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Some Remarks About Berkovits' Superstring Field Theory: In this short note we would like to discuss general solutions of the Berkovits superstring field theory, in particular the string field action for fluctuation around such a solution. We will find that fluctuations obey the same equation of motion as the original field with the new BRST operator. Then we will argue that the superstring field theory action for fluctuation field has the same form as the original one.
Effective holographic models for QCD: Thermodynamics and viscosity coefficients: A finite temperature extension of the effective holographic models for QCD (EHQCD), proposed in Ref.[1], is investigated in the present work. EHQCD models are characterized by two parameters, the conformal dimension of the relevant operator that deforms the CFT and the associated coupling. We find that black hole solutions appear at temperatures higher than some temperature $T_{min}$ and can be categorized in two classes: large and small black holes. A large black hole is thermally stable and it is therefore interpreted as the gravity dual of a non-conformal plasma. A small black hole, on the other hand, is thermally unstable. We show that thermodynamic quantities such as the entropy density $s$, specific heat $C_V$, and speed of sound $c_s$ are sensitive to the model parameters. We investigate perturbations of the black hole solutions and calculate the viscosity coefficients of the corresponding dual non-conformal plasma. For the shear viscosity, we confirm that the ratio $\eta/s$ is given by the universal result $1/4\pi$. For the bulk viscosity, the ratio $\zeta/s$ varies with the temperature, displaying a rapid growth close to $T_{min}$, and it is sensitive to the model parameters. We compare our results for the thermodynamic quantities with the lattice $SU(N_C)$ results and find that they are compatible as long as the coupling is fixed appropriately as a function of the conformal dimension. We also compare our results for the viscosity coefficients against the JETSCAPE results that are obtained from the analysis of experimental data on heavy ion collisions.
Vilkovisky-DeWitt Effective Action for Einstein Gravity on Kaluza-Klein Spacetimes $M^4\times S^N$: We evaluate the divergent part of the Vilkovisky-DeWitt effective action for Einstein gravity on even-dimensional Kaluza-Klein spacetimes of the form $M^{4}\times S^{N}$. Explicit results are given for $N$=2, 4, and 6. Trace anomalies for gravitons are also given for these cases. Stable Kaluza-Klein configurations are sought, unsuccessfully, assuming the divergent part of the effective action dominates the dynamics.
Strong coupling in Horava gravity: By studying perturbations about the vacuum, we show that Horava gravity suffers from two different strong coupling problems, extending all the way into the deep infra-red. The first of these is associated with the principle of detailed balance and explains why solutions to General Relativity are typically not recovered in models that preserve this structure. The second of these occurs even without detailed balance and is associated with the breaking of diffeomorphism invariance, required for anisotropic scaling in the UV. Since there is a reduced symmetry group there are additional degrees of freedom, which need not decouple in the infra-red. Indeed, we use the Stuckelberg trick to show that one of these extra modes become strongly coupled as the parameters approach their desired infra-red fixed point. Whilst we can evade the first strong coupling problem by breaking detailed balance, we cannot avoid the second, whatever the form of the potential. Therefore the original Horava model, and its "phenomenologically viable" extensions do not have a perturbative General Relativity limit at any scale. Experiments which confirm the perturbative gravitational wave prediction of General Relativity, such as the cumulative shift of the periastron time of binary pulsars, will presumably rule out the theory.
Effects of Noncommutativity on the Black Hole Entropy: In this paper the BTZ black hole geometry is probed with a noncommutative scalar field which obeys the $\kappa$-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton's constant due to the effects of the noncommutativity.
Entanglement and Chaos in De Sitter Holography: An SYK Example: Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for black holes. There are similarities and great differences between AdS and dS in how these concepts are manifested in the space-time geometry. In the first part of this paper the Ryu-Takayanagi prescription, the theory of fast scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be "hyperfast." In the later part of the paper I show that a certain limit of SYK is a concrete, computable, holographic model of de Sitter space. Calculations are described which support the conjecture.
On the Heat Kernel and Weyl Anomaly of Schrödinger invariant theory: We propose a method inspired from discrete light cone quantization (DLCQ) to determine the heat kernel for a Schr\"odinger field theory (Galilean boost invariant with $z=2$ anisotropic scaling symmetry) living in $d+1$ dimensions, coupled to a curved Newton-Cartan background starting from a heat kernel of a relativistic conformal field theory ($z=1$) living in $d+2$ dimensions. We use this method to show the Schr\"odinger field theory of a complex scalar field cannot have any Weyl anomalies. To be precise, we show that the Weyl anomaly $\mathcal{A}^{G}_{d+1}$ for Schr\"odinger theory is related to the Weyl anomaly of a free relativistic scalar CFT $\mathcal{A}^{R}_{d+2}$ via $\mathcal{A}^{G}_{d+1}= 2\pi \delta (m) \mathcal{A}^{R}_{d+2}$ where $m$ is the charge of the scalar field under particle number symmetry. We provide further evidence of vanishing anomaly by evaluating Feynman diagrams in all orders of perturbation theory. We present an explicit calculation of the anomaly using a regulated Schr\"odinger operator, without using the null cone reduction technique. We generalise our method to show that a similar result holds for one time derivative theories with even $z>2$.
Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices: We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$, concentrating on the case $p=3$. Explicit expressions are given for most of the relevant vertex operators, and we consider the locality relations necessary for these to define a consistent conformal field theory. A relation to constructions of lattices from codes, analogous to that found in earlier work in the $p=2$ case which led to a generalisation of the triality structure of the Monster module, is also demonstrated.
An N=8 Superaffine Malcev Algebra and Its N=8 Sugawara: A supersymmetric affinization of the algebra of octonions is introduced. It satisfies a super-Malcev property and is N=8 supersymmetric. Its Sugawara construction recovers, in a special limit, the non-associative N=8 superalgebra of Englert et al. This paper extends to supersymmetry the results obtained by Osipov in the bosonic case.
Boundary action of free AdS higher-spin gauge fields and the holographic correspondence: We determine the boundary terms of the free higher-spin action which reproduce the AdS Fronsdal equations in an AdS manifold with a finite distance boundary. The boundary terms are further constrained by the gauge invariance of the total action. We show that, for spins larger than two, no local boundary term can restore the full gauge symmetry, and the broken symmetry corresponds to higher-spin Weyl transformations on the boundary CFT. The boundary action is used for the evaluation of the on-shell higher-spin AdS action in terms of the boundary data given by a conformal higher-spin field.
Classification of Supersymmetric Flux Vacua in M Theory: We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In particular, we find for N = 2 supersymmetry, that the external space-time is Minkowski and the base manifold of the internal space is conformally K\"ahler for SU(2) structures, while for SU(3) structures the internal space has to be Einstein-Sasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with N = 1 supersymmetry and SU(3) structure, where all fluxes are non-zero and the first order differential equations are solved.
Gravitational Thermodynamics of Causal Diamonds in (A)dS: The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a "first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the "entanglement equilibrium" result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.
Operators with large R charge in N=4 Yang-Mills theory: It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong/weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant $\lambda$ and have a well defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two loop level that the anomalous dimension has a finite limit when the R charge $J\to \infty$ keeping $\lambda/J^2$ finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.
Double Yang-Baxter deformation of spinning strings: We study the reduction of classical strings rotating in the deformed three-sphere truncation of the double Yang-Baxter deformation of the $\hbox{AdS}_3 \times \hbox{S}^3 \times \hbox{T}^4$ background to an integrable mechanical model. The use of the generalized spinning-string ansatz leads to an integrable deformation of the Neumann-Rosochatius system. Integrability of this system follows from the fact that the usual constraints for the Uhlenbeck constants apply to any deformation that respects the isometric coordinates of the three-sphere. We construct solutions to the system in terms of the underlying ellipsoidal coordinate. The solutions depend on the domain of the deformation parameters and the reality conditions of the roots of a fourth order polynomial. We obtain constant-radii, giant-magnon and trigonometric solutions when the roots degenerate, and analyze the possible solutions in the undeformed limit. In the case where the deformation parameters are purely imaginary and the polynomial involves two complex-conjugated roots, we find a new class of solutions. The new class is connected with twofold giant-magnon solutions in the degenerate limit of infinite period.
NLIE for the Sausage model: The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to "sausage" shape by a deformation parameter \nu. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter \lambda. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/\lambda integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonliear integral equations (NLIEs), which are applicable to generic value of \lambda. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between \nu and \lambda. This paper is a tribute to the memory of Prof. Petr Kulish.
Chiral Green's Functions in Superconformal Field Theory: By solving the Ward identities in a superconformal field theory we find the unique three-point Green's functions composed of chiral superfields for N = 1,2,3,4 supersymmetry. We show that the N=1 four-point function with R-charge equal to one is uniquely determined by the Ward identities up to the specification of four constants. We discuss why chiral Green's functions above three-points, with total R-charge greater than N, are not uniquely determined.
Supergravity currents and linearized interactions for Matrix Theory configurations with fermionic backgrounds: The leading terms in the long-range interaction potential between an arbitrary pair of matrix theory objects are calculated at one-loop order. This result generalizes previous calculations by including arbitrary fermionic background field configurations. The interaction potential at orders 1/r^7 and 1/r^8 is shown to correspond precisely with the leading terms expected from linearized supergravity interactions between arbitrary objects in M-theory. General expressions for the stress tensor, membrane current and 5-brane current of an arbitrary matrix configuration are derived, including fermionic contributions. Supergravity effects which are correctly reproduced include membrane/5-brane interactions, 0-brane/6-brane interactions, supercurrent/supercurrent interactions and the spin contributions to moments of the supergravity currents. The matrix theory description of the supergravity stress tensor, membrane current and 5-brane current are used to propose an explicit formulation of matrix theory in an arbitrary background metric and 3-form field.
Signals of Confinement in the Dyson-Schwinger Equation for the Gauge Boson Propagator: In the first part of this thesis a coupled truncated set of Dyson-Schwinger equations (DSEs) including the one for the gluon-propagator is solved self-consistently over the whole momentum range. In Landau gauge the truncation of the coupled set of DSEs for the ghost and gluon propagators is improved by the first full inclusion of the sunset diagram. A solution method which avoids all overlapping divergences is presented. In the Maximal Abelian gauge a truncation is developed with respectively one infrared and one ultraviolet leading diagram included. A first solution of the ghost equation is presented. In the second part generalizations of the Kugo-Ojima confinement scenario to other gauges than the linear covariant gauge are investigated. In the generalized covariant gauge no contradiction is found by using a Faddeev-Popov conjugation invariant assignment of the asymptotic fields. In the last section a gauge-independent generalized criterion is developed which allows for the identification of the Coulomb, Higgs- and confining phases of Yang-Mills theory in terms of the infrared limit of the Dyson-Schwinger equation of the gauge boson propagator. While in a Coulomb phase the photon is massless, dominating the infrared of the equation, in the Higgs phase this equation is dominated by the physical mass of the gauge boson. In the confining phase the equation is saturated by unphysical degrees of freedom in the infrared limit only. This proposal is tested in a variety of gauges and the corresponding unphysical terms are identified.
Natural F-theory constructions of Standard Model structure from $E_7$ flux breaking: We describe a broad class of 4D F-theory models in which an $E_7$ gauge group is broken through fluxes to the Standard Model gauge group. These models are ubiquitous in the 4D F-theory landscape and can arise from flux breaking of most models with $E_7$ factors. While in many cases the $E_7$ breaking leads to exotic matter, there are large families of models in which the Standard Model gauge group and chiral matter representations are obtained through an intermediate $\mathrm{SU}(5)$ group. The number of generations of matter appearing in these models can easily be small. We demonstrate the possibility of getting three generations of chiral matter as the preferred matter content.
The Yang-Mills theory as a massless limit of a massive nonabelian gauge model: A gauge invariant infrared regularization of the Yang-Mills theory applicable beyond perturbation theory is constructed.
Black Hole Meiosis: The enumeration of BPS bound states in string theory needs refinement. Studying partition functions of particles made from D-branes wrapped on algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow trees, we extend the method for computing a refined BPS index, arXiv:0810.4301. For certain D-particles, a finite number of microstates, namely polar states, exclusively realized as bound states, determine an entire partition function (elliptic genus). This underlines their crucial importance: one might call them the `chromosomes' of a D-particle or a black hole. As polar states also can be affected by our refinement, previous predictions on elliptic genera are modified. This can be metaphorically interpreted as `crossing-over in the meiosis of a D-particle'. Our results improve on hep-th/0702012, provide non-trivial evidence for a strong split attractor flow tree conjecture, and thus suggest that we indeed exhaust the BPS spectrum. In the D-brane description of a bound state, the necessity for refinement results from the fact that tachyonic strings split up constituent states into `generic' and `special' states. These are enumerated separately by topological invariants, which turn out to be partitions of Donaldson-Thomas invariants. As modular predictions provide a check on many of our results, we have compelling evidence that our computations are correct.
M-theory on Calabi-Yau Five-Folds: We study the compactification of M-theory on Calabi-Yau five-folds and the resulting N=2 super-mechanics theories. By explicit reduction from 11 dimensions, including both bosonic and fermionic terms, we calculate the one-dimensional effective action and show that it can be derived from an N=2 super-space action. We find that the Kahler and complex structure moduli of the five-fold reside in 2a and 2b super-multiplets, respectively. Constrained 2a super-multiplets arise from zero-modes of the M-theory three-form and lead to cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise from the (1,3) sector of the 11-dimensional gravitino do not have bosonic super-partners and have to be described by purely fermionic super-multiplets in one dimension. We also study the inclusion of flux and discuss the consistency of the scalar potential with one-dimensional N=2 supersymmetry and how it can be described in terms of a superpotential. This superpotential can also be obtained from a Gukov-type formula which we present. Supersymmetric vacua, obtained by solving the F-term equations, always have vanishing vacuum energy due to the form of this scalar potential. We show that such supersymmetric solutions exist for particular examples. Two substantial appendices develop the topology and geometry of Calabi-Yau five-folds and the structure of one-dimensional N=2 supersymmetry and supergravity to the level of generality required for our purposes.
An approach to the quasi-equilibrium state of a self-gravitating system: We propose an approach to find out when a self-gravitating system is in a quasi-equilibrium state. This approach is based on a comparison between two quantities identifying behavior of the system: a measure of interactions intensity and the area. Gravitational scattering cross section of the system, defined by using the two-particle scattering cross section formula, is considered as the measure of interactions intensity here. A quasi-equilibrium state of such system is considered as a state when there is a balance between these two quantities. As a result, we obtain an equation which relates density and temperature for such a system in the non-relativistic classical limit. This equation is consistent with the TOV equation as expected.
Quantum Tachyon Dynamics: It is suggested that charged tachyons of extremely large mass M could not only contribute to the dark matter needed to fit astrophysical observations, but could also provide an explanation for gamma ray bursts and ultra high energy cosmic rays. The present paper defines a quantum field theory of tachyons, the latter similar to ordinary leptons, but with momenta larger than energy.
Integrable coupled sigma-models: A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realisations of affine Gaudin models. In this language, one can associate integrable field theories with affine Gaudin models having arbitrarily many sites. We present the result of applying this general procedure to couple together an arbitrary number of principal chiral model fields on the same Lie group, each with a Wess-Zumino term.
Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space: Considering the variable cosmological constant in the extended phase space has a significant background in the black hole physics. It was shown that the thermodynamic behavior of charged AdS black hole surrounded by the quintessence in the extended phase space is similar to the van der Waals fluid. In this paper, we indicate that such a black hole admits the same criticality and van der Waals like behavior in the non-extended phase space. In other words, we keep the cosmological constant as a fixed parameter, and instead, we consider the normalization factor as a thermodynamic variable. We show that there is a first-order small/large black hole phase transition which is analogous to the liquid/gas phase transition in fluids. We introduce a new picture of the equation of state and then we calculate the corresponding critical quantities. Moreover, we obtain the critical exponents and show that they are the same values as the van der Waals system. Finally, we study the photon sphere and the shadow observed by a distant observer and investigate how the shadow radius may be affected by the variation of black hole parameters. We also investigate the relations between shadow radius and phase transitions and calculate the critical shadow radius where the black hole undergoes a second-order phase transition.
Seiberg duality in three dimensions: We analyze three dimensional gauge theories with $Sp$ gauge group. We find that in some regime the theory should be described in terms of a dual theory, very much in the spirit of Seiberg duality in four dimensions. This duality does not coincide with mirror symmetry.
The gauge structure of generalised diffeomorphisms: We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.
Contrasting confinement in superQCD and superconductors: The vacuum of supersymmetric gauge theories (SQCD) with N=2 softly broken to N=1 resembles that of a BCS superconductor in that it has a condensate which collimates flux into vortices, leading to confinement. We embed the SQCD vortex into the BCS theory by identifying the N=1 vector multiplet mass and lightest massive chiral multiplet mass with the Fermi velocity divided by the London penetration depth and coherence length respectively. Thus embedded the superconductivity is type I and so the vortex core is smaller than the coherence length. Therefore nonlocal effects (Pippard electrodynamics) imply that the vortex solution is beyond the range of validity of the Landau-Ginzburg approximation implicit in the gauge theory. In other words, the vortex solution contains gradients greater than those for which the BCS and gauge theory descriptions agree. We consider more general superpotentials which are polynomial in the chiral multiplets and find that, unless one adds a SUSY breaking sector, one obtains type II superconductivity only when the superpotential perturbation is at least quadratic in the fundamental chiral multiplets and at least linear in the adjoint chiral multiplets, in which case there is no N=2 supersymmetry in the ultraviolet.
Ambitwistor formulations of $R^2$ gravity and $(DF)^2$ gauge theories: We consider $D$-dimensional amplitudes in $R^2$ gravities (conformal gravity in $D=4$) and in the recently introduced $(DF)^2$ gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the $(DF)^2$ gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to $D$ dimensions. The ambitwistor is also interpreted as a $D$-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another $(DF)^2$ gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.
D-particle polarizations with multipole moments of higher-dimensional branes: We study the polarization states of the D0-brane in type IIA string theory. In addition to states with angular momentum and magnetic dipole moments, there are polarization states of a single D0-brane with nonzero D2-brane dipole and magnetic H-dipole moments, as well as quadrupole and higher moments of various charges. These fundamental moments of the D0-brane polarization states can be determined directly from the linearized couplings of background fields to the D0-brane world-volume fermions. These couplings determine the long range supergravity fields produced by a general polarization state, which typically have non-zero values for all the bosonic fields of type IIA supergravity. We demonstrate the precise cancellation between spin-spin and magnetic dipole-dipole interactions and an analogous cancellation between 3-form and H-field dipole-dipole interactions for a pair of D0-branes. The first of these cancellations follows from the fact that spinning D0-brane states have gyromagnetic ratio g = 1, and the second follows from the fact that the ratio between the 3-form and H-field dipole moments is also 1 in natural units. Both of these relationships can be seen immediately from the couplings in the D0-brane world-volume action.
Three-point correlators of twist-2 operators in N=4 SYM at Born approximation: We calculate two different types of 3-point correlators involving twist-2 operators in the leading weak coupling approximation and all orders in N_c in N=4 SYM theory. Each of three operators in the first correlator can be any component of twist-2 supermultiplet, though the explicit calculation was done for a particular component which is an SU(4) singlet. It is calculated in the leading, Born approximation for arbitrary spins j_1,j_2,j_3. The result significantly simplifies when at least one of the spins is large or equal to zero and the coordinates are restricted to the 2d plane spanned by two light-rays. The second correlator involves two twist-2 operators Tr X\nabla^{j_1}X +..., Tr Z\nabla^{j_2}Z+... and one Konishi operator Tr[\bar Z,\bar X]^2. It vanishes in the lowest g^0 order and is computed at the leading g^2 approximation.
Complex Path Integrals and the Space of Theories: The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is related to certain Dp-branes and their properties, which can be further understood in terms of the "physical states" of another theory. We also look into representations of the Feynman Path Integral in terms of a Mellin-Barnes transform, bringing the singularity structure of the theory to the foreground. This implies that, as a sum over paths, we should consider more generic paths than just Brownian ones. Finally, we are able to study the Space of Theories through our examples in terms of their Quantum Phases and associated Stokes' Phenomena (wall-crossing).
Affleck-Dine Baryogenesis in Effective Supergravity: We investigate the viability of Affleck-Dine baryogenesis in D=4, N=1 supergravity descending from string theory. The process relies on an initial condition where visible sector supersymmetric flat directions obtain tachyonic masses during inflation. We discuss this condition for a variety of cases where supersymmetry is broken during inflation by a geometric modulus or hidden sector scalar, and outline scenarios where the initial condition is satisfied.
Gauge Theory And Wild Ramification: The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities, Stokes phenomena, isomonodromic deformation, and, from a physical point of view, new surface operators associated with higher order singularities.
Uses of Sigma Models: This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to K\"ahler, hyperk\"ahler, hyperk\"ahler with torsion and generalised K\"ahler geometries is described.
The central dogma and cosmological horizons: The central dogma of black hole physics -- which says that from the outside a black hole can be described in terms of a quantum system with exp$(\text{Area}/4G_N)$ states evolving unitarily -- has recently been supported by computations indicating that the interior of the black hole is encoded in the Hawking radiation of the exterior. In this paper, we probe whether such a dogma for cosmological horizons has any support from similar computations. The fact that the de Sitter bifurcation surface is a minimax surface (instead of a maximin surface) causes problems with this interpretation when trying to import calculations analogous to the AdS case. This suggests anchoring extremal surfaces to the horizon itself, where we formulate a two-sided extremization prescription and find answers consistent with general expectations for a quantum theory of de Sitter space: vanishing total entropy, an entropy of $A/4G_N$ when restricting to a single static patch, an entropy of a subregion of the horizon which grows as the region size grows until an island-like transition at half the horizon size when the entanglement wedge becomes the entire static patch interior, and a de Sitter version of the Hartman-Maldacena transition.
On Fock Space Representations of quantized Enveloping Algebras related to Non-Commutative Differential Geometry: In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of the quantum group and introduce the differential operators on the corresponding $q$-deformed flag manifold (asuumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, we express the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group as first-order differential operators on the $q$-deformed flag manifold.
Functional Callan-Symanzik equation: We describe a functional method to obtain the exact evolution equation of the effective action with a parameter of the bare theory. When this parameter happens to be the bare mass of the scalar field, we find a functional generalization of the Callan-Symanzik equations. Another possibility is when this parameter is the Planck constant and controls the amplitude of the fluctuations. We show the similarity of these equations with the Wilsonian renormalization group flows and also recover the usual one loop effective action.
More about wormholes in generalized Galileon theories: We consider a class of generalized Galileon theories within General Relativity in space-times of more than two spatial dimensions. We show that these theories do not admit stable, static, spherically symmetric, asymptotically flat and traversable Lorentzian wormholes.
Linear Dilaton Background and Fully Localized Intersecting Five-branes: We investigate a near-horizon geometry of NS5-branes wrapping on a Riemann surface, which asymptotically approaches to linear dilaton backgrounds. We concretely find a fully localized solution of the near-horizon geometry of intersecting NS5-branes. We also discuss a relation to a description of Landau-Ginzburg theories.
Applying the variational principle to (1+1)-dimensional quantum field theories: We extend the recently introduced continuous matrix product state (cMPS) variational class to the setting of (1+1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman concerning the variational procedure applied to relativistic theories, and provides a new way to regularize quantum field theories. A fermionic version of the continuous matrix product state is introduced which is manifestly free from fermion doubling and sign problems. We illustrate the power of the formalism with the simulation of free massive Dirac fermions, the Gross-Neveu model, and the Casimir effect. We find that cMPS can capture chiral symmetry breaking with absolute scaling of the chiral parameter, and that boundary effects can be accommodated with modest computational effort.
Equivalence between various versions of the self-dual action of the Ashtekar formalism: Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of an Ashtekar formalism in eight dimensions.
Floccinaucinihilipilification: Semisimple extensions of the Standard Model gauge algebra: We show how one may classify all semisimple algebras containing the $\mathfrak{su}(3)\oplus \mathfrak{su}(2) \oplus \mathfrak{u}(1)$ symmetry of the Standard Model and acting on some given matter sector, enabling theories beyond the Standard Model with unification (partial or total) of symmetries (gauge or global) to be catalogued. With just a single generation of Standard Model fermions plus a singlet neutrino, the only {gauge} symmetries correspond to the well-known algebras $\mathfrak{su}(5),\mathfrak{so}(10),$ and $\mathfrak{su}(4)\oplus \mathfrak{su}(2) \oplus \mathfrak{su}(2)$, but with two or more generations a limited number of exotic symmetries mixing flavour, colour, and electroweak degrees of freedom become possible. We provide a complete catalogue in the case of 3 generations or fewer and outline how our method generalizes to cases with additional matter.
Lorentz harmonics and superfield action. D=10, N=1 superstring: We propose a new version of the superfield action for a closed D=10, N=1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called 'Wess-Zumino part' of the superfield action is basically a Lagrangian form of the generalized action principle. We propose to use the second Noether theorem to handle the essential terms in the transformation lows of hidden gauge symmetries, which remove dynamical degrees of freedom from the Lagrange multiplier superfield.
The Exact Effective Couplings of 4D N=2 gauge theories: The anomalous dimensions of operators in the purely gluonic SU(2,1|2) sector of any planar conformal N=2 theory can be read off from the N=4 SYM results by replacing the N=4 coupling constant by an interpolating function of the N=2 coupling constants, to which we refer to as the effective coupling. For a large class of N=2 theories we compute the weak coupling expansion of these functions as well as the leading strong coupling term by employing supersymmetric localization. Via Feynman diagrams, we interpret our results as the relative (between N=2 and N=4) finite renormalization of the coupling constant. Using the AdS/CFT dictionary, we identify the effective couplings with the effective string tensions of the corresponding gravity dual theories. Thus, any observable in the SU(2,1|2) sector can be obtained from its N=4 counterpart by replacing the N=4 coupling constant by the universal, for a given theory, effective coupling.
Superconformal Calogero models as a gauged matrix mechanics: We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle systems possessing SU(1,1|1) and D(2,1;\alpha) supersymmetries, as well as by the model of new N=4 superconformal quantum mechanics.
Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs: We discuss numerically the non-perturbative effects in exponential random graphs which are analogue of eigenvalue instantons in matrix models. The phase structure of exponential random graphs with chemical potential for 4-cycles and degree preserving constraint is clarified. The first order phase transition at critical value of chemical potential for 4-cycles into bipartite phase with a formation of fixed number of bipartite clusters is found for ensemble of random regular graphs (RRG). We consider the similar phase transition in combinatorial quantum gravity based of the Ollivier graph curvature for RRG supplemented with hard-core constraint and show that a order of a phase transition and the structure of emerging phase depend on a vertex degree d in RRG. For d = 3 the bipartite closed ribbon emerges at bipartite phase while for d > 3 the ensemble of isolated or weakly interacting hypercubes supplemented with the bipartite closed ribbon gets emerged at the first order phase transition with a clear-cut hysteresis. If the additional connectedness condition is imposed the bipartite phase gets identified as the closed chain of weakly coupled hypercubes. Since the ground state of isolated hypercube is the thermofield double (TFD) we suggest that the dual holographic picture involves multiboundary wormholes. Treating RRG as a model of a Hilbert space for a interacting many-body system we discuss the patterns of the Hilbert space fragmentation at the phase transition. We also briefly comment on a possible relation of the found phase transition to the problem of holographic interpretation of a partial deconfinement transition in the gauge theories.
Dual gravitational charges and soft theorems: We consider the consequences of the dual gravitational charges for the phase space of radiating modes, and find that they imply a new soft NUT theorem. In particular, we argue that the existence of these new charges removes the need for imposing boundary conditions at spacelike infinity that would otherwise preclude the existence of NUT charges.
A Remark on Witten Effect for QCD Monopoles in Matrix Quantum Mechanics: In a recent work (hep-th/9905198) we argued that a certain matrix quantum mechanics may describe 't Hooft's monopoles which emerge in QCD when the theory is projected to its maximal Abelian subgroup. In this note we find further evidence which supports this interpretation. We study the theory with a non-zero theta-term. In this case, 't Hooft's QCD monopoles become dyons since they acquire electric charges due to the Witten effect. We calculate a potential between a dyon and an anti-dyon in the matrix quantum mechanics, and find that the attractive force between them grows as the theta angle increases.
Quantum Hall fluids in the presence of topological defects: We review our recent results on the physics of quantum Hall fluids at Jain and non conventional fillings within a general field theoretic framework. We focus on a peculiar conformal field theory (CFT), the one obtained by means of the m-reduction technique, and stress its power in describing strongly correlated low dimensional condensed matter systems in the presence of localized impurities or topological defects. By exploiting the notion of Morita equivalence for field theories on noncommutative two-tori and choosing rational values of the noncommutativity parameter, we find a general one-to-one correspondence between the m-reduced conformal field theory describing the quantum Hall fluid and an Abelian noncommutative field theory. As an example of application of the formalism, we study a quantum Hall bilayer at nonconventional fillings in the presence of a localized topological defect and briefly recall its boundary state structure corresponding to two different boundary conditions, the periodic as well as the twisted boundary conditions respectively, which give rise to different topological sectors on a torus. Then we introduce generalized magnetic translation operators as tensor products, which act on the quantum Hall fluid and defect space respectively, and compute their action on the boundary partition functions: in this way their role as boundary condition changing operators is fully evidenced. From such results we infer the general structure of generalized magnetic translations in our model and clarify the deep relation between noncommutativity and non-Abelian statistics of quasi-hole excitations, which is crucial for physical implementations of topological quantum computing.
Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament: The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential geometry of this system. A geometrical structure related to the integrability of this system is revealed. It is not a bi-Hamiltonian structure but similar one. As a related topic, a remark on the inspection of J.Langer and R.Perline, J.Nonlinear Sci.1, 71 (1991), is given.
Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions: We calculate the background field equations for the T-duality symmetric string building on previous work by including the effect of the Dilaton up to two-loops. Inclusion of the Dilaton allows us to obtain the full beta functionals of the duality symmetric sigma model. We are able to interpret the result in terms of a dimensionally reduced O(d,d) invariant target space effective action.
Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities: We consider the simplest bosonic-type S-matrix which is usually regarded as unphysical due to the complex values of the finite volume ground state energy. While a standard quantum field theory interpretation of such a scattering theory is precluded, we argue that the physical situation described by this S-matrix is of a massive Ising model perturbed by a particular set of irrelevant operators. The presence of these operators drastically affects the stability of the original vacuum of the massive Ising model and its ultraviolet properties.
Renormalization group improvement of the effective potential in six dimensions: Using the renormalization group improvement technique, we study the effective potential of a model consisting of $N$ scalar fields $\phi^i$ transforming in the fundamental representation of $O(N)$ group coupled to an additional scalar field $\sigma$ via cubic interactions, defined in a six-dimensional spacetime. We find that the model presents a metastable vacuum, that can be long-lived, where the particles become massive. The existence of attractive and repulsive interactions plays a crucial role in such phenomena.
T-duality and Gauge Theories from Near Horizon Dp-branes: We study the significance of T-duality in the context of the gravitational description of gauge theories. We found that T-duality relates the deferents points of the moduli of a given gauge theory always far from the conformal fixed point. Also the described gauge theories seems to flow naturally to the able conformal points, those that naturally saturate all the possible known examples of near horizon geometries. Supersymmetry properties and T-duality breaking of it are discuss.
Spontaneous supersymmetry breaking in N=3 supergravity with matter: In this paper we investigate the problem of spontaneous supersymmetry breaking without a cosmological term in $N=3$ supergravity with matter vector multiplets, scalar fields geometry being $SU(3,m)/SU(3)\otimes SU(m)\otimes U(1)$. At first, we consider the case of minimal coupling with different possible gaugings (compact as well as non-compact). Then we show that there exist dual version of such a theory (with the same scalar field geometry), which turns out to be the generalization of the $N=3$ hidden sector, constructed some time ago by one of us, to the case of arbitrary number of vector multiplets. We demonstrate that spontaneous supersymmetry breaking is still possible in the presence of matter multiplets.
Scalar potential in F(R) supergravity: We derive a scalar potential in the recently proposed N=1 supersymmetric generalization of f(R) gravity in four space-time dimensions. Any such higher-derivative supergravity is classically equivalent to the standard N=1 supergravity coupled to a chiral (matter) superfield, via a Legendre-Weyl transform in superspace. The Kaehler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function. We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine-tuning, which define a no-scale F(R) supergravity. The F(R) supergravities are suitable for physical applications in the inflationary cosmology based on supergravity and superstrings.
N-flation: The presence of many axion fields in four-dimensional string vacua can lead to a simple, radiatively stable realization of chaotic inflation.
On the glueball spectrum of walking backgrounds from wrapped-D5 gravity duals: We compute the mass spectrum of glueball excitations of a special class of strongly-coupled field theories via their type-IIB supergravity dual. We focus on two subclasses of backgrounds, which have different UV-asymptotics, but both of which exhibit walking behavior, in the weak sense that the gauge coupling of the dual field theory exhibits a quasi-constant behavior at strong coupling over a range of energies, before diverging in the deep IR. We improve on earlier calculations, by making use of the fully rigorous treatment of the 5-dimensional consistent truncation, including the rigorous form of the boundary conditions. In both cases there is a parametrically light scalar glueball. In the first case, this is a physical state, while in the second case this result is unphysical, since the presence of higher-order operators in the dual field theory makes the whole (physical) spectrum depend explicitly on a (unphysical) UV-cutoff scale.
On the Equivalence between SRS and PCO Formulations of Superstring Perturbation Theory: We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with insertions of picture changing operators (PCO) on the worldsheet and the vertical integration prescription, by showing how the latter arises from a specific construction of the supermoduli integration contour.
Quantum correction to a new Wilson line-based action for Gluodynamics: We discuss a new classical action that enables efficient computation of the gluonic tree amplitudes but does not contain any triple point vertices. This new formulation is obtained via a canonical transformation of the light-cone Yang-Mills action, with the field transformations based on Wilson line functionals. In addition to MHV vertices, the action contains also $\mathrm{N}^k\mathrm{MHV}$ vertices, where $1 \leq k \leq (n - 4)$, and $n$ is the number of external legs. We computed tree-level amplitudes up to 8 gluons and found agreement with standard results. The classical action is however not sufficient to obtain rational parts of amplitudes, in particular the finite amplitudes with all same helicity gluons. In order to systematically develop quantum corrections to this new action, we derive the one-loop effective action, in such a way there are no quantum contributions missing at one loop.
Lorentz Violating Inflation: We explore the impact of Lorentz violation on the inflationary scenario. More precisely, we study the inflationary scenario in the scalar-vector-tensor theory where the vector is constrained to be unit and time like. It turns out that the Lorentz violating vector affects the dynamics of the chaotic inflationary model and divides the inflationary stage into two parts; the Lorentz violating stage and the standard slow roll stage. We show that the universe is expanding as an exact de Sitter spacetime in the Lorentz violating stage although the inflaton field is rolling down the potential. Much more interestingly, we find exact Lorentz violating inflationary solutions in the absence of the inflaton potential. In this case, the inflation is completely associated with the Lorentz violation. We also mention some consequences of Lorentz violating inflation which can be tested by observations.
Effective Action from the Functional Renormalization Group: We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the "exact" or "functional" renormalization group equation to derive the effective action $\Gamma_0$ by integrating the flow equation from the ultraviolet scale down to $k=0$. The resulting effective action consists of local terms and nonlocal terms with unique coefficients.
Magnetic charge quantization from SYM considerations: An intersecting D3-D3' system contains magnetic monopole solutions due to D- strings stretched between two branes. These magnetic charges satisfy the usual Dirac quantization relation. We show that this quantization condition can also be obtained directly by SUSY and gauge invariance arguments of the theory and conclude that the independence of physics from a shift of holonomy is exactly equivalent to regarding a {\it Fayet-Iliopoulos (FI) gauge} for our set-up. So we are led to conjecture that there is a correspondence between the topological point of view of magnetic charges and SYM considerations of their theories. This picture implies that one can attribute a definite quantity to the integration of the vector multiplet over the singular region such that we can identify it with magnetic flux. It also indicates that the FI parameter is proportional to the magnetic charge so it is a quantized number.
M-theory, Cosmological Constant and Anthropic Principle: We discuss the theory of dark energy based on maximally extended supergravity and suggest a possible anthropic explanation of the present value of the cosmological constant and of the observed ratio between dark energy and energy of matter.
Complex Multiplication of Exactly Solvable Calabi-Yau Varieties: We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi-Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi-Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and the conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.
Sharpened Information-Theoretic Uncertainty Relations and the Histories Approach to Quantum Mechanics: In this paper alternative formulations of the conventional uncertainty relation are studied in the context of decoherent histories. The results are given in terms of Shannon information. A variety of methods are developed to evaluate the upper bound for the probability of two or more projection histories. The methods employed give improved limits for the maximal achievable probability and an improved lower bound for the Shannon information. The results are then applied to a number of physically relevant situations.
Spontaneously Broken Lorentz Invariance in Three-Dimensional Gauge Theories: In a wide class of three-dimensional Abelian gauge theories with a bare Chern-Simons term, the Lorentz invariance is spontaneously broken by dynamical generation of a non-vanishing magnetic field. A detailed computation of an energy density of the true vacuum is given. The originally massive photon becomes massless, fulfilling the role of a Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance.
Dirac Gauginos, Negative Supertraces and Gauge Mediation: In an attempt to maximize General Gauge Mediated parameter space, I propose simple models in which gauginos and scalars are generated from disconnected mechanisms. In my models Dirac gauginos are generated through the supersoft mechanism, while independent R-symmetric scalar masses are generated through operators involving non-zero messenger supertrace. I propose several new methods for generating negative messenger supertraces which result in viable positive mass squareds for MSSM scalars. The resultant spectra are novel, compressed and may contain light fermionic SM adjoint fields.
Crossing Symmetric Dispersion Relations for Mellin Amplitudes: We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories (CFTs). This allows us to set up the non-perturbative Polyakov bootstrap for CFTs in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain "locality" constraints replacing the requirement of crossing symmetry in the usual fixed-$t$ dispersion relation. Using these constraints we show that the sum rules based on the two channel dispersion relations and the present dispersion relations are identical. Our framework allows us to connect with the conceptually rich picture of the Polyakov blocks being Witten diagrams in anti-de Sitter (AdS) space. We also give two sided bounds for Wilson coefficients for effective field theories in AdS space.
Harmonic Superspace: New Directions: We sketch recent applications of the harmonic superspace approach for off-shell formulations of $(4,4)$, $2D$ sigma models with torsion and for constructing super KdV hierarchies associated with "small" and "large" $N=4$ superconformal algebras.
Supersymmetric Janus solutions in $ω$-deformed N=8 gauged supergravity: We give a large class of supersymmetric Janus solutions in $\omega$-deformed (dyonic) $SO(8)$ maximal gauged supergravity with $\omega=\frac{\pi}{8}$. Unlike the purely electric counterpart, the dyonic $SO(8)$ gauged supergravity exhibits a richer structure of $AdS_4$ vacua with $N=8,2,1,1$ supersymmetries and $SO(8)$, $U(3)$, $G_2$ and $SU(3)$ symmetries, respectively. Similarly, domain walls interpolating among these critical points show a very rich structure as well. In this paper, we show that this gauged supergravity also accommodates a number of interesting supersymmetric Janus solutions in the form of $AdS_3$-sliced domain walls asymptotically interpolating between the aforementioned $AdS_4$ geometries. These solutions could be holographically interpreted as two-dimensional conformal defects within the superconformal field theories (SCFTs) of ABJM type dual to the $AdS_4$ vacua. We also give a class of solutions interpolating among the $SO(8)$, $G_2$ and $U(3)$ $AdS_4$ vacua in the case of $\omega=0$ which have not previously appeared in the presently known Janus solutions of electric $SO(8)$ gauged supergravity.
Quantum Gates to other Universes: We present a microscopic model of a bridge connecting two large Anti-de-Sitter Universes. The Universes admit a holographic description as three-dimensional ${\cal N}=4$ supersymmetric gauge theories based on large linear quivers, and the bridge is a small rank-$n$ gauge group that acts as a messenger. On the gravity side, the bridge is a piece of a highly-curved AdS$_5\times$S$_5$ throat carrying $n$ units of five-form flux. We derive a universal expression for the mixing of the two massless gravitons: $M^2 \simeq 3n^2 (\kappa_4^2 + \kappa_4^{\prime\,2})/16\pi^2$, where $M$ is the mass splitting of the gravitons, $\kappa_4^2, \kappa_4^{\prime\,2}$ are the effective gravitational couplings of the AdS$_4$ Universes, and $n$ is the quantized charge of the gate. This agrees with earlier results based on double-trace deformations, with the important difference that the effective coupling is here quantized. We argue that the apparent non-localities of holographic double-trace models are resolved by integrating-in the (scarce) degrees of freedom of the gate.
The Resolution of an Entropy Puzzle for 4D non-BPS Black Holes: We show the equality between macroscopic and microscopic black hole entropy for a class of four dimensional non-supersymmetric black holes in ${\cal N}=2$ supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of \cite{{Butter:2013lta}}, connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term.
The Embedding of Superstring Backgrounds in Einstein Gravity: A theorem of differential geometry is employed to locally embed a wide class of superstring backgrounds that admit a covariantly constant null Killing vector field in eleven-dimensional, Ricci-flat spaces. Included in this class are exact type IIB superstring backgrounds with non-trivial Ramond-Ramond fields and a class of supersymmetric string waves. The embedding spaces represent exact solutions to eleven-dimensional, vacuum Einstein gravity. A solution of eleven-dimensional supergravity is also embedded in a twelve--dimensional, Ricci-flat space.
Path Integral for Stochastic Inflation: Non-Perturbative Volume Weighting, Complex Histories, Initial Conditions and the End of Inflation: In this paper we present a path integral formulation of stochastic inflation, in which volume weighting can easily be implemented. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow-roll. The slow-roll end of inflation mitigates certain "Youngness Paradox"-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper time volume weighting as a viable measure for answering at least some interesting cosmological questions.
Quark-Monopole Potentials in Large N Super Yang-Mills: We compute the quark-monopole potential for ${\cal N}=4$ super Yang-Mills in the large $N$ limit. We find an attractive potential that falls off as 1/L and is manifestly invariant under $g\to 1/g$. The strength of the potential is less than the quark-antiquark and monopole-antimonopole potentials.
Chern-Simons Gravity Dual of BCFT: In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.
Quantization of Scalar Field Theory with Internal Symmetry: A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum properties. Using the collective coordinates method for the Schr\"{o}dinger equation allows the development of a perturbation theory that accurately describes the symmetry properties of the theory. Examples of $U(1)$ and $SU (2)$ symmetries are analyzed and the discreteness of the energy of bound states is shown as a result of the symmetry of the theory.
Towards open-closed string duality: Closed Strings as Open String Fields: We establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, (off-shell) level-matched closed string states are represented by star algebra projectors in open string field theory. Particular attention is paid to the zero mode sector, which is indispensable in order to generate closed string states with momentum. As an outcome of our identification, we show that boundary states, which in closed string theory represent D-branes, correspond to the identity string field in the open string side. It is to be remarked that closed string theory D-branes are thus given by an infinite superposition of star algebra projectors.
Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry: We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups - including abelian factors - and non-abelian matter representations is finite. We also identify infinite families of theories with distinct U(1) charges that cannot be ruled out using known quantum consistency conditions, though only a finite subset of these can arise from known string constructions.
Chern-Simons Gauge Theory As A String Theory: Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time interpretations. For instance, three-dimensional Chern-Simons gauge theory can arise as a string theory. The world-sheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the space-time Chern-Simons theory. A certain holomorphic analog of Chern-Simons theory can also arise as a string theory.
Holographic metals and the fractionalized Fermi liquid: We show that there is a close correspondence between the physical properties of holographic metals near charged black holes in anti-de Sitter (AdS) space, and the fractionalized Fermi liquid phase of the lattice Anderson model. The latter phase has a "small" Fermi surface of conduction electrons, along with a spin liquid of local moments. This correspondence implies that certain mean-field gapless spin liquids are states of matter at non-zero density realizing the near-horizon, AdS_2 x R^2 physics of Reissner-Nordstrom black holes.
Two Field Matter Bounce Cosmology: We re-examine the non-singular Matter Bounce scenario first developed in [arXiv:1206.2382], which starts with a matter-dominated period of contraction and transitions into an Ekpyrotic phase of contraction. We consider both matter fields, the first of which plays the role of regular matter, and the second of which is responsible for the non-singular bounce. Since the dominant matter field is massive, the induced curvature fluctuations are initially not scale-invariant, whereas the fluctuations of the second scalar field (which are initially entropy fluctuations) are scale-invariant. We study the transfer of the initial entropy perturbations into curvature fluctuations in the matter-dominated phase of contraction and show that the latter become nearly scale invariant on large scales but are blue tilted on small scales. We study the evolution of both curvature and entropy fluctuations through the bounce, and show that both have a scale-invariant spectrum which is blue-tilted on small scales. However, we find that the entropy fluctuations have an amplitude that is much smaller than that of the curvature perturbations, due to gravitational amplification of curvature perturbations during the bounce phase.
Equivalence between Born-Infeld tachyon and effective real scalar field theories for brane structures in warped geometry: An equivalence between Born-Infeld and effective real scalar field theories for brane structures is built in some specific warped space-time scenarios. Once the equations of motion for tachyon fields related to the Born-Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, $T_{00}(y)$, in the $5^{th}$ dimension, $y$. Our results indicate that thick brane solutions realized by the Born-Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.
Vacuum decay and internal symmetries: We study the effects of internal symmetries on the decay by bubble nucleation of a metastable false vacuum. The zero modes about the bounce solution that are associated with the breaking of continuous internal symmetries result in an enhancement of the tunneling rate into vacua in which some of the symmetries of the initial state are spontaneously broken. We develop a general formalism for evaluating the effects of these zero modes on the bubble nucleation rate in both flat and curved space-times.
Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory: We continue the investigation of massive integrable models by means of the bootstrap fusion procedure, started in our previous work on O(3) nonlinear sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear sigma model we prove a similar relation between sine-Gordon theory and a one-parameter deformation of the O(3) sigma model, the sausage model. This allows us to write down a free field representation for the Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral representation for the generating functions of form-factors in this theory. We also clear up the origin of the singularities in the bootstrap construction and the reason for the problem with the kinematical poles.
Conformal Theory of M2, D3, M5 and `D1+D5' Branes: The bosonic actions for M2, D3 and M5 branes in their own d-dimensional near-horizon background are given in a manifestly SO(p+1,2) x SO(d-p-1) invariant form (p=2,3,5). These symmetries result from a breakdown of ISO(d,2) (with d=10 for D3 and d=11 for M2 and M5) symmetry by the Wess-Zumino term and constraints. The new brane actions, reduce after gauge-fixing and solving constraints to (p+1) dimensional interacting field theories with a non-linearly realized SO(p+1,2) conformal invariance. We also present an interacting two-dimensional conformal field theory on a D-string in the near-horizon geometry of a D1+D5 configuration.
On the analytic computation of massless propagators in dimensional regularization: We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ and show examples at four and more loops. Further we prove that all coefficients of the $\varepsilon$-expansion of these integrals are rational linear combinations of multiple zeta values and in some cases possibly also alternating Euler sums.
Superentropic Black Hole Shadows in Arbitrary Dimensions: We investigate the shadow behaviors of the superentropic black holes in arbitrary dimensions. Using the Hamilton-Jacobi mechanism, we first obtain the associated null geodesic equations of motion. By help of a spheric stereographic projection, we discuss the shadows in terms of one-dimensional real curves. Fixing the mass parameter m, we obtain certain shapes being remarkably different than four dimensional geometric configurations. We then study theirs behaviors by varying the black hole mass parameter. We show that the shadows undergo certain geometric transitions depending on the spacetime dimension. In terms of a critical value mc, we find that the four dimensional shadows exhibit three configurations being the D-shape, the cardioid and the naked singularity associated with m > mc, m = mc and m < mc, respectively. We reveal that the D-shape passes to the naked singularity via a critical curve called cardioid. In higher dimensions, however, we show that such transitional behaviors are removed.
More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve: We perform exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $\mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. In particular, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.
The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian: The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell $\Gr$ of the Sato Grassmannian $Gr$. This is a consequence of a well-defined continuum limit in which the string equation has the simple form $\lb \cp ,\cq_- \rb =\hbox{\rm 1}$, with $\cp$ and $\cq_-$ $2\times 2$ matrices of differential operators. These conditions on $V_1$ and $V_2$ yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints $\L_n\,(n\geq 0)$, where $\L_n$ annihilate the two modified-KdV $\t$-functions whose product gives the partition function of the Unitary Matrix Model.
Relaxing to a three dimensional brane junction: We suggest a mechanism which leads to 3+1 space-time dimensions. The Universe assumed to have nine spatial dimensions is regarded as a special nonlinear oscillatory system -- a kind of Einstein solid. There are p-brane solutions which manifest as phase oscillations separating different phase states. The presence of interactions allows for bifurcations of higher dimensional spaces to lower dimensional ones in the form of brane junctions. We argue this is a natural way to select lower dimensions.
Mixed Symmetries of SPT Phases: Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to predict the results of gauging part or all of the symmetries of these theories.
Renormalisation of φ^4-theory on noncommutative R^4 to all orders: We present the main ideas and techniques of the proof that the duality-covariant four-dimensional noncommutative \phi^4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the free theory by orthogonal polynomials as well as the renormalisation by flow equations involving power-counting theorems for ribbon graphs drawn on Riemann surfaces.
A Note on Agegraphic Dark Energy: Recently a new model of dynamical dark energy, or time-varying $\Lambda$, was proposed by Cai [arXiv:0707.4049] by relating the energy density of quantum fluctuations in a Minkowski space-time, namely $\rho_q \equiv 3 n^2 m_P^2/t^2$, where $n\sim {\cal O}(1)$ and t is the cosmic time, to the present day dark energy density. In this note, we show that the model can be adjusted to the present values of dark energy density parameter $\Omega_q$ ($\simeq 0.73$) and the equation of state ${\rm w}\Z{q}$ ($\simeq -1$) only if the numerical coefficient $n$ takes a reasonably large value ($n\gtrsim 3$) or the present value of the gravitational coupling of q-field to (dark) matter is also nonzero, namely, $\tilde{Q}\simeq \frac{2}{n}(\Omega\Z{q0})^{3/2}>0$ where $\Omega\Z{q0}$ is the present value of dark energy density fraction. We also discuss some of the difficulties of this proposal as a viable dark energy model with a constant $n$; especially, the bound imposed on the dark energy density parameter $\Omega_q <0.1$ during big bang nucleosynthesis (BBN) requires $n< 1/6$. To overcome this drawback, we outline a few modifications where such constraints can be weakened or relaxed. Finally, by establishing a correspondence between the agegraphic dark energy scenario and the standard scalar-field model, we also point out some interesting features of an agegraphic quintessence model.
Geodesic Witten diagrams with an external spinning field: We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show our construction agrees with the known result of the conformal partial waves.
Axion Isocurvature Collider: Cosmological colliders can preserve information from interactions at very high energy scale, and imprint them on cosmological observables. Taking the squeezed limit of cosmological perturbation bispectrum, information of the intermediate particle can be directly extracted from observations such as cosmological microwave background (CMB). Thus cosmological colliders can be powerful and promising tools to test theoretical models. In this paper, we study extremely light axions (including QCD axions and axion-like-particles), and consider them constituting cold dark matter (CDM) at late times. We are interested in inflationary isocurvature modes by such axions, and try to figure out how axion perturbations can behave as isocurvature colliders. We work out an example where the intermediate particle is a boson, and show that, in the squeezed limit, it is possible to provide a clock signal of significant amplitudes, with a characteristic angular dependence. This provides a channel to contribute and analyze clock signals of isocurvature bispectrum, which we may hopefully see in future experiments.
Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity: Hairy black holes and gravitational solitons in three dimensions for the new massive gravity theory proposed by Bergshoeff, Hohm and Townsend (BHT) are considered at the special case when there is a unique maximally symmetric solution. Following the Brown-York approach with suitable counterterms, it is shown that the soliton possesses a fixed negative mass which coincides with the one of AdS spacetime regardless the value of the integration constant that describes it. Hence, the soliton can be naturally regarded as a degenerate ground state labeled by a single modulus parameter. The Euclidean action, endowed with suitable counterterms, is shown to be finite and independent of modulus and hair parameters for both classes of solutions, and in the case of hairy black holes the free energy in the semiclassical approximation is reproduced. Modular invariance allows to show that the gravitational hair turns out to be determined by the modulus parameter. According to Cardy's formula, it is shown that the semiclassical entropy agrees with the microscopic counting of states provided the modulus parameter of the ground state is spontaneously fixed, which suggests that the hairy black hole is in a broken phase of the theory. Indeed, it is found that there is a critical temperature characterizing a first order phase transition between the static hairy black hole and the soliton which, due to the existence of gravitational hair, can take place in the semiclassical regime.
On the Natural Gauge Fields of Manifolds: The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge invariant equations for the displacement field have been derived. It has been shown that the energy-momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations we have derived the general form of the displacement field in Minkowski space-time which is invariant under rotation and space and time inversion. With this anzats we found spherically-symmetric solutions of the equations in question.
Positive Mass from Holographic Causality: For n+1 dimensional asymptotically AdS spacetimes which have holographic duals on their n dimensional conformal boundaries, we show that the imposition of causality on the boundary theory is sufficient to prove positivity of mass for the spacetime when n > 2, without the assumption of any local energy condition. We make crucial use of a generalization of the time-delay formula calculated in gr-qc/9404019, which relates the time delay of a bulk null curve with respect to a boundary null geodesic to the Ashtekar-Magnon mass of the spacetime. We also discuss holographic causality for the negative mass AdS soliton and its implications for the positive energy conjecture of Horowitz and Myers.
B-modes and the sound speed of primordial fluctuations: It was recently shown that a large value of the tensor to scalar ratio $r$ implies a constraint on the minimum value of the sound speed $c_s$ of primordial curvature perturbations during inflation that is stronger than current bounds coming from non-Gaussianity measurements. Here we consider additional aspects related to the measurement of B-modes that may provide additional leverage to constrain the sound speed parametrizing non-canonical models of inflation. We find that a confirmation of the consistency relation $r = -8 n_t$ between the tensor to scalar ratio $r$ and the tensor spectral index $n_t$ is not enough to rule out non-canonical models of inflation with a sound speed $c_s$ different from unity. To determine whether inflation was canonical or not, one requires knowledge of additional parameters, such as the running of the spectral index of scalar perturbations $\alpha$. We also study how other parameters related to the ultra violet completion of inflation modify the dependence of $r$ on $c_s$. For instance, we find that heavy degrees of freedom interacting with curvature fluctuations generically tend to make the constraint on the sound speed stronger. Our results, combined with future observations of primordial B-modes, may help to constrain the background evolution of non-canonical models of inflation.
Weyl anomaly of conformal higher spins on six-sphere: This paper is a sequel to arXiv:1309.0785 were we computed the Weyl anomaly a-coefficient on d-sphere for higher-derivative conformal higher spin field in d=4 and shown that it matches the expression found in arXiv:1306.5242 by a "holographic" method from a ratio of massless higher spin determinants in AdS_5. Here we repeat the same computation on 6-sphere and demonstrate that the result agrees again with the one following from AdS_7. We also discuss explicitly similar matching in the d=2 case.
Geometry of spin-field coupling on the worldline: We derive a geometric representation of couplings between spin degrees of freedom and gauge fields within the worldline approach to quantum field theory. We combine the string-inspired methods of the worldline formalism with elements of the loop-space approach to gauge theory. In particular, we employ the loop (or area) derivative operator on the space of all holonomies which can immediately be applied to the worldline representation of the effective action. This results in a spin factor that associates the information about spin with "zigzag" motion of the fluctuating field. Concentrating on the case of quantum electrodynamics in external fields, we obtain a purely geometric representation of the Pauli term. To one-loop order, we confirm our formalism by rederiving the Heisenberg-Euler effective action. Furthermore, we give closed-form worldline representations for the all-loop order effective action to lowest nontrivial order in a small-N_f expansion.
SU(2) Action-Angle Variables: Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a novel non commutative Hopf algebra. The group contraction is used to make the connection with the harmonic oscillator.
Notes on Vanishing Cosmological Constant without Bose-Fermi Cancellation: In this article we discuss how one can systematically construct the point particle theories that realize the vanishing one-loop cosmological constant without the bose-fermi cancellation. Our construction is based on the asymmetric (or non-geometric) orbifolds of supersymmetric string vacua. Using the building blocks of their partition functions and their modular properties, we construct the theories which would be naturally identified with certain point particle theories including infinite mass spectra, but not with string vacua. They are obviously non-supersymmetric due to the mismatch of the bosonic and fermionic degrees of freedom at each mass level. Nevertheless, it is found that the one-loop cosmological constant vanishes, after removing the parameter effectively playing the role of the UV cut-off. As concrete examples we demonstrate the constructions of the models based on the toroidal asymmetric orbifolds with the Lie algebra lattices (Englert-Neveu lattices) by making use of the analysis given in [26].
Nonabelian Monopoles: We study topological as well as dynamical properties of BPS nonabelian magnetic monopoles of Goddard-Nuyts-Olive-Weinberg type in $ G=SU(N)$, $USp(2N)$ and SO(N) gauge theories, spontaneously broken to nonabelian subgroups $H$. We find that monopoles transform under the group dual to $H$ in a tensor representation of rank determined by the corresponding element in $\pi_1(H)$. When the system is embedded in a ${\cal N}=2$ supersymmetric theory with an appropriate set of flavors with appropriate bare masses, the BPS monopoles constructed semiclassically persist in the full quantum theory. This result supports the identification of ``dual quarks'' found at $r$-vacua of ${\cal N}=2$ theories with the nonabelian magnetic monopoles. We present several consistency checks of our monopole spectra.
Emergent Gravity from a Mass Deformation in Warped Spacetime: We consider a deformation of five-dimensional warped gravity with bulk and boundary mass terms to quadratic order in the action. We show that massless zero modes occur for special choices of the masses. The tensor zero mode is a smooth deformation of the Randall-Sundrum graviton wavefunction and can be localized anywhere in the bulk. There is also a vector zero mode with similar localization properties, which is decoupled from conserved sources at tree level. Interestingly, there are no scalar modes, and the model is ghost-free at the linearized level. When the tensor zero mode is localized near the IR brane, the dual interpretation is a composite graviton describing an emergent (induced) theory of gravity at the IR scale. In this case Newton's law of gravity changes to a new power law below the millimeter scale, with an exponent that can even be irrational.
Anisotropic Cosmology and (Super)Stiff Matter in Hořava's Gravity Theory: We study anisotropic cosmology in Ho\v{r}ava's gravity theory and obtain Kasner type solutions, valid for any number d of spatial dimensions. The corresponding exponents satisfy two relations, one involving the marginal coupling \lambda. Also, Ho\v{r}ava's (super)renormalisable theory predicts (super)stiff matter whose equation of state is p = w \rho with w \ge 1. We discuss briefly the implications of these results for the nature of cosmological collapse.
Generalized Rindler Wedge and Holographic Observer Concordance: We study the most general horizons of accelerating observers and find that in a general spacetime, only spacelike surfaces satisfying a global condition could become horizons of well-defined accelerating observers, which we name the Rindler-convexity condition. The entanglement entropy associated with a Rindler-convex region is proportional to the area of the enclosing surface. This observer physics provides a novel perspective to define a well-defined subregion in spacetime, named the generalized Rindler wedge, whose degrees of freedom should be fully encoded within the subregion. We propose the holographic interpretation of generalized Rindler wedges and provide evidence from the observer correspondence, the subregion subalgebra duality, and the equality of the entanglement entropy, respectively. We introduce time/space cutoffs in the bulk to substantiate this proposition, generalize it, and establish a holographic observer concordance framework, which asserts that the partitioning of degrees of freedom through observation is holographically concordant.
Zeta Function Method for Repulsive Casimir Forces at Finite Temperature: We compute the Casimir energy between an unusual pair of parallel plates at finite temperature, namely, a perfectely conducting plate ($\epsilon\to\infty$) and an infinitely permeable one ($\mu\to\infty$) by applying the generalized zeta function method. We also compute the Casimir pressure and discuss the high and the low temperature limits.
Conformal anomaly and gravitational pair production: We argue that the rate density of particle pair production $\Gamma$ in background fields in conformal field theories is determined by the conformal anomaly and related to anomalous trace of the energy-momentum tensor as $\Gamma = (\pi/2) \langle T^\mu_{\ \mu}\rangle$ if the trace is positive (and $\Gamma = 0$ otherwise). This formula perfectly reproduces (presumably, non-Hawking) radiation generated by static gravitational fields in the absence of an event horizon via a new evaporation mechanism suggested recently. Our relation also correctly describes the one-loop Schwinger pair creation in massless (scalar and spinor) quantum electrodynamics. It also accurately points to the Savvidi instability of the gluonic vacuum towards the formation of the chromomagnetic condensate. Photon and neutrino pair production are also discussed.
Deriving covariant holographic entanglement: We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
The dyon charge in noncommutative gauge theories: We present an explicit classical dyon solution for the noncommutative version of the Yang-Mills-Higgs model (in the Prasad-Sommerfield limit) with a tehta term. We show that the relation between classical electric and magnetic charges also holds in noncommutative space. Extending the Noether approach to the case of a noncommutative gauge theory, we analyze the effect of CP violation at the quantum level, induced both by the theta term and by noncommutativity and we prove that the Witten effect formula for the dyon charge remains the same as in ordinary space.
Analytic treatment of the excited instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes: The magnetically charged SU(2) Reissner-Nordstr\"om black-hole solutions of the coupled nonlinear Einstein-Yang-Mills field equations are known to be characterized by infinite spectra of unstable (imaginary) resonances $\{\omega_n(r_+,r_-)\}_{n=0}^{n=\infty}$ (here $r_{\pm}$ are the black-hole horizon radii). Based on direct {\it numerical} computations of the black-hole instability spectra, it has recently been observed that the excited instability eigenvalues of the magnetically charged black holes exhibit a simple universal behavior. In particular, it was shown that the numerically computed instability eigenvalues of the magnetically charged black holes are characterized by the small frequency universal relation $\omega_n(r_+-r_-)=\lambda_n$, where $\{\lambda_n\}$ are dimensionless constants which are independent of the black-hole parameters. In the present paper we study analytically the instability spectra of the magnetically charged SU(2) Reissner-Nordstr\"om black holes. In particular, we provide a rigorous {\it analytical} proof for the {\it numerically}-suggested universal behavior $\omega_n(r_+-r_-)=\lambda_n$ in the small frequency $\omega_n r_+\ll (r_+-r_-)/r_+$ regime. Interestingly, it is shown that the excited black-hole resonances are characterized by the simple universal relation $\omega_{n+1}/\omega_n=e^{-2\pi/\sqrt{3}}$. Finally, we confirm our analytical results for the black-hole instability spectra with numerical computations.
Conformal Turbulence with Boundary: Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum confined in the upper half plane are obtained using the image method. This result enables us to address the infrared problem of the theory of conformal turbulence.
Direct Calculation of the Boundary $S$ Matrix for the Open Heisenberg Chain: We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with ``fixed'' boundary conditions.
On Affleck-Dine-Seiberg Superpotential and Magnetic Monopoles in Supersymmetric QCD: Certain exact results in supersymmetric gauge theories are generated by non-perturbative effects different from instantons. In supersymmetric QCD with N colours and Nf fundamental flavours we examine the Affleck-Dine-Seiberg (ADS) superpotential using controlled semi-classical analysis. We show how for Nf < N-1 the ADS superpotential arises from monopole contributions to the path integral of the supersymmetric gauge theory compactified on R^3*S^1. These are the monopole effects leading to gaugino condensation and confinement of the low-energy SU(N-Nf) supersymmetric gauge theory.
de Sitter Complementarity, TCC, and the Swampland: Motivated by the coincidence of scrambling time in de Sitter and maximum lifetime given by the $\textit{Trans-Planckian Censorship Conjecture}$ (TCC), we study the relation between the de Sitter complementarity and the Swampland conditions. We study thermalization in de Sitter space from different perspectives and show that TCC implies de Sitter space cannot live long enough to be considered a thermal background. We also revisit $\alpha$-vacua in light of this work and show that TCC imposes multiple initial condition/fine-tuning problems on any conventional inflationary scenario.
D$_4$-flops of the E$_7$-model: We study the geography of crepant resolutions of E$_7$-models. An E$_7$-model is a Weierstrass model corresponding to the output of Step 9 of Tate's algorithm characterizing the Kodaira fiber of type III$^*$ over the generic point of a smooth prime divisor. The dual graph of the Kodaira fiber of type III$^*$ is the affine Dynkin diagram of type E$_7$. A Weierstrass model of type E$_7$ is conjectured to have eight distinct crepant resolutions whose flop diagram is a Dynkin diagram of type E$_8$. We construct explicitly four of these eight crepant resolutions forming a sub-diagram of type D$_4$. We explain how the flops between these four crepant resolutions can be understood using the flops between the crepant resolutions of two well-chosen suspended pinch points.
BRST Analysis of Physical States in Two-Dimensional Black Hole: We study the BRST cohomology for $SL(2,R)/U(1)$ coset model, which describes an exact string black hole solution. It is shown that the physical spectrum could contain not only the extra discrete states corresponding to those in $c=1$ two-dimensional gravity but also many additional new states with ghost number $N_{FP}= -1 \sim 2$. We also discuss characters for nonunitary representations and the relation of our results to other approaches.
A novel holographic quantum phase transition and butterfly velocity: In this paper, we make a systematical and in-depth exploration on the phase structure and the behaviors of butterfly velocity in an Einstein-Maxwell-dilaton-axions (EMDA) model. Depending on the model parameter, there are two kinds of mechanisms driving quantum phase transition (QPT) in this model. One is the infrared (IR) geometry to be renormalization group (RG) unstable, and the other is the strength of lattice deformation leading to some kind of bifurcating solution. We also find a novel QPT in the metal phases. The study on the behavior of the butterfly velocity crossing QPT indicates that the butterfly velocity or its first derivative exhibiting local extreme depends on the QPT mechanism. Further, the scaling behaviors of the butterfly velocity in the zero-temperature limit confirm that different phases are controlled by different IR geometries. Therefore, the butterfly velocity is a good probe to QPT and it also provides a possible way to study QPT beyond holography.
Tensor Self Energy in a Vector-Tensor Model: The tensor self energy is computed at one loop order in a model in which a vector and tensor interact in a way that eliminates all tensor degrees of freedom. Divergencies arise which cannot be eliminated without introducing a kinetic term for the tensor field which does not appear in the classical action. We comment on a possible resolution of this puzzle.
Ghost spectral function from the spectral Dyson-Schwinger equation: We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.
An interplay between static potential and Reggeon trajectory for QCD string: I consider two cases where QCD string is described by an effective theory of long strings: the static potential and meson scattering amplitudes in the Regge regime. I show how they can be solved in the mean-field approximation, justified by the large number of space-time dimensions, and argue that it turns out to be exact. I compare contributions from QCD string and perturbative QCD and discuss experimental consequences for the scattering amplitudes.
Tree-level gluon amplitudes on the celestial sphere: Pasterski, Shao and Strominger have recently proposed that massless scattering amplitudes can be mapped to correlators on the celestial sphere at infinity via a Mellin transform. We apply this prescription to arbitrary $n$-point tree-level gluon amplitudes. The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian $Gr(4,n)$, while generic non-MHV amplitudes are given by more complicated Gelfand $A$-hypergeometric functions.
Quantization of Noncommutative Scalar Solitons at finite $θ$: We start by discussing the classical noncommutative (NC) Q-ball solutions near the commutative limit, then generalize the virial relation. Next we quantize the NC Q-ball canonically. At very small theta quantum correction to the energy of the Q-balls is calculated through summation of the phase shift. UV/IR mixing terms are found in the quantum corrections which cannot be renormalized away. The same method is generalized to the NC GMS soliton for the smooth enough solution. UV/IR mixing is also found in the energy correction and UV divergence is shown to be absent. In this paper only (2+1) dimensional scalar field theory is discussed.
Impact Factors for Reggeon-Gluon Transitions: General expressions for the impact factors up to terms vanishing at the space-time dimension $D\rightarrow 4$ are presented. Their infrared behaviour is analysed and calculation of exact in $D\rightarrow 4$ asymptotics at small momenta of Reggeized gluons is discussed.
Cosmology in the Einstein-Electroweak Theory and Magnetic Fields: In the SU(2)_{L} x U(1)_{Y} standard electroweak theory coupled with the Einstein gravity, new topological configurations naturally emerge, if the spatial section of the universe is globally a three-sphere(S^3) with a small radius. The SU(2)_L gauge fields and Higgs fields wrap the space nontrivially, residing at or near a local minimum of the potential. As the universe expands, however, the shape of the potential rapidly changes and the local minimum eventually disappears. The fields then start to roll down towards the absolute minimum. In the absence of the U(1)_Y gauge interaction the resulting space is a homogeneous and isotropic S^3, but the U(1)_Y gauge interaction necessarily induces anisotropy while preserving the homogeneity of the space. Large magnetic fields are generically produced over a substantial period of the rolling-over transition. The magnetic field configuration is characterized by the Hopf map.
E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology: It is shown that the never ending oscillatory behaviour of the generic solution, near a cosmological singularity, of the massless bosonic sector of superstring theory can be described as a billiard motion within a simplex in 9-dimensional hyperbolic space. The Coxeter group of reflections of this billiard is discrete and is the Weyl group of the hyperbolic Kac-Moody algebra E$_{10}$ (for type II) or BE$_{10}$ (for type I or heterotic), which are both arithmetic. These results lead to a proof of the chaotic (``Anosov'') nature of the classical cosmological oscillations, and suggest a ``chaotic quantum billiard'' scenario of vacuum selection in string theory.
Field theory in 4D N=2 conformally flat superspace: Building on the superspace formulation for four-dimensional N=2 matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon a general setting for field theory in N=2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the N=2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the N=2 AdS supergeometry in a conformally flat frame. Moreover, it emerges as a building block in the construction of various supersymmetric actions. Such a vector multiplet, which can be identified with one of the two compensators of N=2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction N=2 to N=1 is performed for the action principle in general conformally flat N=2 backgrounds, and examples of such reduction are given.
Multi-Monopole Moduli Spaces for SU(n) Gauge Group: The moduli space describing the low-energy dynamics of BPS multi-monopoles for several charge configurations is presented. We first prove the conjectured form of the moduli space of $n-1$ distinct monopoles in a spontaneously broken SU(n) gauge theory. We further propose the solution where one of the charge components has two units, hence asymptotically corresponds to embeddings of two monopoles of one charge type and the rest different. The latter hyperk\"ahler metrics possess features of the two-monopole Atiyah-Hitchin metric. We also conjecture classes of solutions to multi-monopole moduli spaces with arbitrary charge and no more than two units in each component, which models the gluing together of Atiyah-Hitchin metrics. Our approach here uses the generalized Legendre transform technique to find the new hyperk\"ahler manifolds and rederive previously conjectured ones.
Lorentz invariance violations in the interplay of quantum gravity with matter: We explore the interplay of matter with quantum gravity with a preferred frame to highlight that the matter sector cannot be protected from the symmetry-breaking effects in the gravitational sector. Focusing on Abelian gauge fields, we show that quantum gravitational radiative corrections induce Lorentz-invariance-violating couplings for the Abelian gauge field. In particular, we discuss how such a mechanism could result in the possibility to translate observational constraints on Lorentz violation in the matter sector into strong constraints on the Lorentz-violating gravitational couplings.
Compact dimensions and the Casimir effect: the Proca connection: We study the Casimir effect in the presence of an extra dimension compactified on a circle of radius R ($M^4\times S^1$ spacetime). Our starting point is the Kaluza Klein decomposition of the 5D Maxwell action into a massless sector containing the 4D Maxwell action and an extra massless scalar field and a Proca sector containing 4D gauge fields with masses $m_n=n/R$ where $n$ is a positive integer. An important point is that, in the presence of perfectly conducting parallel plates, the three degrees of freedom do not yield three discrete (non-penetrating) modes but two discrete modes and one continuum (penetrating) mode. The massless sector reproduces Casimir's original result and the Proca sector yields the corrections. The contribution from the Proca continuum mode is obtained within the framework of Lifshitz theory for plane parallel dielectrics whereas the discrete modes are calculated via 5D formulas for the piston geometry. An interesting manifestation of the extra compact dimension is that the Casimir force between perfectly conducting plates depends on the thicknesses of the slabs.
A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories: Some BPS quantities of $\mathcal{N}=1$ 5D quiver gauge theories, like instanton partition functions or qq-characters, can be constructed as algebraic objects of the Ding-Iohara-Miki (DIM) algebra. This construction is applied here to $\mathcal{N}=2$ super Yang-Mills theories in four dimensions using a degenerate version of the DIM algebra. We build up the equivalent of horizontal and vertical representations, the first one being defined using vertex operators acting on a free boson's Fock space, while the second one is essentially equivalent to the action of Vasserot-Shiffmann's Spherical Hecke central algebra. Using intertwiners, the algebraic equivalent of the topological vertex, we construct a set of $\mathcal{T}$-operators acting on the tensor product of horizontal modules, and the vacuum expectation values of which reproduce the instanton partition functions of linear quivers. Analysing the action of the degenerate DIM algebra on the $\mathcal{T}$-operator in the case of a pure $U(m)$ gauge theory, we further identify the degenerate version of Kimura-Pestun's quiver W-algebra as a certain limit of q-Virasoro algebra. Remarkably, as previously noticed by Lukyanov, this particular limit reproduces the Zamolodchikov-Faddeev algebra of the sine-Gordon model.
Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension: The CPT-even gauge sector of the Standard Model Extension is composed of nineteen components comprised in the tensor $(K_{F})_{\mu \nu\rho\sigma}$, of \ which nine do not yield birefringence. In this work, we examine the Maxwell electrodynamics supplemented by these nine nonbirefringent CPT-even components in aspects related to the Feynman propagator and full consistency (stability, causality, unitarity). We adopt a prescription that parametrizes the nonbirefringent components in terms of a symmetric and traceless tensor, $K_{\mu\nu},$ and second parametrization that writes $K_{\mu\nu}$ in terms of two arbitrary four-vectors, $U_{\mu}$ and $V_{\nu}.$ We then explicitly evaluate the gauge propagator of this electrodynamics in a tensor closed way. In the sequel, we show that this propagator and involved dispersion relations can be specialized for the parity-odd\ and parity-even sectors of the tensor $(K_{F})_{\mu\nu\rho\sigma}$. In this way, we reassess some results of the literature and derive some new outcomes showing that the parity-even anisotropic sector engenders a stable, noncausal and unitary electrodynamics.
Non-Relativistic Maxwell Chern-Simons Gravity: We consider a non-relativistic (NR) limit of $(2+1)$-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] $\oplus \ u(1)\oplus u(1)$. We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out of this difficulty: To consider i) [Maxwell] $\oplus\ u(1)$, which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] $\oplus\ u(1)\oplus u(1)\oplus u(1)$, which is a Maxwellian generalization of the EBG.
Gepner-like boundary states on $T^4$: We present exact expressions for elementary boundary states which describe D-branes preserving 16 or fewer supercharges in type II superstring compactified on certain self-dual 4-tori. While being manifestly superconformal, our boundary states are not a priori required to satisfy the usual free-field gluing conditions along the internal directions of the 4-tori. Our calculations proceed along the lines of Gepner's construction by recasting the $\mathcal{N}=(2,2)$ worldsheet sigma model on the 4-tori in terms of $\mathcal{N}=2$ minimal models. Imposing general permutation gluing conditions on the $\mathcal{N}=(2,2)$ generators is shown to yield various stable and unstable D-branes, where the stable ones include the known 1/2-BPS and 1/4-BPS bound states of D$p$-branes, as well as new non-BPS D-branes, which do not carry RR charges.
A Non-perturbative Evidence toward the Positive Energy Conjecture for asymptotically locally AdS_5 IIB Supergravity on S^5: We consider the classical solution of the type IIB supergravity spontaneously compactified on S^5, whose metric depends only on the radial coordinate and whose asymptotic geometry is locally that of AdS_5, i.e., R \times S^1 \times T^2. We solve the equations of motion to obtain the general solutions satisfying these conditions, and find that the only naked-singularity-free solutions are the AdS black holes and AdS solitons. The other solutions, that smoothly interpolate these two solutions, are shown to have naked singularities even though their Ricci tensor is proportional to the metric with a negative constant. Thus, among the possible solutions of this type, the AdS solitons are the unique lowest energy solution; this result is consistent with the recently proposed positive energy conjecture for the IIB AdS supergravity on S^5.
Supersymmetric Yang-Mills Theories in $D\ge 12$: We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9+m,1+m) where $m=0,1,2,...$ beyond ten-dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous work in 10+2 dimensions to arbitrary even dimensions with the above signature. We have overcome the previously-observed obstruction beyond 11+3 dimensions, by the aid of projection operators. Both component and superspace formulations are presented. This also suggests the possibility of consistent supergravity theories in any even dimensions beyond 10+1 dimensions.
Fast QSC Solver: tool for systematic study of N=4 Super-Yang-Mills spectrum: Integrability methods give us access to a number of observables in the planar N=4 SYM. Among them, the Quantum Spectral Curve (QSC) governs the spectrum of anomalous dimensions. Low lying states were successfully studied in the past using the QSC. However, with the increased demand for a systematic study of a large number of states for various applications, there is a clear need for a fast QSC solver which can easily access a large number of excited states. Here, we fill this gap by developing a new algorithm and applied it to study all 219 states with the bare dimension $\Delta_0 \leq 6$ in a wide range of couplings. The new algorithm has an improved performance at weak coupling and allows to glue numerics smoothly the available perturbative data, resolving the previous obstruction. Further ~ 8-fold efficiency gain comes from C++ implementation over the best available Mathematica implementation. We have made the code and the data to be available via a GitHub repository. The method is generalisable for non-local observables as well as for other theories such as deformations of N=4 SYM and ABJM. It may find applications in the separation of variables and bootstrability approaches to the correlation functions. Some applications to correlators at strong coupling are also presented.
Quadrics on Complex Riemannian Spaces of Constant Curvature, Separation of Variables and the Gaudin Magnet: We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to coordinates of this type. The complete classification of these separable coordinate systems is provided by means of the corresponding $L$-matrices for the Gaudin magnet. The limiting procedures (or $\epsilon $ calculus) which relate various degenerate orthogonal coordinate systems play a crucial result in the classification of all such systems.
Compact analytical form for non-zeta terms in critical exponents at order 1/N^3: We simplify, to a single integral of dilogarithms, the least tractable O(1/N^3) contribution to the large-N critical exponent $\eta$ of the non-linear sigma-model, and hence $\phi^4$-theory, for any spacetime dimensionality, D. It is the sole generator of irreducible multiple zeta values in epsilon-expansions with $D=2-2\epsilon$, for the sigma-model, and $D=4-2\epsilon$, for $\phi^4$-theory. In both cases we confirm results of Broadhurst, Gracey and Kreimer (BGK) that relate knots to counterterms. The new compact form is much simpler than that of BGK. It enables us to develop 8 new terms in the epsilon-expansion with $D=3-2\epsilon$. These involve alternating Euler sums, for which the basis of irreducibles is larger. We conclude that massless Feynman diagrams in odd spacetime dimensions share the greater transcendental complexity of massive diagrams in even dimensions, such as those contributing to the electron's magnetic moment and the electroweak $\rho$-parameter. Consequences for the perturbative sector of Chern-Simons theory are discussed.
Cosmology in generalized Horndeski theories with second-order equations of motion: We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\chi$ associated with the gravitational sector, we take into account multiple scalar fields $\phi_I$ ($I=1,2\cdots,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I=\partial_{\mu}\phi_I\partial^{\mu}\phi_I$. These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $\phi_I$ are generally suppressed relative to that for the dark energy field $\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.
An infinite supermultiplet of massive higher-spin fields: The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.
Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering: We study compatibility of the Standard Model of particle physics and General Relativity by means of gravitational positivity bounds, which provide a necessary condition for a low-energy gravitational theory to be UV completable within the weakly coupled regime of gravity. In particular, we identify the cutoff scale of the Standard Model coupled to gravity by studying consistency of light-by-light scattering. While the precise value depends on details of the Pomeron effects in QCD, the cutoff scale reads $10^{16}$GeV if the single-Pomeron exchange picture works well up to this scale. We also demonstrate that the cutoff scale is lowered to $10^{13}$GeV if we consider the electroweak theory without the QCD sector.
Racah Sum Rule and Biedenharn-Elliott Identity for the Super-Rotation $6-j$ symbols: It is shown that the well known Racah sum rule and Biedenharn-Elliott identity satisfied by the recoupling coefficients or by the $6-j$ symbols of the usual rotation $SO(3)$ algebra can be extended to the corresponding features of the super-rotation $osp(1|2)$ superalgebra. The structure of the sum rules is completely similar in both cases, the only difference concerns the signs which are more involved in the super-rotation case.
Multiple Inflationary Stages with Varying Equation of State: We consider a model of inflation consisting a single fluid with a time-dependent equation of state. In this phenomenological picture, two periods of inflation are separated by an intermediate non-inflationary stage which can be either a radiation dominated, matter dominated or kinetic energy dominated universe, respectively, with the equation of state $w=1/3$, 0 or 1. We consider the toy model in which the change in $w$ happens instantaneously. Depending on whether the mode of interest leaves the horizon before or after or between the phase transitions, the curvature power spectrum can have non-trivial sinusoidal modulations. This can have interesting observational implications for CMB anisotropies and for primordial black-hole formation.
D--branes and Spinning Black Holes: We obtain a new class of spinning charged extremal black holes in five dimensions, considered both as classical configurations and in the Dirichlet(D)--brane representation. The degeneracy of states is computed from the D--brane side and the entropy agrees perfectly with that obtained from the black hole side.
Cosmic Billiards with Painted Walls in Non-Maximal Supergravities: a worked out example: The derivation of smooth cosmic billiard solutions through the compensator method is extended to non maximal supergravities. A new key feature is the non-maximal split nature of the scalar coset manifold. To deal with this, one needs the theory of Tits Satake projections leading to maximal split projected algebras. Interesting exact solutions that display several smooth bounces can thus be derived. From the analysis of the Tits Satake projection emerges a regular scheme for all non maximal supergravities and a challenging so far unobserved structure, that of the paint group G-paint. This latter is preserved through dimensional reduction and provides a powerful tool to codify solutions. It appears that the dynamical walls on which the cosmic ball bounces come actually in painted copies rotated into each other by G-paint. The effective cosmic dynamics is that dictated by the maximal split Tits Satake manifold plus paint. We work out in details the example provided by N=6,D=4 supergravity, whose scalar manifold is the special Kahlerian SO*(12)}/SU(6)xU(1). In D=3 it maps to the quaternionic E_7(-5)/ SO(12) x SO(3). From this example we extract a scheme that holds for all supergravities with homogeneous scalar manifolds and that we plan to generalize to generic special geometries. We also comment on the merging of the Tits-Satake projection with the affine Kac--Moody extensions originating in dimensional reduction to D=2 and D=1.
(In)stability of de Sitter vacuum in light of distance conjecture and emergence proposal: The distance conjecture claims that as the modulus traverses along the trans-Planckian geodesic distance, the effective field theory becomes invalid by a descent of a tower of states from UV. Moreover, according to the recent emergence proposal, the kinetic term of the modulus is entirely generated by the wavefunction renormalization in which a tower of states are integrated out. Assuming these two conjectures, we explore the role of a tower of states coupled to the modulus in (in)stability of the de Sitter (dS) vacuum by studying the one-loop effective potential generated by a tower of states. We find that a fermionic tower of states makes the effective potential more or less consistent with the dS swampland conjecture : either the slope or the curvature of the potential is sizeable. In contrast, the effective potential generated by a bosonic tower of states seems to allow the stable dS vacuum. Therefore, in order to argue the instability of the dS vacuum, the additional ingredient like supersymmetry breaking needs to be taken into account.
String Models for Locally Supersymmetric Grand Unification: Phenomenologically viable string vacua may require incorporating Kac-Moody algebras at level $\geq 2$. We exploit the free fermionic formulation to construct N=(0,2) world-sheet supersymmetric string models with specific phenomenological input: N=1 spacetime supersymmetry, three generations of chiral fermions in gauge groups $SO(10)$ or $SU(5)$, adjoint Higgses, and a single Yukawa coupling of a fundamental Higgs to the third generation. In this talk, we will show models of gauge group $SO(10)$ and of $SU(5)$ without any gauge singlet moduli, and show some novel features appearing in the connection of these two models. The accompanying, and rather non-trivial, discrete chiral sub-algebras can determine hierarchies in the fermion mass matrix. Our approach to string phenomenology opens up the possibility of {\it concrete} explorations of a wide range of proposals both for dynamical supersymmetry breaking and for the dynamics of the dilaton and other stringy moduli. (Talk presented at DPF 94, Albuquerque, New Mexico)
Supersymmetric wormholes in String theory: We construct a large family of Euclidean supersymmetric wormhole solutions of type IIB supergravity which are asymptotically AdS$_5 \times S^5$. The solutions are constructed using consistent truncation to maximally gauged supergravity in five dimensions which is further truncated to a four scalar model. Within this model we perform a full analytic classification of supersymmetric domain wall solutions with flat Euclidean domain wall slices. On each side of the wormhole, the solution asymptotes to AdS$_5$ dual to ${\cal N}= 4$ supersymmetric Yang-Mills deformed by a supersymmetric mass term.
Holographic conductivity of holographic superconductors with higher order corrections: We analytically as well as numerically disclose the effects of the higher order correction terms in the gravity and in the gauge field on the properties of $s$-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics make the condensation harder. We also study the holographic conductivity of the system and disclose the effects of Gauss-Bonnet and nonlinear parameters $\alpha$ and $b$ on the superconducting gap. We observe that for various values of $\alpha $ and $b$, the real part of conductivity is proportional to the frequency per temperature, $\omega /T$, as frequency is enough large. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing the temperature.
A Crossing-Symmetric OPE Inversion Formula: We derive a Lorentzian OPE inversion formula for the principal series of $sl(2,\mathbb{R})$. Unlike the standard Lorentzian inversion formula in higher dimensions, the formula described here only applies to fully crossing-symmetric four-point functions and makes crossing symmetry manifest. In particular, inverting a single conformal block in the crossed channel returns the coefficient function of the crossing-symmetric sum of Witten exchange diagrams in AdS, including the direct-channel exchange. The inversion kernel exhibits poles at the double-trace scaling dimensions, whose contributions must cancel out in a generic solution to crossing. In this way the inversion formula leads to a derivation of the Polyakov bootstrap for $sl(2,\mathbb{R})$. The residues of the inversion kernel at the double-trace dimensions give rise to analytic bootstrap functionals discussed in recent literature, thus providing an alternative explanation for their existence. We also use the formula to give a general proof that the coefficient function of the principal series is meromorphic in the entire complex plane with poles only at the expected locations.
Partial summation of the nonlocal expansion for the gravitational effective action in 4 dimensions: The vacuum action for the gravitational field admits a known expansion in powers of the Ricci tensor with nonlocal operator coefficients (form factors). We show that going over to a different basis of curvature invariants makes possible a partial summation of this expansion. Only the form factors of the Weyl-tensor invariants need be calculated. The full action is then uniquely recovered to all orders from the knowledge of the trace anomaly. We present an explicit expression for the partially summed action, and point out simplifications resulting in the vertex functions. An application to the effect of the vacuum gravitational waves is discussed.
Extension of the Virasoro and Neveu-Schwartz algebras and generalized Sturm-Liouville operators: We consider the universal central extension of the Lie algebra $\Vect (S^1)${\math \s}$ C^{\infty}(S^1)$. The coadjoint representation of this Lie algebra has a natural geometric interpretation by matrix analogues of the Sturm-Liouville operators. This approach leads to new Lie superalgebras generalizing the well-known Neveu-Schwartz algebra.
Quantum scalar field in FRW Universe with constant electromagnetic background: We discuss massive scalar field with conformal coupling in Friedmann-Robertson-Walker (FRW) Universe of special type with constant electromagnetic field. Treating an external gravitational-electromagnetic background exactly, at first time the proper-time representations for out-in, in-in, and out-out scalar Green functions are explicitly constructed as proper-time integrals over the corresponding (complex) contours. The vacuum-to-vacuum transition amplitudes and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor are evaluated, and different approximations for them are investigated. The back reaction of the particles created to the electromagnetic field is estimated in different regimes. The connection between proper-time method and effective action is outlined. The effective action in scalar QED in weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic field is found as derivative expansion over curvature and electromagnetic field strength. Possible further applications of the results are briefly mentioned.
Chiral de Rham complex and the half-twisted sigma-model: On any Calabi-Yau manifold X one can define a certain sheaf of chiral N=2 superconformal field theories, known as the chiral de Rham complex of X. It depends only on the complex structure of X, and its local structure is described by a simple free field theory. We show that the cohomology of this sheaf can be identified with the infinite-volume limit of the half-twisted sigma-model defined by E. Witten more than a decade ago. We also show that the correlators of the half-twisted model are independent of the Kahler moduli to all orders in worldsheet perturbation theory, and that the relation to the chiral de Rham complex can be violated only by worldsheet instantons.
On Cosmological Constants from alpha'-Corrections: We examine to what extent perturbative alpha'-corrections can generate a small cosmological constant in warped string compactifications. Focusing on the heterotic string at lowest order in the string loop expansion, we show that, for a maximally symmetric spacetime, the alpha'-corrected 4D scalar potential has no effect on the cosmological constant. The only relevant terms are instead higher order products of 4D Riemann tensors, which, however, are found to vanish in the usual perturbative regime of the alpha'-expansion. The heterotic string therefore only allows for 4D Minkowski vacua to all orders in alpha', unless one also introduces string loop and/or nonperturbative corrections or allows for curvatures or field strengths that are large in string units. In particular, we find that perturbative alpha'-effects cannot induce weakly curved AdS_4 solutions.
Phase transitions of neutral planar hairy AdS black holes: We investigate the phase diagram of a general class of $4$-dimensional exact regular hairy planar black holes. For some particular values of the parameters in the moduli potential, these solutions can be embedded in $\omega$-deformed $\mathcal{N}=8$ gauged supergravity. We construct the hairy soliton that is the ground state of the theory and show that there exist first order phase transitions.
Mirror Symmetry And Some Applications: We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.
Explicit boundary form factors: the scaling Lee-Yang model: We provide explicit expressions for boundary form factors in the boundary scaling Lee-Yang model for operators with the mildest ultraviolet behavior for all integrable boundary conditions. The form factors of the boundary stress tensor take a determinant form, while the form factors of the boundary primary field contain additional explicit polynomials.
Dark Fermions and Spontaneous $CP$ violation in $SU(2)$-axion Inflation: Remarkably, if $CP$ was spontaneously broken in the physics of inflation, fermions would notice and remember it. Based on that, we present a new (non-thermal) mechanism for generating self-interacting dark Dirac fermions prior to the Hot Big Bang. The non-Abelian gauge fields and axions are well-motivated matter contents for the particle physics of inflation. In this background, we analytical study Dirac fermion doublets charged under the $SU(2)$ gauge field and use point-splitting technique to regularize the currents. We show that the non-trivial $CP$-violating vacuum structure of $SU(2)$-axion models naturally leads to an efficient mechanism for generating massive fermions during inflation. The size of the fermionic backreaction and the density fraction of dark fermions put upper bounds on the fermion's mass. For a GUT scale inflation, the generated dark fermions, only gravitationally coupled to the visible sector, can be as heavy as $m\lesssim 10 TeV$.
On elliptic genera of 6d string theories: We study the elliptic genera of 6d strings based on their modular properties. They are weak Jacobi forms of weight 0, whose indices are determined from the 2d chiral anomalies. We propose the ansatz for the elliptic genera which reflects the analytic structure of instanton partition functions. Given a finite amount of initial BPS data, we completely determine the elliptic genera of 6d strings in various 6d SCFTs. We also apply our ansatz to study $\mathcal{N}=(2,0)$ and $(1,1)$ little strings as well as $\mathcal{N}=(1,0)$ heterotic little strings, for which T-duality of little string theories supplies a sufficient number of initial BPS data. The anomaly polynomials of 6d little strings are worked out, which is needed for the elliptic genera bootstrap. In some little string theories, the elliptic genera must have the extra contributions from the Coulomb branch, which correspond to the additional zero modes for the full strings. The modified ansatze for such elliptic genera are also discussed.
The Wilson Loop in Yang-Mills Theory in the General Axial Gauge: We test the unified-gauge formalism by computing a Wilson loop in Yang-Mills theory to one-loop order. The unified-gauge formalism is characterized by the abritrary, but fixed, four-vector $N_\mu$, which collectively represents the light-cone gauge $(N^2 = 0)$, the temporal gauge $(N^2 > 0)$, the pure axial gauge $(N^2 < 0)$ and the planar gauge $(N^2 < 0)$. A novel feature of the calculation is the use of distinct sets of vectors, $\{ n_{\mu}, n_{\mu}^{\ast} \}$ and $\{N_{\mu}, N_{\mu}^{\ast}\}$, for the path and for the gauge-fixing constraint, respectively. The answer for the Wilson loop is independent of $N_{\mu}$, and agrees numerically with the result obtained in the Feymman gauge.
Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions): We bootstrap ${\cal N}=(1,0)$ superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming $E_8$ flavor group, we present universal bounds on the central charge $C_T$ and the flavor central charge $C_J$. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on $C_J$, and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS${}_7\times{\rm S}^4$/$\mathbb{Z}_2$.
Connection between the Loop Variable Formalism and the Old Covariant Formalsm for the Open Bosonic String: The gauge invariant loop variable formalism and old covariant formalism for bosonic open string theory are compared in this paper. It is expected that for the free theory, after gauge fixing, the loop variable fields can be mapped to those of the old covariant formalism in bosonic string theory, level by level. This is verified explicitly for the first two massive levels. It is shown that (in the critical dimension) the fields, constraints and gauge transformations can all be mapped from one to the other. Assuming this continues at all levels one can give general arguments that the tree S-matrix (integrated correlation functions for on-shell physical fields) is the same in both formalisms and therefore they describe the same physical theory (at tree level).
Symmetry and holonomy in M Theory: In this PhD Thesis, supersymmetry and its formulation in the context of D=11 supergravity is discussed from several perspectives. The role of generalized holonomy as a classification tool of supersymmetric supergravity solutions is reviewed, with particular emphasis on how successive supercovariant derivatives of the generalized curvature may be needed to properly define the generalized holonomy algebra. The generalized curvature is also shown to contain the supergravity equations of motion, even in the non-vanishing gravitino case. The underlying gauge symmetry of D=11 supergravity is discussed and argued to become manifest when its three-form field A_3 is expressed through a set of one-form gauge fields, associated with the generators of a suitable family of enlarged supersymmetry algebras. This family is related to osp(1|32) through expansion, a method to obtain new Lie (super)algebras of increasing dimensions from given ones. The analysis of the underlying gauge symmetry of D=11 supergravity leads naturally to enlarged supersymmetry algebras and superspaces making, thus, natural to consider actions for objects moving in such spaces. In particular, a string moving in tensorial space is discussed, describing the excitations of a state preserving 30 out of 32 supersymmetries (hence composed of two preons, hypothetical constituents of M Theory preserving 31 supersymmetries). A G-frame method is also discussed to study hypothetical preonic solutions of supergravity.
Holographic Wilsonian RG Flow and Sliding Membrane Paradigm: We study the relations between two different approaches to the holographic Renormalization Group (RG) flow at the dual gravity level: One is the radial evolution of the classical equation of motion and the other is the flow equation given by the holographic Wilsonian RG coming from the cut off independence. Apparently, the two flows look different. We give general proofs that the two flows are actually equivalent. The role of the momentum continuity (MC) is essential. We show that MC together with cutoff independence gives the evolution equation of the boundary values. Equivalence of conductivity flows in two paradigm has been shown as an explicit example. We also get the connecting formula of Green functions and AC conductivity at arbitrary slice in terms of its value at horizon for various geometry backgrounds.
Israel conditions for the Gauss-Bonnet theory and the Friedmann equation on the brane universe: Assuming an Einstein-Gauss-Bonnet theory of gravitation in a ($D \geq 5$)-dimensional spacetime with boundary, we consider the problem of the boundary dynamics given the matter Lagrangian on it. The resulting equation is applied in particular on the derivation of the Friedmann eq. of a 3-brane, understood as the non-orientable boundary of a 5d spacetime. We briefly discuss the contradictory conclusions of the literature.
Functional truncations in asymptotic safety for quantum gravity: Finite dimensional truncations and the single field approximation have thus far played dominant roles in investigations of asymptotic safety for quantum gravity. This thesis is devoted to exploring asymptotic safety in infinite dimensional, or functional, truncations of the effective action as well as the effects that can be caused by the single field approximation in this context. It begins with a comprehensive analysis of the three existing flow equations of the single field f(R) truncation by determining their spaces of global fixed point solutions and, where applicable, of corresponding eigenoperator solutions. As a second result, it is then shown that one incarnation of the single field f(R) approximation actually breaks down in the sense that there is no physical content left to explore. In order to clarify whether such drastic findings can be caused by the approximations used in setting up the renormalisation group flow, we identify the single field approximation as a prime candidate and show in the more familiar context of scalar field theory that it can indeed lead to many types of non-physical results. As a way to avoid such non-physical behaviour we highlight the importance of the previously known split Ward identity and exemplify its usefulness by fully restoring the correct physical picture in scalar field theory. Taking this result as evidence that the split Ward identity may lead to well behaved functional truncations also in gravity, we derive the flow equations of conformal gravity in a bi-field truncation of the effective action that goes beyond the local potential approximation in the fluctuation field. It is found that the split Ward identity leads to a simplified set of renormalisation group equations for the conformal factor that, while differing at crucial points, bear close resemblance to flow equations obtained in scalar field theory.
Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds: We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.
Dangerous implications of a minimum length in quantum gravity: The existence of a minimum length and a generalization of the Heisenberg uncertainty principle seem to be two fundamental ingredients required in any consistent theory of quantum gravity. In this letter we show that they would predict dangerous processes which are phenomenologically unacceptable. For example, long--lived virtual super--Planck mass black holes may lead to rapid proton decay. Possible solutions of this puzzle are briefly discussed.
Nonrelativistic counterparts of twistors and the realizations of Galilean conformal algebra: Using the notion of Galilean conformal algebra (GCA) in arbitrary space dimension d, we introduce for d=3 quantized nonrelativistic counterpart of twistors as the spinorial representation of O(2,1){\oplus}SO(3) which is the maximal semisimple subalgebra of three-dimensional GCA. The GC-covariant quantization of such nonrelativistic spinors, which shall be called also Galilean twistors, is presented. We consider for d=3 the general spinorial matrix realizations of GCA, which are further promoted to quantum-mechanical operator representations, expressed as bilinears in quantized Galilean twistors components. For arbitrary Hermitian quantum-mechanical Galilean twistor realizations we obtain the result that the representations of GCA with positive-definite Hamiltonian do not exist. For non-positive H we construct for N{\geq}2 the Hermitian Galilean N-twistor realizations of GCA; for N=2 such realization is provided explicitly.
3-dimensional scalar-vector dual of topological sigma-model: A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kaehler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.
Quantization of a Theory of 2d Dilaton Gravity: We discuss the quantization of the 2d gravity theory of Callan, Giddings, Harvey, and Strominger (CGHS), following the procedure of David, and of Distler and Kawai. We find that the physics depends crucially on whether the number of matter fields is greater than or less than 24. In the latter case the singularity pointed out by several authors is absent but the physical interpretation is unclear. In the former case (the one studied by CGHS) the quantum theory which gives CGHS in the linear dilaton semi-classical limit, is different from that which gives CGHS in the extreme Liouville regime.
Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective: Connections compatible with degenerate metric structures are known to possess peculiar features: on the one hand, the compatibility conditions involve restrictions on the torsion; on the other hand, torsionfree compatible connections are not unique, the arbitrariness being encoded in a tensor field whose type depends on the metric structure. Nonrelativistic structures typically fall under this scheme, the paradigmatic example being a contravariant degenerate metric whose kernel is spanned by a one-form. Torsionfree compatible (i.e. Galilean) connections are characterised by the gift of a two-form (the force field). Whenever the two-form is closed, the connection is said Newtonian. Such a nonrelativistic spacetime is known to admit an ambient description as the orbit space of a gravitational wave with parallel rays. The leaves of the null foliation are endowed with a nonrelativistic structure dual to the Newtonian one, dubbed Carrollian spacetime. We propose a generalisation of this unifying framework by introducing a new non-Lorentzian ambient metric structure of which we study the geometry. We characterise the space of (torsional) connections preserving such a metric structure which is shown to project to (resp. embed) the most general class of (torsional) Galilean (resp. Carrollian) connections.
The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry: We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$. Using a complex representation of the deformed Heisenberg algebra underlying the Calogero model, we explicitly establish the equivalence between this system and anyons in the lowest Landau level. A construction based on supersymmetry is used to extend our operator method to include fermions, and we obtain an explicit solution of the supersymmetric Calogero model constructed by Freedman and Mende. We also show how the dynamical $OSp(2;2)$ supersymmetry is realized by bilinears of modified creation and annihilation operators, and how to construct a supersymmetic extension of the deformed Heisenberg algebra.
Induced deformation of the canonical structure and UV/IR duality in $(1+1)D$: The purpose of this work is two fold. Working in the framework of $(1+1)D$ Lorentz violating field theories we will investigate in the first place the general claim that fermionic interactions may be equivalent to a deformation of the canonical structure of the theory. Second the deformed theory will be studied using duality reasoning to address the behavior of the Infra-Red and Ultra-Violet regimes.
All genus correlation functions for the hermitian 1-matrix model: We rewrite the loop equations of the hermitian matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological $1/N^2$ expansion, as residues on an hyperelliptical curve. Those residues, can be represented diagrammaticaly as Feynmann graphs of a cubic interaction field theory on the curve.
Quasi-local structure of p-form theory: We show that the Hamiltonian dynamics of the self-interacting, abelian p-form theory in D=2p+2 dimensional space-time gives rise to the quasi-local structure. Roughly speaking, it means that the field energy is localized but on closed 2p-dimensional surfaces (quasi-localized). From the mathematical point of view this approach is implied by the boundary value problem for the corresponding field equations. Various boundary problems, e.g. Dirichlet or Neumann, lead to different Hamiltonian dynamics. Physics seems to prefer gauge-invariant, positively defined Hamiltonians which turn out to be quasi-local. Our approach is closely related with the standard two-potential formulation and enables one to generate e.g. duality transformations in a perfectly local way (but with respect to a new set of nonlocal variables). Moreover, the form of the quantization condition displays very similar structure to that of the symplectic form of the underlying p-form theory expressed in the quasi-local language.
The Quantum 3D Superparticle: The minimal (${\cal N}=1$) superparticle in three spacetime dimensions (3D) is quantized. For non-zero mass it describes a spin-1/4 semion supermultiplet of "relativistic helicities" (-1/4, 1/4). The addition of a parity-violating Lorentz-Wess-Zumino term shifts this to $(\beta-1/4,\beta+1/4)$ for arbitrary $\beta$. For zero mass, in which case spin is not defined, the quantum superparticle describes a supermultiplet of one boson and one fermion.
On gauged maximal d=8 supergravities: We study the gauging of maximal $d=8$ supergravity using the embedding tensor formalism. We focus on SO$(3)$ gaugings, study all the possible choices of gauge fields and construct explicitly the bosonic actions (including the complicated Chern-Simons terms) for all these choices, which are parametrized by a parameter associated to the 8-dimensional SL$(2,\mathbb{R})$ duality group that relates all the possible choices which are, ultimately, equivalent from the purely 8-dimensional point of view. Our result proves that the theory constructed by Salam and Sezgin by Scherk-Schwarz compactification of $d=11$ supergravity and the theory constructed in Ref.~\cite{AlonsoAlberca:2000gh} by dimensional reduction of the so called ``massive 11-dimensional supergravity'' proposed by Meessen and Ort\'{\i}n in Ref.~\cite{Meessen:1998qm} are indeed related by an SL$(2,\mathbb{R})$ duality even though they have two completely different 11-dimensional origins.
No superradiance for the scalar field in the BTZ black hole with reflexive boundary conditions: We show that there is no superradiance in the rotating BTZ black hole for vanishing boundary conditions at infinity for the real scalar field
Small mass graviton propagator via finite-field-dependent BRST transformations in the critical dimension Siegel-Zwiebach action from string theory: We discuss the divergent graviton propagator massless limit problem in $D=26$ and show how it can be rigorously approached by interconnecting distinct gauge-fixed Siegel-Zwiebach generating functionals from string theory in the critical dimension through proper finite-field-dependent BRST (FFBRST) transformations. The massive Fierz-Pauli Lagrangian can be obtained from the gauge-invariant Siegel-Zwiebach one in the unitary gauge as a particular case, however suffering from the van Dam-Veltman-Zakharov discontinuity and possessing a ill-defined propagator in the massless limit. Nevertheless, alternatively working in a more suitable generalized Lorenz type gauge, including the transverse-traceless case, the graviton propagator for the Siegel-Zwiebach Lagrangian in the massless limit can be made finite. Gauge attainability and nilpotent BRST symmetries are explicitly worked out. We write down the complete corresponding generating functional, including the ghosts sector, and construct a convenient FFBRST transformation connecting the unitary gauge to a new bi-parametrized class of gauge-fixings containing the transverse traceless case. By taking into account the corresponding change in the Feynman integral Jacobian, a finite massless continuous limit propagator is achieved and fully justified.
Webs of integrable theories: We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following four fundamental integrable models, the PCM, the YB model, both based on a group $G$, the isotropic $\s$-model on the symmetric space $G/H$ and the YB model on the symmetric space $G/H$. To each vertex of a diagram we assign the matrix of one of the aforementioned fundamental integrable theories. Any two vertices may be connected with a number of lines having an orientation and carrying an integer level $k_i$. Each of these lines is associated with an asymmetrically gauged WZW model at an arbitrary level $k_i$. Gauge invariance of the full action is translated to level conservation at the vertices. We also show how to immediately read from the diagrams the corresponding $\s$-model actions. The most generic of these models depends on at least $n^2+1$ parameters, where $n$ is the total number of vertices/fundamental integrable models. Finally, we discuss the case where the level conservation at the vertices is relaxed and the case where the deformation matrix is not diagonal in the space of integrable models.
Charge varying sine-Gordon deformed defects: Sine-Gordon deformed defects that exhibit unusual phenomenological features on the topological charge are investigated. The possibility of a smooth and continuous transition between topological (non null charge) and non-topological (null charge) scenarios of deformed defects supported by sine-Gordon structures is evinced by the analytical calculation of topological charges and localized energy distributions. By describing cyclic deformation chains, we show that a triggering sine-Gordon model simultaneously supports kink and lump-like defects, whose topological mass values are closed by trigonometric or hyperbolic successive deformations. In spite of preserving analytical closure relations constraining the topological masses of $3$-and $4$-cyclically deformed defects, the deformation chains produce kinks and lumps which exhibit non-monotonic behavior and extra inflection points, respectively. The outcome of our analysis suggests that cyclic deformations create novel scenarios of physical and mathematical applicability of defect structures supported by the sine-Gordon theory.
String Driven Cosmology and its Predictions: We present a minimal model for the Universe evolution fully extracted from effective String Theory. This model is by its construction close to the standard cosmological evolution, and it is driven selfconsistently by the evolution of the string equation of state itself. The inflationary String Driven stage is able to reach enough inflation, describing a Big Bang like evolution for the metric. By linking this model to a minimal but well established observational information, (the transition times of the different cosmological epochs), we prove that it gives realistic predictions on early and current energy density and its results are compatible with General Relativity. Interestingly enough, the predicted current energy density is found Omega = 1 and a lower limit Omega \geq 4/9 is also found. The energy density at the exit of the inflationary stage also gives | Omega |_{inf}=1. This result shows an agreement with General Relativity (spatially flat metric gives critical energy density) within an inequivalent Non-Einstenian context (string low energy effective equations). The order of magnitude of the energy density-dilaton coupled term at the beginning of the radiation dominated stage agrees with the GUT scale. The predicted graviton spectrum is computed and analyzed without any free parameters. Peaks and asymptotic behaviours of the spectrum are a direct consequence of the dilaton involved and not only of the scale factor evolution. Drastic changes are found at high frequencies: the dilaton produces an increasing spectrum (in no string cosmologies the spectrum is decreasing). Without solving the known problems about higher order corrections and graceful exit of inflation, we find this model closer to the observational Universe than the current available string cosmology scenarii.
Casimir force variability in one-dimensional QED systems: The Casimir force between two short-range charge sources, embedded in a background of one dimensional massive Dirac fermions, is explored by means of the original $\ln\text{[Wronskian]}$ contour integration techniques. For identical sources with the same (positive) charge, we find that in the non-perturbative region the Casimir interaction between them can reach sufficiently large negative values and simultaneously reveal the features of a long-range force in spite of nonzero fermion mass, that could significantly influence the properties of such quasi-one-dimensional QED systems. For large distances $s$ between sources we recover that their mutual interaction is governed first of all by the structure of the discrete spectrum of a single source, in dependence on which it can be tuned to give an attractive, a repulsive, or an (almost) compensated Casimir force with various rates of the exponential fall-down, quite different from the standard $\exp (-2 m s)$ law. By means of the same $\ln\text{[Wronskian]}$ techniques, the case of two $\delta$-sources is also considered in a self-consistent manner with similar results for the variability of the Casimir force. A quite different behavior of the Casimir force is found for the antisymmetric source-anti-source system. In particular, in this case, there is no possibility for a long-range interaction between sources. The asymptotics of the Casimir force follows the standard $\exp (-2 m s)$ law. Moreover, for small separations between sources, the Casimir force for symmetric and antisymmetric cases turns out to be of opposite sign.
Non-geometric fluxes and mixed-symmetry potentials: We discuss the relation between generalised fluxes and mixed-symmetry potentials. We first consider the NS fluxes, and point out that the `non-geometric' $R$ flux is dual to a mixed-symmetry potential with a set of nine antisymmetric indices. We then consider the T-duality family of fluxes whose prototype is the Scherk-Schwarz reduction of the S-dual of the RR scalar of IIB supergravity. Using the relation with mixed-symmetry potentials, we are able to give a complete classification of these fluxes, including the ones that are non-geometric. The non-geometric fluxes again turn out to be dual to potentials containing nine antisymmetric indices. Our analysis suggests that all these fluxes can be understood in the context of double field theory, although for the non-geometric ones one expects a violation of the strong constraint.
Exterior Differential Systems for Field Theories: Exterior Differential Systems (EDS) and Cartan forms, set in the state space of field variables taken together with four space-time variables, are formulated for classical gauge theories of Maxwell and SU(2) Yang-Mills fields minimally coupled to Dirac spinor multiplets. Cartan character tables are calculated, showing whether the EDS, and so the Euler-Lagrange partial differential equations, is well-posed. The first theory, with 22 dimensional state space (10 Maxwell field and potential components and 8 components of a Dirac field), anticipates QED. In the second, non-Abelian, case (30 Yang-Mills field components and 16 Dirac), only if three additional "ghost" fields are included (15 more scalar variables) is a well-posed EDS found. This classical formulation anticipates the need for introduction of Fadeev-Popov ghost fields in the quantum standard model.
Dualities in 3D Large $N$ Vector Models: Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large $N$ limit. We first consider a fermionic $U(N)$ vector model coupled to level $k$ Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength $F_{\mu\nu}$ to vanish introducing a Lagrange multiplier $\Lambda$. Exchanging the order of integrations we obtain the bosonized theory with $\Lambda$ as the propagating field using the large $N$ rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar $U(N)$ vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large $N$ limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large $N$ limit. We also present a partial analysis at subleading order in large $N$ and find that the duality does not generically hold at this level.
Bulk Local States and Crosscaps in Holographic CFT: In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. We also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoro symmetry.
Restricted Maximin surfaces and HRT in generic black hole spacetimes: The AdS/CFT understanding of CFT entanglement is based on HRT surfaces in the dual bulk spacetime. While such surfaces need not exist in sufficiently general spacetimes, the maximin construction demonstrates that they can be found in any smooth asymptotically locally AdS spacetime without horizons or with only Kasner-like singularities. In this work, we introduce restricted maximin surfaces anchored to a particular boundary Cauchy slice $C_\partial$. We show that the result agrees with the original unrestricted maximin prescription when the restricted maximin surface lies in a smooth region of spacetime. We then use this construction to extend the existence theorem for HRT surfaces to generic charged or spinning AdS black holes whose mass-inflation singularities are not Kasner-like. We also discuss related issues in time-independent charged wormholes.
Quantum fields in anti de Sitter spacetime and degrees of freedom in the bulk/boundary correspondence: The quantization of a scalar field in anti de Sitter spacetime using Poincar\'e coordinates is considered. We find a discrete spectrum that is consistent with a possible mapping between bulk and boundary quantum states.
Quantum Group Analysis of the Bound States in the Strong Coupling Regime of the Modified Sine-Gordon Model: A quantum group analysis is applied to the Sine-Gordon model (or may be its version) in a strong-coupling regime. Infinitely many bound states are found together with the corresponding S-matrices. These new solutions of the Yang-Baxter eqations are related to some reducible representations of the quantum $sl(2)$ algebra resembling the Kac-Moody algebra representations in the Wess-Zumino-Witten-Novikov conformal field theory.
Gauged Q-balls in the Affleck-Dine mechanism: We consider gauged Q-balls in the gravity-mediation-type model in the Affleck-Dine mechanism, which is described by the potential $V_{\rm grav.}(\phi):=(m_{\rm grav.}^2/2)\phi^2\left[1+K\ln(\phi/M)^2\right]$ with $K<0$. In many models of gauged Q-balls, which were studied in the literature, there are upper limits for charge and size of Q-balls due to repulsive Coulomb force. In the present model, by contrast, our numerical calculation strongly suggests that stable solutions with any amount of charge and size exist. As the electric charge $Q$ increases, the field configuration of the scalar field becomes shell-like; because the charge is concentrated on the surface, the Coulomb force does not destroy the Q-ball configuration. These properties are analogous to those in the V-shaped model, which was studied by Arod\'z and Lis. We also find that for each $K$ there is another sequence of unstable solutions, which is separated from the other sequence of the stable solutions. As $|K|$ increases, the two sequences approach; eventually at some point in $-1.07<K<-1.06$, the "recombination" of the two sequences takes place.
Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions: We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new $G^2v^4$-contributions at order 3PN and outline the generalization to $G^2v^{2n}$. The integrals that represent the essential input for these results are obtained by applying the recent Yangian bootstrap directly to their $\epsilon$-expansion around three dimensions. The coordinate space Yangian generator that we employ to obtain these integrals can be understood as a special conformal symmetry in a dual momentum space.