations perturbatively, and also by\nusing general arguments for the dimension of the space of exactly marginal\ndeformations. We find some cases where the space of perturbative exactly\nmarginal deformations is smaller than the prediction of the general analysis at\nleast up to three-loop order), and other cases where the perturbative result\n(at low orders) has a non-generic form.", "category": "hep-th" }, { "text": "On the holographic duals of N=1 gauge dynamics: We analyze the holographic description of several properties of $\\N=1$\nconfining gauge dynamics. In particular we discuss Wilson loops including the\nissues of a Luscher term and the broadening of the flux tubes, 't Hooft loops,\nbaryons, instantons, chiral symmetry breaking, the gluino condensate and BPS\ndomain walls.", "category": "hep-th" }, { "text": "Holographic non-computers: We introduce the notion of holographic non-computer as a system which\nexhibits parametrically large delays in the growth of complexity, as calculated\nwithin the Complexity-Action proposal. Some known examples of this behavior\ninclude extremal black holes and near-extremal hyperbolic black holes. Generic\nblack holes in higher-dimensional gravity also show non-computing features.\nWithin the $1/d$ expansion of General Relativity, we show that large-$d$\nscalings which capture the qualitative features of complexity, such as a linear\ngrowth regime and a plateau at exponentially long times, also exhibit an\ninitial computational delay proportional to $d$. While consistent for large AdS\nblack holes, the required `non-computing' scalings are incompatible with\nthermodynamic stability for Schwarzschild black holes, unless they are tightly\ncaged.", "category": "hep-th" }, { "text": "Moving Domain Walls in $AdS_5$ and Graceful Exit from Inflation: We consider moving-brane-solutions in AdS type back ground. In the first\nRandall-Sundrum configuration, there are two branes at fixed points of the\norbifold symmetry. We point out that if one brane is fixed and the other brane\nis moving, the configuration is still a solution provided the moving brane has\na specific velocity determined by its tension and bulk cosmological constant.\nIn the absence of the $\\bf Z_2$ symmetry, we can construct multi-brane\nconfigurations by patching AdS-Schwarzshild solutions. In this case, we show\nthat the 4-dimensional effective cosmological constant on the brane world is\nnot well defined. We find a condition for a brane to be stationary. Using the\nbrane scattering, we suggest a scenario of inflation on the brane universe\nduring a finite time, i.e, a scenario of a graceful exit of inflation.", "category": "hep-th" }, { "text": "Dirac operators on the Taub-NUT space, monopoles and SU(2)\n representations: We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT\nmanifold coupled to an abelian gauge field with self-dual curvature, and\ninterpret them in terms of the zero modes of the Dirac operator on the 2-sphere\ncoupled to a Dirac monopole. We show that the space of zero modes decomposes\ninto a direct sum of irreducible SU(2) representations of all dimensions up to\na bound determined by the spinor charge with respect to the abelian gauge\ngroup. Our decomposition provides an interpretation of an index formula due to\nPope and provides a possible model for spin in recently proposed geometric\nmodels of matter.", "category": "hep-th" }, { "text": "Directly from $H$-flux to the family of three nonlocal $R$-flux theories: In this article we consider T-dualization of the 3D closed bosonic string in\nthe weakly curved background - constant metric and Kalb-Ramond field with one\nnon-zero component, $B_{xy}=Hz$, where field strength $H$ is infinitesimal. We\nuse standard and generalized Buscher T-dualization procedure and make\nT-dualization starting from coordinate $z$, via $y$ and finally along $x$\ncoordinate. All three theories are {\\it nonlocal}, because variable $\\Delta V$,\ndefined as line integral, appears as an argument of background fields. After\nthe first T-dualization we obtain commutative and associative theory, while\nafter we T-dualize along $y$, we get, $\\kappa$-Minkowski-like, noncommutative\nand associative theory. At the end of this T-dualization chain we come to the\ntheory which is both noncommutative and nonassociative. The form of the final\nT-dual action does not depend on the order of T-dualization while\nnoncommutativity and nonassociativity relations could be obtained from those in\nthe $x\\to y\\to z$ case by replacing $H\\to - H$.", "category": "hep-th" }, { "text": "Renormalization of Non-Semisimple Gauge Models with the Background Field\n Method: We study the renormalization of non-semisimple gauge models quantized in the\n`t Hooft-background gauge to all orders. We analyze the normalization\nconditions for masses and couplings compatible with the Slavnov-Taylor and\nWard-Takahashi Identities and with the IR constraints. We take into account\nboth the problem of renormalization of CKM matrix elements and the problem of\nCP violation and we show that the Background Field Method (BFM) provides proper\nnormalization conditions for fermion, scalar and gauge field mixings. We\ndiscuss the hard and the soft anomalies of the Slavnov-Taylor Identities and\nthe conditions under which they are absent.", "category": "hep-th" }, { "text": "On RSOS models associated to Lie algebras and RCFT: RSOS models based on the Lie algebras $B_m$, $C_m$ and $D_m$ are derived from\nthe braiding of conformal field theory. This gives the first systematic\nderivation of these models earlier described by Jimbo et al. The general two\nfield Boltzmann weights associated to any RCFT are described, giving in\nparticular the off critical thermalized Boltzmann weights. Crossing properties\nare discussed and are shown to agree with the general theory which connects\nthese with toroidal modular transformations. The soliton systems based on these\nlattice models are described and are conjectured based on the mass formulae and\nthe spins of the integrals of motions to describe perturbations of the RCFT\n$G_k\\times G_1\\over G_{k+1}$, where $G$ is the corresponding Lie algebra.", "category": "hep-th" }, { "text": "Classical stability of stringy wormholes in flat and AdS spaces: We study small fluctuations of the stringy wormhole solutions of\ngraviton-dilaton-axion system in arbitrary dimensions. We show under\nO($d$)-symmetric harmonic perturbation that the Euclidean wormhole solutions\nare unstable in flat space irrespective of dimensions and in anti de Sitter\nspace of $d=3$.", "category": "hep-th" }, { "text": "Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories: M-theory on compact eight-manifolds with $\\mathrm{Spin}(7)$-holonomy is a\nframework for geometric engineering of 3d $\\mathcal{N}=1$ gauge theories\ncoupled to gravity. We propose a new construction of such\n$\\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the\nbuilding blocks are a Calabi-Yau four-fold and a $G_2$-holonomy manifold times\na circle, respectively, which both asymptote to a Calabi-Yau three-fold times a\ncylinder. The generalized connected sum construction is first exemplified for\nJoyce orbifolds, and is then used to construct examples of new compact\nmanifolds with $\\mathrm{Spin}(7)$-holonomy. In instances when there is a\nK3-fibration of the $\\mathrm{Spin}(7)$-manifold, we test the spectra using\nduality to heterotic on a $T^3$-fibered $G_2$-holonomy manifold, which are\nshown to be precisely the recently discovered twisted-connected sum\nconstructions.", "category": "hep-th" }, { "text": "Reflection algebra, Yangian symmetry and bound-states in AdS/CFT: We present the `Heisenberg picture' of the reflection algebra by explicitly\nconstructing the boundary Yangian symmetry of an AdS/CFT superstring which ends\non a boundary with non-trivial degrees of freedom and which preserves the full\nbulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary\nstates and some automorphisms of the underlying algebras.", "category": "hep-th" }, { "text": "Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality: We conjecture closed-form expressions for the Macdonald limits of the\nsuperconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas\n(AD) theories in terms of certain simple deformations of Macdonald polynomials.\nAs checks of our conjectures, we demonstrate compatibility with two\nS-dualities, we show symmetry enhancement for special values of n, and we argue\nthat our expressions encode a non-trivial set of renormalization group flows.\nMoreover, we demonstrate that, for certain values of n, our conjectures imply\nsimple operator relations involving composites built out of the SU(2)_R\ncurrents and flavor symmetry moment maps, and we find a consistent picture in\nwhich these relations give rise to certain null states in the corresponding\nchiral algebras. In addition, we show that the Hall-Littlewood limits of our\nindices are equivalent to the corresponding Higgs branch Hilbert series. We\nexplain this fact by considering the S^1 reductions of our theories and showing\nthat the equivalence follows from an inequality on monopole quantum numbers\nwhose coefficients are fixed by data of the four-dimensional parent theories.\nFinally, we comment on the implications of our work for more general N=2\nsuperconformal field theories.", "category": "hep-th" }, { "text": "Scalar BCJ Bootstrap: In this letter, we study tree-level scattering amplitudes of scalar particles\nin the context of effective field theories. We use tools similar to the soft\nbootstrap to build an ansatz for cyclically ordered amplitudes and impose the\nBern-Carrasco-Johansson (BCJ) relations as a constraint. We obtain a set of\nBCJ-satisfying amplitudes as solutions to our procedure, which can be thought\nof as special higher-derivative corrections to SU(N) non-linear sigma model\namplitudes satisfying BCJ relations to arbitrary multiplicity at leading order.\nThe surprising outcome of our analysis is that BCJ conditions on higher-point\namplitudes impose constraints on lower-point amplitudes, and they relate\ncoefficients at different orders in the derivative expansion. This shows that\nBCJ conditions are much more restrictive than soft limit behavior, allowing\nonly for a very small set of solutions.", "category": "hep-th" }, { "text": "Some approaches to 2+1-dimensional gravity coupled to point-particles: In these notes we will review some approaches to 2+1 dimensional gravity and\nthe way it is coupled to point-particles. First we look into some exact static\nand stationary solutions with and without cosmological constant. Next we study\nthe polygon approach invented by 't Hooft. The third section treats the\nChern-Simonons formulation of 2+1-gravity. In the last part we map the problem\nof finding the gravitational field around point-particles to the\nRiemann-Hilbert problem.", "category": "hep-th" }, { "text": "Topologically Massive Spin-1 Particles and Spin-Dependent Potentials: We investigate the role played by particular field representations of an\nintermediate massive spin-1 boson in the context of spin-dependent\ninterparticle potentials between fermionic sources in the limit of low momentum\ntransfer. The comparison between the well-known case of the Proca field and\nthat of an exchanged spin-1 boson (with gauge-invariant mass) described by a\n2-form potential mixed with a 4-vector gauge field is established in order to\npursue an analysis of spin- as well as velocity-dependent profiles of the\ninterparticle potentials. We discuss possible applications and derive an upper\nbound on the product of vector and pseudo-tensor coupling constants.", "category": "hep-th" }, { "text": "Matrix Model Description of Laughlin Hall States: We analyze Susskind's proposal of applying the non-commutative Chern-Simons\ntheory to the quantum Hall effect. We study the corresponding regularized\nmatrix Chern-Simons theory introduced by Polychronakos. We use holomorphic\nquantization and perform a change of matrix variables that solves the Gauss law\nconstraint. The remaining physical degrees of freedom are the complex\neigenvalues that can be interpreted as the coordinates of electrons in the\nlowest Landau level with Laughlin's wave function. At the same time, a\nstatistical interaction is generated among the electrons that is necessary to\nstabilize the ground state. The stability conditions can be expressed as the\nhighest-weight conditions for the representations of the W-infinity algebra in\nthe matrix theory. This symmetry provides a coordinate-independent\ncharacterization of the incompressible quantum Hall states.", "category": "hep-th" }, { "text": "Spin-Statistics for Black Hole Microstates: The gravitational path integral can be used to compute the number of black\nhole states for a given energy window, or the free energy in a thermal\nensemble. In this article we explain how to use the gravitational path integral\nto compute the separate number of bosonic and fermionic black hole microstates.\nWe do this by comparing the partition function with and without the insertion\nof $(-1)^{\\sf F}$. In particular we introduce a universal rotating black hole\nthat contributes to the partition function in the presence of $(-1)^{\\sf F}$.\nWe study this problem for black holes in asymptotically flat space and in AdS,\nputting constraints on the high energy spectrum of holographic CFTs (not\nnecessarily supersymmetric). Finally, we analyze wormhole contributions to\nrelated quantities.", "category": "hep-th" }, { "text": "Duality between the massive sine-Gordon and the massive Schwinger models\n at finite temperature: The massive Schwinger and the massive sine-Gordon models are proved to be\nequivalent at finite temperature, using the path-integral framework. The well\nknown relations among the parameters of these models to establish the duality\nat $T=0$, also remain valid at non zero temperature.", "category": "hep-th" }, { "text": "$L_\\infty$-Algebras, the BV Formalism, and Classical Fields: We summarise some of our recent works on $L_\\infty$-algebras and quasi-groups\nwith regard to higher principal bundles and their applications in twistor\ntheory and gauge theory. In particular, after a lightning review of\n$L_\\infty$-algebras, we discuss their Maurer-Cartan theory and explain that any\nclassical field theory admitting an action can be reformulated in this context\nwith the help of the Batalin-Vilkovisky formalism. As examples, we explore\nhigher Chern-Simons theory and Yang-Mills theory. We also explain how these\nideas can be combined with those of twistor theory to formulate maximally\nsuperconformal gauge theories in four and six dimensions by means of\n$L_\\infty$-quasi-isomorphisms, and we propose a twistor space action.", "category": "hep-th" }, { "text": "Parity realization in Vector-like theories from Fermion Bilinears: We reconsider in this paper the old aim of trying to understand if the\nobserved realization of discrete symmetries as Parity or CP in the QCD vacuum\ncan be satisfied from first principles. We show how under the appropriate\nassumptions implicitely done by Vafa and Witten in their old paper on parity\nrealization in vector-like theories, all parity and CP odd operators\nconstructed from fermion bilinears of the form $\\bar\\psi\\tilde O\\psi$ should\ntake a vanishing vacuum expectation value in a vector-like theory with N\ndegenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the\nimpossibility to break spontaneously the flavour symmetry in a vector-like\ntheory plays a fundamental role.", "category": "hep-th" }, { "text": "Unitary Realizations of U-duality Groups as Conformal and Quasiconformal\n Groups and Extremal Black Holes of Supergravity Theories: We review the current status of the construction of unitary representations\nof U-duality groups of supergravity theories in five, four and three\ndimensions. We focus mainly on the maximal supergravity theories and on the N=2\nMaxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of\ndegree three in five dimensions and their descendants in four and three\ndimensions. Entropies of the extremal black hole solutions of these theories in\nfive and four dimensions are given by certain invariants of their U-duality\ngroups. The five dimensional U-duality groups admit extensions to spectrum\ngenerating generalized conformal groups which are isomorphic to the U-duality\ngroups of corresponding four dimensional theories. Similarly, the U-duality\ngroups of four dimensional theories admit extensions to spectrum generating\nquasiconformal groups that are isomorphic to the corresponding U-duality groups\nin three dimensions. We outline the oscillator construction of the unitary\nrepresentations of generalized conformal groups that admit positive energy\nrepresentations, which include the U-duality groups of N=2 MESGT's in four\ndimensions. We conclude with a review of the minimal unitary realizations of\nU-duality groups that are obtained by quantizations of their quasiconformal\nactions.", "category": "hep-th" }, { "text": "Positivity, negativity, and entanglement: We explore properties of the universal terms in the entanglement entropy and\nlogarithmic negativity in 4d CFTs, aiming to clarify the ways in which they\nbehave like the analogous entanglement measures in quantum mechanics. We show\nthat, unlike entanglement entropy in finite-dimensional systems, the sign of\nthe universal part of entanglement entropy is indeterminate. In particular, if\nand only if the central charges obey $a>c$, the entanglement across certain\nclasses of entangling surfaces can become arbitrarily negative, depending on\nthe geometry and topology of the surface. The negative contribution is\nproportional to the product of $a-c$ and the genus of the surface. Similarly,\nwe show that in $a>c$ theories, the logarithmic negativity does not always\nexceed the entanglement entropy.", "category": "hep-th" }, { "text": "BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic\n Symmetries: The asymptotic group of symmetries at null infinity of flat spacetimes in\nthree and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS)\ngroup. This has recently been shown to be isomorphic to non-relativistic\nconformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA)\nin 2d and a closely related non-relativistic algebra in 3d [1]. We provide a\nbetter understanding of this surprising connection by providing a spacetime\ninterpretation in terms of a novel contraction. The 2d GCA, obtained from a\nlinear combination of two copies of the Virasoro algebra, is generically\nnon-unitary. The unitary subsector previously constructed had trivial\ncorrelation functions. We consider a representation obtained from a different\nlinear combination of the Virasoros, which is relevant to the relation with the\nBMS algebra in three dimensions. This is realised by a new space-time\ncontraction of the parent algebra. We show that this representation has a\nunitary sub-sector with interesting correlation functions. We discuss\nimplications for the BMS/GCA correspondence and show that the flat space limit\nactually induces precisely this contraction on the boundary conformal field\ntheory. We also discuss aspects of asymptotic symmetries and the consequences\nof this contraction in higher dimensions.", "category": "hep-th" }, { "text": "Lagrange Multiplier Modified Horava-Lifshitz Gravity: We consider RFDiff invariant Horava-Lifshitz gravity action with additional\nLagrange multiplier term that is a function of scalar curvature. We find its\nHamiltonian formulation and we show that the constraint structure implies the\nsame number of physical degrees of freedom as in General Relativity.", "category": "hep-th" }, { "text": "The Holomorphic Anomaly of Topological Strings: We show that the BRS operator of the topological string B model is not\nholomorphic in the complex structure of the target space. This implies that the\nso-called holomorphic anomaly of topological strings should not be interpreted\nas a BRS anomaly.", "category": "hep-th" }, { "text": "Thermal Dark Energy: We present a novel source of dark energy, which is motivated by the\nprevalence of hidden sectors in string theory models and is consistent with all\nof the proposed swampland conjectures. Thermal effects hold a light hidden\nsector scalar at a point in field space that is not a minimum of its zero\ntemperature potential. This leads to an effective \"cosmological constant\", with\nan equation of state $w=-1$, despite the scalar's zero temperature potential\nhaving only a 4D Minkowski or AdS vacuum. For scalar masses $\\lesssim \\mu$eV,\nwhich could be technically natural via sequestering, there are large regions of\nphenomenologically viable parameter space such that the induced vacuum energy\nmatches the measured dark energy density. Additionally, in many models a\nstandard cosmological history automatically leads to the scalar having the\nrequired initial conditions. We study the possible observational signals of\nsuch a model, including at fifth force experiments and through $\\Delta N_{\\rm\neff}$ measurements. Similar dynamics that are active at earlier times could\nresolve the tension between different measurements of $H_0$ and can lead to a\ndetectable stochastic gravitational wave background.", "category": "hep-th" }, { "text": "Bit threads and holographic entanglement: The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region\nin a holographic theory to the area of a corresponding bulk minimal surface.\nUsing the max flow-min cut principle, a theorem from network theory, we rewrite\nthe RT formula in a way that does not make reference to the minimal surface.\nInstead, we invoke the notion of a \"flow\", defined as a divergenceless\nnorm-bounded vector field, or equivalently a set of Planck-thickness \"bit\nthreads\". The entanglement entropy of a boundary region is given by the maximum\nflux out of it of any flow, or equivalently the maximum number of bit threads\nthat can emanate from it. The threads thus represent entanglement between\npoints on the boundary, and naturally implement the holographic principle. As\nwe explain, this new picture clarifies several conceptual puzzles surrounding\nthe RT formula. We give flow-based proofs of strong subadditivity and related\nproperties; unlike the ones based on minimal surfaces, these proofs correspond\nin a transparent manner to the properties' information-theoretic meanings. We\nalso briefly discuss certain technical advantages that the flows offer over\nminimal surfaces. In a mathematical appendix, we review the max flow-min cut\ntheorem on networks and on Riemannian manifolds, and prove in the network case\nthat the set of max flows varies Lipshitz continuously in the network\nparameters.", "category": "hep-th" }, { "text": "Neutrino mixing and cosmological constant: We report on the recent result that the non--perturbative vacuum structure\nassociated with neutrino mixing leads to a non--zero contribution to the value\nof the cosmological constant. Its value is estimated by using the natural\ncut--off appearing in the quantum field theory formalism for neutrino mixing.", "category": "hep-th" }, { "text": "Bogoliubov Renormalization Group and Symmetry of Solution in\n Mathematical Physics: Evolution of the concept known in the theoretical physics as the\nRenormalization Group (RG) is presented. The corresponding symmetry, that has\nbeen first introduced in QFT in mid-fifties, is a continuous symmetry of a\nsolution with respect to transformation involving parameters (e.g., of boundary\ncondition) specifying some particular solution.\n After short detour into Wilson's discrete semi-group, we follow the expansion\nof QFT RG and argue that the underlying transformation, being considered as a\nreparameterisation one, is closely related to the self-similarity property. It\ncan be treated as its generalization, the Functional Self-similarity (FS).\n Then, we review the essential progress during the last decade of the FS\nconcept in application to boundary value problem formulated in terms of\ndifferential equations. A summary of a regular approach recently devised for\ndiscovering the RG = FS symmetries with the help of the modern Lie group\nanalysis and some of its applications are given.\n As a main physical illustration, we give application of new approach to\nsolution for a problem of self-focusing laser beam in a non-linear medium.", "category": "hep-th" }, { "text": "The GUP and quantum Raychaudhuri equation: In this paper, we compare the quantum corrections to the Schwarzschild black\nhole temperature due to quadratic and linear-quadratic generalized uncertainty\nprinciple, with the corrections from the quantum Raychaudhuri equation. The\nreason for this comparison is to connect the deformation parameters $\\beta_0$\nand $ \\alpha_0$ with $\\eta$ which is the parameter that characterizes the\nquantum Raychaudhuri equation. The derived relation between the parameters\nappears to depend on the relative scale of the system (black hole), which could\nbe read as a beta function equation for the quadratic deformation parameter\n$\\beta_0$. This study shows a correspondence between the two phenomenological\napproaches and indicates that quantum Raychaudhuri equation implies the\nexistence of a crystal-like structure of spacetime.", "category": "hep-th" }, { "text": "Enhanced Gauge Symmetry in Type II String Theory: We show how enhanced gauge symmetry in type II string theory compactified on\na Calabi--Yau threefold arises from singularities in the geometry of the target\nspace. When the target space of the type IIA string acquires a genus $g$ curve\n$C$ of $A_{N-1}$ singularities, we find that an $SU(N)$ gauge theory with $g$\nadjoint hypermultiplets appears at the singularity. The new massless states\ncorrespond to solitons wrapped about the collapsing cycles, and their dynamics\nis described by a twisted supersymmetric gauge theory on $C\\times \\R^4$. We\nreproduce this result from an analysis of the $S$-dual $D$-manifold. We check\nthat the predictions made by this model about the nature of the Higgs branch,\nthe monodromy of period integrals, and the asymptotics of the one-loop\ntopological amplitude are in agreement with geometrical computations. In one of\nour examples we find that the singularity occurs at strong coupling in the\nheterotic dual proposed by Kachru and Vafa.", "category": "hep-th" }, { "text": "Derivative self-interactions for a massive vector field: In this work we revisit the construction of theories for a massive vector\nfield with derivative self-interactions such that only the 3 desired\npolarizations corresponding to a Proca field propagate. We start from the\ndecoupling limit by constructing healthy interactions containing second\nderivatives of the Stueckelberg field with itself and also with the transverse\nmodes. The resulting interactions can then be straightforwardly generalized\nbeyond the decoupling limit. We then proceed to a systematic construction of\nthe interactions by using the Levi-Civita tensors. Both approaches lead to a\nfinite family of allowed derivative self-interactions for the Proca field. This\nconstruction allows us to show that some higher order terms recently introduced\nas new interactions trivialize in 4 dimensions by virtue of the Cayley-Hamilton\ntheorem. Moreover, we discuss how the resulting derivative interactions can be\nwritten in a compact determinantal form, which can also be regarded as a\ngeneralization of the Born-Infeld lagrangian for electromagnetism. Finally, we\ngeneralize our results for a curved background and give the necessary\nnon-minimal couplings guaranteeing that no additional polarizations propagate\neven in the presence of gravity.", "category": "hep-th" }, { "text": "The double cone geometry is stable to brane nucleation: In gauge/gravity duality, the bulk double cone geometry has been argued to\naccount for a key feature of the spectral form factor known as the ramp. This\nfeature is deeply associated with quantum chaos in the dual field theory. The\nconnection with the ramp has been demonstrated in detail for two-dimensional\ntheories of bulk gravity, but it appears natural in higher dimensions as well.\nIn a general bulk theory the double cone might thus be expected to dominate the\nsemiclassical bulk path integral for the boundary spectral form factor in the\nramp regime. While other known spacetime wormholes have been shown to be\nunstable to brane nucleation when they dominate over known disconnected\n(factorizing) solutions, we argue that the double cone is stable to\nsemiclassical brane nucleation at the probe-brane level in a variety of string-\nand M-theory settings. Possible implications for the AdS/CFT factorization\nproblem are briefly discussed.", "category": "hep-th" }, { "text": "Flow of shear response functions in hyperscaling violating Lifshitz\n theories: We study the flow equations of the shear response functions for hyperscaling\nviolating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating\nexponents $z$ and $\\theta$. Adapting the membrane paradigm approach of\nanalysing response functions as developed by Iqbal and Liu, we focus\nspecifically on the shear gravitational modes which now are coupled to the\nperturbations of the background gauge field. Restricting to the zero momenta\nsector, we make further simplistic assumptions regarding the hydrodynamic\nexpansion of the perturbations. Analysing the flow equations shows that the\nshear viscosity at leading order saturates the Kovtun-Son-Starinets (KSS) bound\nof $\\frac{1}{4\\pi}$. When $z=d_i-\\theta$, ($d_i$ being the number of spatial\ndimension in the dual field theory) the first-order correction to shear\nviscosity exhibits logarithmic scaling, signalling the emergence of a scale in\nthe UV regime for this class of hvLif theories. We further show that the\nresponse function associated to the gauge field perturbations diverge near the\nboundary when $z>d_i+2-\\theta$. This provides a holographic understanding of\nthe origin of such a constraint and further vindicates results obtained in\nprevious works that were obtained through near horizon and quasinormal mode\nanalysis.", "category": "hep-th" }, { "text": "\u03b8-angle monodromy in two dimensions: \"\\theta-angle monodromy\" occurs when a theory possesses a landscape of\nmetastable vacua which reshuffle as one shifts a periodic coupling \\theta by a\nsingle period. \"Axion monodromy\" models arise when this parameter is promoted\nto a dynamical pseudoscalar field. This paper studies the phenomenon in\ntwo-dimensional gauge theories which possess a U(1) factor at low energies: the\nmassive Schwinger and gauged massive Thirring models, the U(N) 't Hooft model,\nand the {\\mathbb CP}^N model. In all of these models, the energy dependence of\na given metastable false vacuum deviates significantly from quadratic\ndependence on \\theta just as the branch becomes completely unstable (distinct\nfrom some four-dimensional axion monodromy models). In the Schwinger, Thirring,\nand 't Hooft models, the meson masses decrease as a function of \\theta. In the\nU(N) models, the landscape is enriched by sectors with nonabelian \\theta terms.\nIn the {\\mathbb CP}^N model, we compute the effective action and the size of\nthe mass gap is computed along a metastable branch.", "category": "hep-th" }, { "text": "The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube\n II.Simple Cases of Symmetry Breakdown and Restoration: This paper continues a study of field theories specified for the nonuniform\nlattice in the finite-dimensional hypercube with the use of the earlier\ndescribed deformation parameters. The paper is devoted to spontaneous breakdown\nand restoration of symmetry in simple quantum-field theories with scalar\nfields. It is demonstrated that an appropriate deformation opens up new\npossibilities for symmetry breakdown and restoration. To illustrate, at low\nenergies it offers high-accuracy reproducibility of the same results as with a\nnondeformed theory. In case of transition from low to higher energies and vice\nversa it gives description for new types of symmetry breakdown and restoration\ndepending on the rate of the deformation parameter variation in time, and\nindicates the critical points of the previously described lattice associated\nwith a symmetry restoration. Besides, such a deformation enables one to find\nimportant constraints on the initial model parameters having an explicit\nphysical meaning.", "category": "hep-th" }, { "text": "Monopole-fermion scattering and varying Fock space: We propose a four-dimensional interpretation of the outgoing state of the\nscattering of a massless fermion off a Dirac monopole. It has been known that\nsuch a state has fractional fermion numbers and is necessarily outside the Fock\nspace on top of ordinary perturbative vacuum, when more than two flavours of\ncharged Dirac fermions are considered. In this paper, we point out that the\nFock space of the fermions depends on the rotor degree of freedom of the\nmonopole and changes by a monopole-fermion s-wave scattering. By uplifting the\nfermion-rotor system introduced by Polchinski, from two to four dimensions, we\nargue that the outgoing state can be understood as a state in a different Fock\nspace.", "category": "hep-th" }, { "text": "Topologically massive gravity and complex Chern-Simons terms: This paper is withdrawn because its results have been previously reported in\narxiv hep-th/0507200.", "category": "hep-th" }, { "text": "Entropic destruction of heavy quarkonium in non-Abelian plasma from\n holography: Lattice QCD indicates a large amount of entropy associated with the heavy\nquark-antiquark pair immersed in the quark-gluon plasma. This entropy grows as\na function of the inter-quark distance giving rise to an entropic force that\ncan be very effective in dissociating the bound quarkonium states. In addition,\nthe lattice data show a very sharp peak in the heavy quark-antiquark entropy at\nthe deconfinement transition. Since the quark-gluon plasma around the\ndeconfinement transition is strongly coupled, we employ the holographic\ncorrespondence to study the entropy associated with the heavy quark-antiquark\npair in two theories: i) ${\\cal{N}}=4$ supersymmetric Yang-Mills and ii) a\nconfining Yang-Mills theory obtained by compactification on a Kaluza-Klein\ncircle. In both cases we find the entropy growing with the inter-quark distance\nand evaluate the effect of the corresponding entropic forces. In the case ii),\nwe find a sharp peak in the entropy near the deconfinement transition, in\nagreement with the lattice QCD results. This peak in our holographic\ndescription arises because the heavy quark pair acts as an eyewitness of the\nblack hole formation in the bulk -- the process that describes the\ndeconfinement transition. In terms of the boundary theory, this entropy likely\nemerges from the entanglement of a \"long string\" connecting the quark and\nantiquark with the rest of the system.", "category": "hep-th" }, { "text": "Perturbative instabilities in Horava gravity: We investigate the scalar and tensor perturbations in Horava gravity, with\nand without detailed balance, around a flat background. Once both types of\nperturbations are taken into account, it is revealed that the theory is plagued\nby ghost-like scalar instabilities in the range of parameters which would\nrender it power-counting renormalizable, that cannot be overcome by simple\ntricks such as analytic continuation. Implementing a consistent flow between\nthe UV and IR limits seems thus more challenging than initially presumed,\nregardless of whether the theory approaches General Relativity at low energies\nor not. Even in the phenomenologically viable parameter space, the tensor\nsector leads to additional potential problems, such as fine-tunings and\nsuper-luminal propagation.", "category": "hep-th" }, { "text": "Lattice W algebras and quantum groups: We represent Feigin's construction [11] of lattice W algebras and give some\nsimple results: lattice Virasoro and $W_3$ algebras. For simplest case\n$g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We\nfind simplest two-dimensional module as well as exchange relations and define\nlattice Virasoro algebra as algebra of invariants of $U_q(sl(2))$. Another\ngeneralization is connected with lattice integrals of motion as the invariants\nof quantum affine group $U_q(\\hat{n}_{+})$. We show that Volkov's scheme leads\nto the system of difference equations for the function from non-commutative\nvariables.Continium limit of this lattice algebras are considered.", "category": "hep-th" }, { "text": "Galilean Conformal Electrodynamics: Maxwell's Electrodynamics admits two distinct Galilean limits called the\nElectric and Magnetic limits. We show that the equations of motion in both\nthese limits are invariant under the Galilean Conformal Algebra in D=4, thereby\nexhibiting non-relativistic conformal symmetries. Remarkably, the symmetries\nare infinite dimensional and thus Galilean Electrodynamics give us the first\nexample of an infinitely extended Galilean Conformal Field Theory in D>2. We\nexamine details of the theory by looking at purely non-relativistic conformal\nmethods and also use input from the limit of the relativistic theory.", "category": "hep-th" }, { "text": "BPS Boojums in N=2 supersymmetric gauge theories II: We continue our study of 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite\nsolitons of vortex strings, domain walls and boojums in N=2 supersymmetric\nAbelian gauge theories in four dimensions. In this work, we numerically confirm\nthat a boojum appearing at an end point of a string on a thick domain wall\nbehaves as a magnetic monopole with a fractional charge in three dimensions. We\nintroduce a \"magnetic\" scalar potential whose gradient gives magnetic fields.\nHeight of the magnetic potential has a geometrical meaning that is shape of the\ndomain wall. We find a semi-local extension of boojum which has an additional\nsize moduli at an end point of a semi-local string on the domain wall. Dyonic\nsolutions are also studied and we numerically confirm that the dyonic domain\nwall becomes an electric capacitor storing opposite electric charges on its\nskins. At the same time, the boojum becomes fractional dyon whose charge\ndensity is proportional to ${\\vec E} \\cdot {\\vec B}$. We also study dual\nconfigurations with an infinite number of boojums and anti-boojums on parallel\nlines and analyze the ability of domain walls to store magnetic charge as\nmagnetic capacitors. In understanding these phenomena, the magnetic scalar\npotential plays an important role. We study the composite solitons from the\nviewpoints of the Nambu-Goto and Dirac-Born-Infeld actions, and find the\nsemi-local BIon as the counterpart of the semi-local Boojum.", "category": "hep-th" }, { "text": "Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex: In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic\nvertex for self-interacting massless fields of spin three in flat spacetime.\nHowever, they also found that this deformation is inconsistent at higher order\nfor any multiplet of spin-three fields. For arbitrary symmetric gauge fields,\nwe severely constrain the possible nonabelian deformations of the gauge algebra\nand, using these results, prove that the BBvD obstruction cannot be cured by\nany means, even by introducing fields of spin higher (or lower) than three.", "category": "hep-th" }, { "text": "Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double\n Copy: Using the double-copy construction of Yang-Mills-Einstein theories formulated\nin our earlier work, we obtain compact presentations for single-trace\nYang-Mills-Einstein tree amplitudes with up to five external gravitons and an\narbitrary number of gluons. These are written as linear combinations of\ncolor-ordered Yang-Mills trees, where the coefficients are given by\ncolor/kinematics-satisfying numerators in a Yang-Mills+\\phi^3 theory. The\nconstruction outlined in this paper holds in general dimension and extends\nstraightforwardly to supergravity theories. For one, two, and three external\ngravitons, our expressions give identical or simpler presentations of\namplitudes already constructed through string-theory considerations or the\nscattering equations formalism. Our results are based on color/kinematics\nduality and gauge invariance, and strongly hint at a recursive structure\nunderlying the single-trace amplitudes with an arbitrary number of gravitons.\nFor the single-graviton case, we give amplitudes to any loop order and obtain,\nthrough gauge invariance, new loop-level amplitude relations for Yang-Mills\ntheory.", "category": "hep-th" }, { "text": "Analytical study of superradiant instability for five-dimensional\n Kerr-G\u00f6del black hole: We present an analytical study of superradiant instability of rotating\nasymptotically G\\\"{o}del black hole (Kerr-G\\\"{o}del black hole) in\nfive-dimensional minimal supergravity theory. By employing the matched\nasymptotic expansion method to solve Klein-Gordon equation of scalar field\nperturbation, we show that the complex parts of quasinormal frequencies are\npositive in the regime of superradiance. This implies the growing instability\nof superradiant modes. The reason for this kind of instability is the Dirichlet\nboundary condition at asymptotic infinity, which is similar to that of rotating\nblack holes in anti-de Sitter (AdS) spacetime.", "category": "hep-th" }, { "text": "A differential-geometry approach to operator mixing in massless QCD-like\n theories and Poincar\u00e9-Dulac theorem: We review recent progress on operator mixing in the light of the theory of\ncanonical forms for linear systems of differential equations and, in\nparticular, of the Poincar\\'e-Dulac theorem. We show that the matrix $A(g) =\n-\\frac{\\gamma(g)}{\\beta(g)} =\\frac{\\gamma_0}{\\beta_0}\\frac{1}{g} + \\cdots $\ndetermines which different cases of operator mixing can occur, and we review\ntheir classification. We derive a sufficient condition for $A(g)$ to be set in\nthe one-loop exact form $A(g) = \\frac{\\gamma_0}{\\beta_0}\\frac{1}{g}$. Finally,\nwe discuss the consequences of the unitarity requirement in massless QCD-like\ntheories, and we demonstrate that $\\gamma_0$ is always diagonalizable if the\ntheory is conformal invariant and unitary in its free limit at $g =0$.", "category": "hep-th" }, { "text": "Scaling Exponents for Lattice Quantum Gravity in Four Dimensions: In this work nonperturbative aspects of quantum gravity are investigated\nusing the lattice formulation, and some new results are presented for critical\nexponents, amplitudes and invariant correlation functions. Values for the\nuniversal scaling dimensions are compared with other nonperturbative approaches\nto gravity in four dimensions, and specifically to the conjectured value for\nthe universal critical exponent $\\nu =1 /3$. It is found that the lattice\nresults are generally consistent with gravitational anti-screening, which would\nimply a slow increase in the strength of the gravitational coupling with\ndistance, and here detailed estimates for exponents and amplitudes\ncharacterizing this slow rise are presented. Furthermore, it is shown that in\nthe lattice approach (as for gauge theories) the quantum theory is highly\nconstrained, and eventually by virtue of scaling depends on a rather small set\nof physical parameters. Arguments are given in support of the statement that\nthe fundamental reference scale for the growth of the gravitational coupling\n$G$ with distance is represented by the observed scaled cosmological constant\n$\\lambda$, which in gravity acts as an effective nonperturbative infrared\ncutoff. In the vacuum condensate picture a fundamental relationship emerges\nbetween the scale characterizing the running of $G$ at large distances, the\nmacroscopic scale for the curvature as described by the observed cosmological\nconstant, and the behavior of invariant gravitational correlation functions at\nlarge distances. Overall, the lattice results suggest that the infrared slow\ngrowth of $G$ with distance should become observable only on very large\ndistance scales, comparable to $\\lambda$. It is hoped that future high\nprecision satellite experiments will possibly come within reach of this small\nquantum correction, as suggested by a vacuum condensate picture of quantum\ngravity.", "category": "hep-th" }, { "text": "Comment on `Index-free Heat Kernel Coefficients': The article by Anton E. M. van de Ven, Class. Quantum Grav. \\textbf{15}\n(1998), is one of the fundamental references for higher-order heat kernel\ncoefficients in curved backgrounds and with non-abelian gauge connections. In\nthis manuscript, we point out two errors and ambiguities in the $\\mathsf{a}_5$\ncoefficient, which may also affect the higher-order ones.", "category": "hep-th" }, { "text": "Conformal Symmetry, Rindler Space and The AdS/CFT Correspondence: Field theories in black hole spacetimes undergo dimensional reduction near\nhorizon (in the Rindler limit) to two dimensional conformal field theories. We\ninvestigate this enhancement of symmetries in the context of gauge/gravity\nduality by considering Rindler space as boundary of Anti-de Sitter space in\nthree spacetime dimensions. We show that the loxodromy conjugacy class of the\nSO(2,2) isometry group is responsible for generating the special conformal\ntransformations on the boundary under RG flow. We use this approach to present\nan alternative derivation of the two-point function in Rindler space using\nAdS/CFT correspondence.", "category": "hep-th" }, { "text": "Optics, Mechanics and Quantization of Reparametrization Systems: In this paper we regard the dynamics obtained from Fermat principle as begin\nthe classical theory of light. We (first-)quantize the action and show how\nclose we can get to the Maxwell theory. We show that Quantum Geometric Optics\nis not a theory of fields in curved space. Considering Classical Mechanics to\nbe on the same footing, we show the parallelism between Quantum Mechanics and\nQuantum Geometric Optics. We show that, due to the reparametrization invariance\nof the classical theories, the dynamics of the quantum theories is given by a\nHamiltonian constraint. Some implications of the above analogy in the\nquantization of true reparameterization invariant systems are discussed.", "category": "hep-th" }, { "text": "Do the gravitational corrections to the beta functions of the quartic\n and Yukawa couplings have an intrinsic physical meaning?: We study the beta functions of the quartic and Yukawa couplings of General\nRelativity and Unimodular Gravity coupled to the $\\lambda\\phi^4$ and Yukawa\ntheories with masses. We show that the General Relativity corrections to those\nbeta functions as obtained from the 1PI functional by using the standard MS\nmultiplicative renormalization scheme of Dimensional Regularization are gauge\ndependent and, further, that they can be removed by a non-multiplicative,\nthough local, field redefinition. An analogous analysis is carried out when\nGeneral Relativity is replaced with Unimodular Gravity. Thus we show that any\nclaim made about the change in the asymptotic behaviour of the quartic and\nYukawa couplings made by General Relativity and Unimodular Gravity lack\nintrinsic physical meaning.", "category": "hep-th" }, { "text": "Flat space (higher spin) gravity with chemical potentials: We introduce flat space spin-3 gravity in the presence of chemical potentials\nand discuss some applications to flat space cosmology solutions, their entropy,\nfree energy and flat space orbifold singularity resolution. Our results include\nflat space Einstein gravity with chemical potentials as special case. We\ndiscover novel types of phase transitions between flat space cosmologies with\nspin-3 hair and show that the branch that continuously connects to spin-2\ngravity becomes thermodynamically unstable for sufficiently large temperature\nor spin-3 chemical potential.", "category": "hep-th" }, { "text": "Relative scale separation in orbifolds of $S^2$ and $S^5$: In orbifold vacua containing an $S^q/\\Gamma$ factor, we compute the relative\norder of scale separation, $r$, defined as the ratio of the eigenvalue of the\nlowest-lying $\\Gamma$-invariant state of the scalar Laplacian on $S^q$, to the\neigenvalue of the lowest-lying state. For $q=2$ and $\\Gamma$ finite subgroup of\n$SO(3)$, or $q=5$ and $\\Gamma$ finite subgroup of $SU(3)$, the maximal relative\norder of scale separation that can be achieved is $r=21$ or $r=12$,\nrespectively. For smooth $S^5$ orbifolds, the maximal relative scale separation\nis $r=4.2$. Methods from invariant theory are very efficient in constructing\n$\\Gamma$-invariant spherical harmonics, and can be readily generalized to other\norbifolds.", "category": "hep-th" }, { "text": "Special holonomy sigma models with boundaries: A study of (1,1) supersymmetric two-dimensional non-linear sigma models with\nboundary on special holonomy target spaces is presented. In particular, the\nconsistency of the boundary conditions under the various symmetries is studied.\nModels both with and without torsion are discussed.", "category": "hep-th" }, { "text": "Further comments on BPS systems: We look at BPS systems involving two interacting Sine-Gordon like fields both\nwhen one of them has a kink solution and the second one either a kink or an\nantikink solution. The interaction between the two fields is controlled by a\nparameter $\\lambda$ which has to satisfy $| \\lambda|< 2$. We then take these\nsolitonic static solutions (with solitons well localised) and construct from\nthem systems involving two solitons in each field (kinks and antikinks) and\nthen use them as initial conditions for their evolution in Lorentz covariant\nversions of such models. This way we study their interactions and compare them\nwith similar interactions involving only one Sine-Gordon field. In particular,\nwe look at the behaviour of two static kinks in each field (which for one field\nrepel each other) and of a system involving kinks and anti-kinks (which for one\nfield attract each other) and look how their behaviour depends on the strength\nof the interaction $\\lambda$ between the two fields. Our simulations have led\nus to look again at the static BPS solutions of systems involving more fields.\nWe have found that such ostensibly 'static' BPS solutions can exhibit small\nmotions due to the excitation of their zero modes. These excitations arise from\nsmall unavoidable numerical errors (the overall translation is cancelled by the\nconservation of momentum) but as systems of two or more fields have more that\none zero mode such motions can be generated and are extremely small. The energy\nof our systems has been conserved to within $10^{-5}\\%$.", "category": "hep-th" }, { "text": "Nonlinear Fluid Dynamics from Gravity: Black branes in AdS5 appear in a four parameter family labeled by their\nvelocity and temperature. Promoting these parameters to Goldstone modes or\ncollective coordinate fields -- arbitrary functions of the coordinates on the\nboundary of AdS5 -- we use Einstein's equations together with regularity\nrequirements and boundary conditions to determine their dynamics. The resultant\nequations turn out to be those of boundary fluid dynamics, with specific values\nfor fluid parameters. Our analysis is perturbative in the boundary derivative\nexpansion but is valid for arbitrary amplitudes. Our work may be regarded as a\nderivation of the nonlinear equations of boundary fluid dynamics from gravity.\nAs a concrete application we find an explicit expression for the expansion of\nthis fluid stress tensor including terms up to second order in the derivative\nexpansion.", "category": "hep-th" }, { "text": "The periodic sl(2|1) alternating spin chain and its continuum limit as a\n bulk Logarithmic Conformal Field Theory at c=0: The periodic sl(2|1) alternating spin chain encodes (some of) the properties\nof hulls of percolation clusters, and is described in the continuum limit by a\nlogarithmic conformal field theory (LCFT) at central charge c=0. This theory\ncorresponds to the strong coupling regime of a sigma model on the complex\nprojective superspace $\\mathbb{CP}^{1|1} = \\mathrm{U}(2|1) / (\\mathrm{U}(1)\n\\times \\mathrm{U}(1|1))$, and the spectrum of critical exponents can be\nobtained exactly. In this paper we push the analysis further, and determine the\nmain representation theoretic (logarithmic) features of this continuum limit by\nextending to the periodic case the approach of [N. Read and H. Saleur, Nucl.\nPhys. B 777 316 (2007)]. We first focus on determining the representation\ntheory of the finite size spin chain with respect to the algebra of local\nenergy densities provided by a representation of the affine Temperley-Lieb\nalgebra at fugacity one. We then analyze how these algebraic properties carry\nover to the continuum limit to deduce the structure of the space of states as a\nrepresentation over the product of left and right Virasoro algebras. Our main\nresult is the full structure of the vacuum module of the theory, which exhibits\nJordan cells of arbitrary rank for the Hamiltonian.", "category": "hep-th" }, { "text": "Teleparallel Geroch geometry: We construct the teleparallel dynamics for extended geometry where the\nstructure algebra is (an extension of) an untwisted affine Kac-Moody algebra.\nThis provides a geometrisation of the Geroch symmetry appearing on dimensional\nreduction of a gravitational theory to two dimensions. The formalism is adapted\nto the underlying tensor hierarchy algebra, and will serve as a stepping stone\ntowards the geometrisation of other infinite-dimensional, e.g. hyperbolic,\nsymmetries.", "category": "hep-th" }, { "text": "Shadow multiplets and superHiggs mechanism: We discuss a general feature of Freund Rubin compactifications that was\npreviously overlooked. It consist in a curious pairing, which we call a shadow\nrelation, of completely different (in terms of spin and mass) fields of the\ndimensionally reduced theory. Particularly interesting is the case where the\ncompactification preserves a certain amount of supersymmetry, giving rise to a\nshadowing phenomenon between whole supermultiplets of fields. In particular,\nthere are strong suggestions about the consistency of a massive truncation of\n11D supergravity to the massless modes of the graviton supermultiplet plus the\nmassive modes of its shadow partner. This fact has important consequences in\nthe ${\\cal N}=2$ and ${\\cal N}=3$ cases, which seem to realize respectively a\nHiggs or a superHiggs phenomenon. In other words, we are led to reinterpret the\ndimensionally reduced theory as a spontaneously broken phase of some higher\n(super)symmetric theory.", "category": "hep-th" }, { "text": "The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories: We consider N = 3 supersymmetric Chern-Simons gauge theories with product\nunitary and orthosymplectic groups and bifundamental and fundamental fields. We\nstudy the partition functions on an S^3 by using the Kapustin-Willett-Yaakov\nmatrix model. The saddlepoint equations in a large N limit lead to a constraint\nthat the long range forces between the eigenvalues must cancel; the resulting\nquiver theories are of affine Dynkin type. We introduce a folding/unfolding\ntrick which lets us, at the level of the large N matrix model, (i) map quivers\nwith orthosymplectic groups to those with unitary groups, and (ii) obtain\nnon-simply laced quivers from the corresponding simply laced quivers using a\nZ_2 outer automorphism. The brane configurations of the quivers are described\nin string theory and the folding/unfolding is interpreted as the\naddition/subtraction of orientifold and orbifold planes. We also relate the\nU(N) quiver theories to the affine ADE quiver matrix models with a\nStieltjes-Wigert type potential, and derive the generalized Seiberg duality in\n2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.", "category": "hep-th" }, { "text": "High temperature asymptotics of thermodynamic functions of\n electromagnetic field subjected to boundary conditions on a sphere and\n cylinder: The high temperature asymptotics of thermodynamic functions of\nelectromagnetic field subjected to boundary conditions with spherical and\ncylindrical symmetries are constructed by making use of a general expansion in\nterms of heat kernel coefficients and the related determinant. For this, some\nnew heat kernel coefficients and determinants had to be calculated for the\nboundary conditions under consideration. The obtained results reproduce all the\nasymptotics derived by other methods in the problems at hand and involve a few\nnew terms in the high temperature expansions. An obvious merit of this approach\nis its universality and applicability to any boundary value problem correctly\nformulated.", "category": "hep-th" }, { "text": "Banana integrals in configuration space: We reconsider the computation of banana integrals at different loops, by\nworking in the configuration space, in any dimension. We show how the 2-loop\nbanana integral can be computed directly from the configuration space\nrepresentation, without the need to resort to differential equations, and we\ninclude the analytic extension of the diagram in the space of complex masses.\nWe also determine explicitly the $\\varepsilon$ expansion of the two loop banana\nintegrals, for $d=j-2\\varepsilon$, $j=2,3,4$.", "category": "hep-th" }, { "text": "Oscillators from nonlinear realizations: We construct the systems of the harmonic and Pais-Uhlenbeck oscillators,\nwhich are invariant with respect to arbitrary noncompact Lie algebras. The\nequations of motion of these systems can be obtained with the help of the\nformalism of nonlinear realizations. We prove that it is always possible to\nchoose time and the fields within this formalism in such a way that the\nequations of motion become linear and, therefore, reduce to ones of ordinary\nharmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce\nthese equations, can also be provided. As particular examples of this\nconstruction, we discuss the $so(2,3)$ and $G_{2(2)}$ algebras.", "category": "hep-th" }, { "text": "Self-dual solutions of a field theory model of two linked rings: In this work the connection established in [7, 8] between a model of two\nlinked polymers rings with fixed Gaussian linking number forming a 4-plat and\nthe statistical mechanics of non-relativistic anyon particles is explored. The\nexcluded volume interactions have been switched off and only the interactions\nof entropic origin arising from the topological constraints are considered. An\ninterpretation from the polymer point of view of the field equations that\nminimize the energy of the model in the limit in which one of the spatial\ndimensions of the 4-plat becomes very large is provided. It is shown that the\nself-dual contributions are responsible for the long-range interactions that\nare necessary for preserving the global topological properties of the system\nduring the thermal fluctuations. The non self-dual part is also related to the\ntopological constraints, and takes into account the local interactions acting\non the monomers in order to prevent the breaking of the polymer lines. It turns\nout that the energy landscape of the two linked rings is quite complex.\nAssuming as a rough approximation that the monomer densities of half of the\n4-plat are constant, at least two points of energy minimum are found. Classes\nof non-trivial self-dual solutions of the self-dual field equations are\nderived. ... .", "category": "hep-th" }, { "text": "Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x\n S5 superstrings: We construct supergravity backgrounds for the integrable eta-deformations of\nthe AdS2 x S2 x T6 and AdS5 x S5 superstring sigma models. The eta-deformation\nis governed by an R-matrix that solves the non-split modified classical\nYang-Baxter equation on the superisometry algebra of the model. Such R-matrices\ninclude those of Drinfel'd-Jimbo type, which are constructed from a Dynkin\ndiagram and the associated Cartan-Weyl basis. Drinfel'd-Jimbo R-matrices\nassociated with inequivalent bases will typically lead to different deformed\nbackgrounds. For the two models under consideration we find that the\nunimodularity condition, implying that there is no Weyl anomaly, is satisfied\nif and only if all the simple roots are fermionic. For AdS2 x S2 x T6 we\nconstruct backgrounds corresponding to the three Dynkin diagrams. When all the\nsimple roots are fermionic we find a supergravity background previously\nobtained by directly solving the supergravity equations. For AdS5 x S5 we\nconstruct a supergravity background corresponding to the Dynkin diagram with\nall fermionic simple roots.", "category": "hep-th" }, { "text": "11d Electric-Magnetic Duality and the Dbrane Spectrum: We consider the gedanken calculation of the pair correlation function of\nspatially-separated macroscopic string solitons in strongly coupled type IIA\nstring/M theory, with the macroscopic strings wrapping the eleventh dimension.\nThe supergravity limit of this correlation function with well-separated,\npointlike macroscopic strings corresponds to having also taken the IIA string\ncoupling constant to zero. Thus, the pointlike limit of the gedanken\ncorrelation function can be given a precise worldsheet description in the 10D\nweakly-coupled type IIA string theory, analysed by us in hep-th/0007056 [Nucl.\nPhys. B591 (2000) 243]. The requisite type IIA string amplitude is the\nsupersymmetric extension of the worldsheet formulation of an off-shell closed\nstring tree propagator in bosonic string theory, a 1986 analysis due to Cohen,\nMoore, Nelson, and Polchinski. We point out that the evidence for pointlike\nsources of the zero-form field strength provided by our worldsheet results\nclarifies that the electric-magnetic duality in the Dirichlet-brane spectrum of\ntype II string theories is eleven-dimensional.", "category": "hep-th" }, { "text": "Remarks on the harmonic oscillator with a minimal position uncertainty: We show that this problem gives rise to the same differential equation of a\nwell known potential of ordinary quantum mechanics. However there is a subtle\ndifference in the choice of the parameters of the hypergeometric function\nsolving the differential equation which changes the physical discussion of the\nspectrum.", "category": "hep-th" }, { "text": "On first order formulations of supergravities: Supergravities are usually presented in a so-called 1.5 order formulation.\nHere we present a general scheme to derive pure 1^{st} order formulations of\nsupergravities from the 1.5 order ones. The example of N_4=1 supergravity will\nbe rederived and new results for N_4=2 and N_11=1 will be presented. It seems\nthat beyond four dimensions the auxiliary fields introduced to obtain first\norder formulations of SUGRA theories do not admit supergeometrical\ntransformation laws at least before a full superfield treatment. On the other\nhand first order formalisms simplify eventually symmetry analysis and the study\nof dimensional reductions.", "category": "hep-th" } ]