anchor
stringlengths
50
3.92k
positive
stringlengths
55
6.16k
Critical Phenomena, Strings, and Interfaces: Some points concerning the relation of strings to interfaces in statistical systems are discussed.
Supercurrent in p-wave Holographic Superconductor: The p-wave and $p+ip$-wave holographic superconductors with fixed DC supercurrent are studied by introducing a non-vanishing vector potential. We find that close to the critical temperature $T_c$ of zero current, the numerical results of both the p wave model and the $p+ip$ model are the same as those of Ginzburg-Landau (G-L) theory, for example, the critical current $j_c \sim (T_c-T)^{3/2}$ and the phase transition in the presence of a DC current is a first order transition. Besides the similar results between both models, the $p+ip$ superconductor shows isotropic behavior for the supercurrent, while the p-wave superconductor shows anisotropic behavior for the supercurrent.
Spiky Strings, Giant Magnons and beta-deformations: We study rigid string solutions rotating on the S^3 subspace of the beta-deformed AdS_5xS^5 background found by Lunin and Maldacena. For particular values of the parameters of the solutions we find the known giant magnon and single spike strings. We present a single spike string solution on the deformed S^3 and find how the deformation affects the dispersion relation. The possible relation of this string solution to spin chains and the connection of the solutions on the undeformed S^3 to the sine-Gordon model are briefly discussed.
F and M Theories as Gauge Theories of Area Preserving Algebra: F theory and M theory are formulated as gauge theories of area preserving diffeomorphism algebra. Our M theory is shown to be 1-brane formulation rather than 0-brane formulation of M theory of Banks, Fischler, Shenker and Susskind and the F theory is shown to be 1-brane formulation rather than -1-brane formulation of type IIB matrix theory of Ishibashi, Kawai, Kitazawa and Tsuchiya.
Chiral algebras from Ω-deformation: In the presence of an $\Omega$-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional $\mathcal{N} = 2$ supersymmetric field theory. We show that for a unitary $\mathcal{N} = 2$ superconformal field theory, the chiral algebra thus defined is isomorphic to the one introduced by Beem et al. Our definition of the chiral algebra covers nonconformal theories with insertions of suitable surface defects.
The Renormalization Group and the Effective Potential in a Curved Spacetime with Torsion: The renormalization group method is employed to study the effective potential in curved spacetime with torsion. The renormalization-group improved effective potential corresponding to a massless gauge theory in such a spacetime is found and in this way a generalization of Coleman-Weinberg's approach corresponding to flat space is obtained. A method which works with the renormalization group equation for two-loop effective potential calculations in torsionful spacetime is developed. The effective potential for the conformal factor in the conformal dynamics of quantum gravity with torsion is thereby calculated explicitly. Finally, torsion-induced phase transitions are discussed.
Some Remarks on the Two Parameters Quantum Algebra $SU_{p,k}$}: The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a single parameter algebra $SU_q(2)$. This fact gives some relations between $SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra. In this paper are mentioned the relations concerning: Casimir operators, eigenvectors, matrix elements, Clebsch Gordan coefficients and irreducible tensors.
BPS Electromagnetic Waves on Giant Gravitons: We find new 1/8-BPS giant graviton solutions in $AdS_5 \times S^5$, carrying three angular momenta along $S^5$, and investigate their properties. Especially, we show that nonzero worldvolume gauge fields are admitted preserving supersymmetry. These gauge field modes can be viewed as electromagnetic waves along the compact D3 brane, whose Poynting vector contributes to the BPS angular momenta. We also analyze the (nearly-)spherical giant gravitons with worldvolume gauge fields in detail. Expressing the $S^3$ in Hopf fibration ($S^1$ fibred over $S^2$), the wave propagates along the $S^1$ fiber.
On the Null Energy Condition and Cosmology: Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w<-1$. We discuss the consistency of two recently proposed models that violate the NEC. The ghost condensate model requires higher-order derivative terms in the action. It leads to a heavy ghost field and unbounded energy. We estimate the rates of particles decay and discuss possible mass limitations to protect stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to unbounded energy. In this case the spectrum of energy is continuous and there are no particle like excitations. This model admits a natural UV completion since it comes from superstring theory.
SU(2) Poisson-Lie T duality: Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the pair of sigma models defined by the double SO(3,1) in the Iwasawa decomposition.
Super-Geometrodynamics: We present explicit solutions of the time-symmetric initial value constraints, expressed in terms of freely specfiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string theory. These results are a prequisite for the study of the time-evolution of topologically non-trivial initial data for supergravity theories, thus generalising the "Geometrodynamics" program of Einstein-Maxwell theory to that of supergravity theories. Specifically, we focus on examples of multiple electric Maxwell and scalar fields, and analyse the initial data problem for the general Einstein-Maxwell-Dilaton theory both with one and two Maxwell fields, and the STU model. The solutions are given in terms of up to eight arbitrary harmonic functions in the STU model. As a by-product, in order compare our results with known static solutions, the metric in isotropic coordinates and all the sources of the non-extremal black holes are expressed entirely in terms of harmonic functions. We also comment on generalizations to time-nonsymmetric initial data and their relation to cosmological solutions of gauged so-called fake supergravities with positive cosmological constant.
Dynamics of dark energy: In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.
Infrared behavior of dynamical fermion mass generation in QED$_{3}$: Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.
A Lie Algebra for Closed Strings, Spin Chains and Gauge Theories: We consider quantum dynamical systems whose degrees of freedom are described by $N \times N$ matrices, in the planar limit $N \to \infty$. Examples are gauge theoires and the M(atrix)-theory of strings. States invariant under U(N) are `closed strings', modelled by traces of products of matrices. We have discovered that the U(N)-invariant opertors acting on both open and closed string states form a remarkable new Lie algebra which we will call the heterix algebra. (The simplest special case, with one degree of freedom, is an extension of the Virasoro algebra by the infinite-dimensional general linear algebra.) Furthermore, these operators acting on closed string states only form a quotient algebra of the heterix algebra. We will call this quotient algebra the cyclix algebra. We express the Hamiltonian of some gauge field theories (like those with adjoint matter fields and dimensionally reduced pure QCD models) as elements of this Lie algebra. Finally, we apply this cyclix algebra to establish an isomorphism between certain planar matrix models and quantum spin chain systems. Thus we obtain some matrix models solvable in the planar limit; e.g., matrix models associated with the Ising model, the XYZ model, models satisfying the Dolan-Grady condition and the chiral Potts model. Thus our cyclix Lie algebra described the dynamical symmetries of quantum spin chain systems, large-N gauge field theories, and the M(atrix)-theory of strings.
Surface defects and elliptic quantum groups: A brane construction of an integrable lattice model is proposed. The model is composed of Belavin's R-matrix, Felder's dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional $\mathcal{N} = 1$ supersymmetric field theories as transfer matrices related to elliptic quantum groups.
Multifield Dynamics in Higgs-otic Inflation: In Higgs-otic inflation a complex neutral scalar combination of the $h^0$ and $H^0$ MSSM Higgs fields plays the role of inflaton in a chaotic fashion. The potential is protected from large trans-Planckian corrections at large inflaton if the system is embedded in string theory so that the Higgs fields parametrize a D-brane position. The inflaton potential is then given by a DBI+CS D-brane action yielding an approximate linear behaviour at large field. The inflaton scalar potential is a 2-field model with specific non-canonical kinetic terms. Previous computations of the cosmological parameters (i.e. scalar and tensor perturbations) did not take into account the full 2-field character of the model, ignoring in particular the presence of isocurvature perturbations and their coupling to the adiabatic modes. It is well known that for generic 2-field potentials such effects may significantly alter the observational signatures of a given model. We perform a full analysis of adiabatic and isocurvature perturbations in the Higgs-otic 2-field model. We show that the predictivity of the model is increased compared to the adiabatic approximation. Isocurvature perturbations moderately feed back into adiabatic fluctuations. However, the isocurvature component is exponentially damped by the end of inflation. The tensor to scalar ratio varies in a region $r=0.08-0.12$, consistent with combined Planck/BICEP results.
Stability and Negative Tensions in 6D Brane Worlds: We investigate the dynamical stability of warped, axially symmetric compactifications in anomaly free 6D gauged supergravity. The solutions have conical defects, which we source by 3-branes placed on orbifold fixed points, and a smooth limit to the classic sphere-monopole compactification. Like for the sphere, the extra fields that are generically required by anomaly freedom are especially relevant for stability. With positive tension branes only, there is a strict stability criterion (identical to the sphere case) on the charges present under the monopole background. Thus brane world models with positive tensions can be embedded into anomaly free theories in only a few ways. Meanwhile, surprisingly, in the presence of a negative tension brane the stability criteria can be relaxed. We also describe in detail the geometries induced by negative tension codimension two branes.
Quantization of the Superstring with Manifest U(5) Super-Poincare Invariance: The superstring is quantized in a manner which manifestly preserves a U(5) subgroup of the (Wick-rotated) ten-dimensional super-Poincar\'e invariance. This description of the superstring contains critical N=2 worldsheet superconformal invariance and is a natural covariantization of the U(4)-invariant light-cone Green-Schwarz description.
The Operator Product Expansion of the Lowest Higher Spin Current at Finite N: For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.
Minimal Scales from an Extended Hilbert Space: We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry. We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.
The 1/2 BPS Wilson loop in ABJM theory at two loops: We compute the expectation value of the 1/2 BPS circular Wilson loop in ABJM theory at two loops in perturbation theory. The result shows perfect agreement with the prediction from localization and the proposed framing factor.
Electric shocks: bounding Einstein-Maxwell theory with time delays on boosted RN backgrounds: The requirement that particles propagate causally on non-trivial backgrounds implies interesting constraints on higher-derivative operators. This work is part of a systematic study of the positivity bounds derivable from time delays on shockwave backgrounds. First, we discuss shockwaves in field theory, which are infinitely boosted Coulomb-like field configurations. We show how a positive time delay implies positivity of four-derivative operators in scalar field theory and electromagnetism, consistent with the results derived using dispersion relations, and we comment on how additional higher-derivative operators could be included. We then turn to gravitational shockwave backgrounds. We compute the infinite boost limit of Reissner-Nordstr\"om black holes to derive charged shockwave backgrounds. We consider photons traveling on these backgrounds and interacting through four-derivative corrections to Einstein-Maxwell theory. The inclusion of gravity introduces a logarithmic term into the time delay that interferes with the straightforward bounds derivable in pure field theory, a fact consistent with CEMZ and with recent results from dispersion relations. We discuss two ways to extract a physically meaningful quantity from the logarithmic time delay -- by introducing an IR cutoff, or by considering the derivative of the time delay -- and comment on the bounds implied in each case. Finally, we review a number of additional shockwave backgrounds which might be of use in future applications, including spinning shockwaves, those in higher dimensions or with a cosmological constant, and shockwaves from boosted extended objects.
Enhanced corrections near holographic entanglement transitions: a chaotic case study: Recent work found an enhanced correction to the entanglement entropy of a subsystem in a chaotic energy eigenstate. The enhanced correction appears near a phase transition in the entanglement entropy that happens when the subsystem size is half of the entire system size. Here we study the appearance of such enhanced corrections holographically. We show explicitly how to find these corrections in the example of chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry. With the help of an emergent rotational symmetry, the sum over all saddle points is written in terms of an effective action for cosmic branes. The resulting Renyi and entanglement entropies are then naturally organized in a basis of fixed-area states and can be evaluated directly, showing an enhanced correction near holographic entanglement transitions. We comment on several intriguing features of our tractable example and discuss the implications for finding a convincing derivation of the enhanced corrections in other, more general holographic examples.
On the constraints defining BPS monopoles: We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an important role in our analysis.
Microcausality and quantization of the fermionic Myers-Pospelov model: We study the fermionic sector of the Myers and Pospelov theory with a general background $n$. The spacelike case without temporal component is well defined and no new ingredients came about, apart from the explicit Lorentz invariance violation. The lightlike case is ill defined and physically discarded. However, the other case where a nonvanishing temporal component of the background is present, the theory is physically consistent. We show that new modes appear as a consequence of higher time derivatives. We quantize the timelike theory and calculate the microcausality violation which turns out to occur near the light cone.
Quasilocal Thermodynamics of Kerr de Sitter Spacetimes and the dS/CFT Correspondence: We consider the quasilocal thermodynamics of rotating black holes in asymptotic de Sitter spacetimes. Using the minimal number of intrinsic boundary counterterms, we carry out an analysis of the quasilocal thermodynamics of Kerr-de Sitter black holes for virtually all possible values of the mass, rotation parameter and cosmological constant that leave the quasilocal boundary inside the cosmological event horizon. Specifically, we compute the quasilocal energy, the conserved charges, the temperature and the heat capacity for the $(3+1)$-dimensional Kerr-dS black holes. We perform a quasilocal stability analysis and find phase behavior that is commensurate with previous analysis carried out through the use of Arnowitt-Deser-Misner (ADM) parameters. Finally, we investigate the non-rotating case analytically.
Pomeron-Odderon Interactions: A Functional RG Flow Analysis: In the quest for an effective field theory which could help to understand some non perturbative feature of the QCD in the Regge limit, we consider a Reggeon Field Theory (RFT) for both Pomeron and Odderon interactions and perform an analysys of the critical theory using functional renormalization group techniques, unveiling a novel symmetry structure.
The Newman-Penrose Map and the Classical Double Copy: Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories---a correspondence dubbed the "double copy". Recently, double copies have also been realized in a classical setting, as maps between exact solutions of gauge theories and gravity. We present here a novel map between a certain class of real, exact solutions of Einstein's equations and self-dual solutions of the flat-space vacuum Maxwell equations. This map, which we call the "Newman-Penrose map", is well-defined even for non-vacuum, non-stationary spacetimes, providing a systematic framework for exploring gravity solutions in the context of the double copy that have not been previously studied in this setting. To illustrate this, we present here the Newman-Penrose map for the Schwarzschild and Kerr black holes, and Kinnersley's photon rocket.
$1/L^2$ corrected soft photon theorem from a CFT$_3$ Ward identity: Classical soft theorems applied to probe scattering processes on AdS$_4$ spacetimes predict the existence of $1/L^2$ corrections to the soft photon and soft graviton factors of asymptotically flat spacetimes. In this paper, we establish that the $1/L^2$ corrected soft photon theorem can be derived from a large $N$ CFT$_3$ Ward identity. We derive a perturbed soft photon mode operator on a flat spacetime patch in global AdS$_4$ in terms of an integrated expression of the boundary CFT current. Using the same in the CFT$_3$ Ward identity, we recover the $1/L^2$ corrected soft photon theorem derived from classical soft theorems.
Weyl Connections and their Role in Holography: It is a well-known property of holographic theories that diffeomorphism invariance in the bulk space-time implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of background metrics. The usual Fefferman-Graham formalism, which provides us with a holographic dictionary between the two theories, breaks explicitly this symmetry by choosing a specific boundary metric and a corresponding specific metric ansatz in the bulk. In this paper, we show that a simple extension of the Fefferman-Graham formalism allows us to sidestep this explicit breaking; one finds that the geometry of the boundary includes an induced metric and an induced connection on the tangent bundle of the boundary that is a Weyl connection (rather than the more familiar Levi-Civita connection uniquely determined by the induced metric). Properly invoking this boundary geometry has far-reaching consequences: the holographic dictionary extends and naturally encodes Weyl-covariant geometrical data, and, most importantly, the Weyl anomaly gains a clearer geometrical interpretation, cohomologically relating two Weyl-transformed volumes. The boundary theory is enhanced due to the presence of the Weyl current, which participates with the stress tensor in the boundary Ward identity.
Lorentz symmetry breaking and supersymmetry: We discuss three manners to implement Lorentz symmetry breaking in a superfield theory formulated within the superfield formalism, that is, deformation of the supersymmetry algebra, introducing of an extra superfield whose components can depend on Lorentz-violating (LV) vectors (tensors), and adding of new terms proportional to LV vectors (tensors) to the superfield action. We illustrate these methodologies with examples of quantum calculations.
Geometric Aspects of Holographic Bit Threads: We revisit the recent reformulation of the holographic prescription to compute entanglement entropy in terms of a convex optimization problem, introduced by Freedman and Headrick. According to it, the holographic entanglement entropy associated to a boundary region is given by the maximum flux of a bounded, divergenceless vector field, through the corresponding region. Our work leads to two main results: (i) We present a general algorithm that allows the construction of explicit thread configurations in cases where the minimal surface is known. We illustrate the method with simple examples: spheres and strips in vacuum AdS, and strips in a black brane geometry. Studying more generic bulk metrics, we uncover a sufficient set of conditions on the geometry and matter fields that must hold to be able to use our prescription. (ii) Based on the nesting property of holographic entanglement entropy, we develop a method to construct bit threads that maximize the flux through a given bulk region. As a byproduct, we are able to construct more general thread configurations by combining (i) and (ii) in multiple patches. We apply our methods to study bit threads which simultaneously compute the entanglement entropy and the entanglement of purification of mixed states and comment on their interpretation in terms of entanglement distillation. We also consider the case of disjoint regions for which we can explicitly construct the so-called multi-commodity flows and show that the monogamy property of mutual information can be easily illustrated from our constructions.
The Most General Propagator in Quantum Field Theory: One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In the present paper, by exploiting what is called polar form, we find the most general propagator in the case of spinors, whether regular or singular, and we give a general discussion in the case of vectors.
Double Ernst Solution in Einstein-Kalb-Ramond Theory: The K\"ahler formulation of 5-dimensional Einstein-Kalb-Ramond (EKR) theory admitting two commuting Killing vectors is presented. Three different Kramer-Neugebauer-like maps are established for the 2-dimensional case. A class of solutions constructed on the double Ernst one is obtained. It is shown that the double Kerr solution corresponds to a EKR dipole configuration with horizon.
Bi-partite entanglement entropy in massive two-dimensional quantum field theory: Recently, Cardy, Castro Alvaredo and the author obtained the first exponential correction to saturation of the bi-partite entanglement entropy at large region length, in massive two-dimensional integrable quantum field theory. It only depends on the particle content of the model, and not on the way particles scatter. Based on general analyticity arguments for form factors, we propose that this result is universal, and holds for any massive two-dimensional model (also out of integrability). We suggest a link of this result with counting pair creations far in the past.
Brief review on higher spin black holes: We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-3 fields, being nonperturbatively described by a Chern-Simons theory of two independent sl(3,R) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of their basic aspects in this context; and as a warming up exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well as the BTZ black hole and its thermodynamics, exclusively in terms of gauge fields. The discussion is then extended to the case of black holes endowed with higher spin fields, briefly signaling the agreements and discrepancies found through different approaches. We conclude explaining how the puzzles become resolved once the fall off of the fields is precisely specified and extended to include chemical potentials, in a way that it is compatible with the asymptotic symmetries. Hence, the global charges become completely identified in an unambiguous way, so that different sets of asymptotic conditions turn out to contain inequivalent classes of black hole solutions being characterized by a different set of global charges.
Interpolating Gauges,Parameter Differentiability,WT-identities and the epsilon term: Evaluation of variation of a Green's function in a gauge field theory with a gauge parameter theta involves field transformations that are (close to) singular. Recently, we had demonstrated {hep-th/0106264}some unusual results that follow from this fact for an interpolating gauge interpolating between the Feynman and the Coulomb gauge (formulated by Doust). We carry out further studies of this model. We study properties of simple loop integrals involved in an interpolating gauge. We find that the proof of continuation of a Green's function from the Feynman gauge to the Coulomb gauge via such a gauge in a gauge-invariant manner seems obstructed by the lack of differentiability of the path-integral with respect to theta (at least at discrete values for a specific Green's function considered) and/or by additional contributions to the WT-identities. We show this by the consideration of simple loop diagrams for a simple scattering process. The lack of differentiability, alternately, produces a large change in the path-integral for a small enough change in theta near some values. We find several applications of these observations in a gauge field theory. We show that the usual procedure followed in the derivation of the WT-identity that leads to the evaluation of a gauge variation of a Green's function involves steps that are not always valid in the context of such interpolating gauges. We further find new results related to the need for keeping the epsilon-term in the in the derivation of the WT-identity and and a nontrivial contribution to gauge variation from it. We also demonstrate how arguments using Wick rotation cannot rid us of these problems. This work brings out the pitfalls in the use of interpolating gauges in a clearer focus.
Low-energy general relativity with torsion: a systematic derivative expansion: We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action of a general form containing vector-vector, axial-vector and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the "spin fluid" approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.
Non-Linear Resonance in Relativistic Preheating: Inflation in the early Universe can be followed by a brief period of preheating, resulting in rapid and non-equilibrium particle production through the dynamics of parametric resonance. However, the parametric resonance effect is very sensitive to the linearity of the reheating sector. Additional self-interactions in the reheating sector, such as non-canonical kinetic terms like the DBI Lagrangian, may enhance or frustrate the parametric resonance effect of preheating. In the case of a DBI reheating sector, preheating is described by parametric resonance of a damped relativistic harmonic oscillator. In this paper, we illustrate how the non-linear terms in the relativistic oscillator shut down the parametric resonance effect. This limits the effectiveness of preheating when there are non-linear self-interactions.
(2+1)-dimensional Chern-Simons bi-gravity with AdS Lie bialgebra as an interacting theory of two massless spin-2 fields: We introduce a new Lie bialgebra structure for the anti de Sitter (AdS) Lie algebra in (2+1)-dimensional spacetime. By gauging the resulting \textit{AdS Lie bialgebra}, we write a Chern-Simons gauge theory of bi-gravity involving two dreibeins rather than two metrics, which describes two interacting massless spin-2 fields. Our ghost-free bi-gravity model which has no any local degrees of freedom, has also a suitable free field limit. By solving its equations of motion, we obtain a \textit{new black hole} solution which has two curvature singularities and two horizons. We also study cosmological implications of this massless bi-gravity model.
Casimir Self-Entropy of a Spherical Electromagnetic $δ$-Function Shell: In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic $\delta$-function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The TE self-entropy is negative as expected, but the TM self-entropy requires ultraviolet and infrared subtractions, and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes.
Krylov Complexity in Calabi-Yau Quantum Mechanics: Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, as well as some non-relativistic models. We find that for the Calabi-Yau models, the Lanczos coefficients grow slower than linearly for small $n$'s, consistent with the behavior of integrable models. On the other hand, for the non-relativistic models, the Lanczos coefficients initially grow linearly for small $n$'s, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope.
Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT: Crossing symmetry (CS) is the main tool in the bootstrap program applied to CFT models. This consists in an equality which imposes restrictions on the CFT data of a model, i.e, the OPE coefficients and the conformal dimensions. Reflection positivity (RP) has also played a role, since this condition lead to the unitary bound and reality of the OPE coefficients. In this paper we show that RP can still reveal more information, showing how RP itself can capture an important part of the restrictions imposed by the full CS equality. In order to do that, we use a connection used by us in a previous work between RP and positive definiteness of a function of a single variable. This allows to write constraints on the OPE coefficients in a concise way, encoding in the conditions that certain functions of the crossratio will be positive defined and in particular completely monotonic. We will consider how the bounding of scalar conformal dimensions and OPE coefficients arise in this RP based approach. We will illustrate the conceptual and practical value of this view trough examples of general CFT models in $d$-dimensions.
Horizons and Correlation Functions in 2D Schwarzschild-de Sitter Spacetime: Two-dimensional Schwarzschild-de Sitter is a convenient spacetime in which to study the effects of horizons on quantum fields since the spacetime contains two horizons, and the wave equation for a massless minimally coupled scalar field can be solved exactly. The two-point correlation function of a massless scalar is computed in the Unruh state. It is found that the field correlations grow linearly in terms of a particular time coordinate that is good in the future development of the past horizons, and that the rate of growth is equal to the sum of the black hole plus cosmological surface gravities. This time dependence results from additive contributions of each horizon component of the past Cauchy surface that is used to define the state. The state becomes the Bunch-Davies vacuum in the cosmological far field limit. The two point function for the field velocities is also analyzed and a peak is found when one point is between the black hole and cosmological horizons and one point is outside the future cosmological horizon.
Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures: In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct the $W_n^l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.
Defects, modular differential equations, and free field realization of N = 4 VOAs: For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we show that the residues of the integrands in the $\mathcal{N} = 4$ Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the vacuum characters of rank$G$ copies of $bc \beta \gamma$ systems that provide the free field realization of associated $\mathcal{N} = 4$ VOAs. This result predicts that these residues, as module characters, are additional solutions to the flavored modular differential equations satisfied by the original Schur index. The prediction is verified in the $G = SU(2)$ case, where an additional logarithmic solution is constructed.
Free Energy of D_n Quiver Chern-Simons Theories: We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of N=3 Chern-Simons matter theories with D_n quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these D_n quivers to A_{2n-5} quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.
States and Observables in Semiclassical Field Theory: a Manifestly Covariant Approach: A manifestly covariant formulation of quantum field Maslov complex-WKB theory (semiclassical field theory) is investigated for the case of scalar field. The main object of the theory is "semiclassical bundle". Its base is the set of all classical states, fibers are Hilbert spaces of quantum states in the external field. Semiclassical Maslov states may be viewed as points or surfaces on the semiclassical bundle. Semiclassical analogs of QFT axioms are formulated. A relationship between covariant semiclassical field theory and Hamiltonian formulation is discussed. The constructions of axiomatic field theory (Schwinger sources, Bogoliubov $S$-matrix, Lehmann-Symanzik-Zimmermann $R$-functions) are used in constructing the covariant semiclassical theory. A new covariant formulation of classical field theory and semiclassical quantization proposal are discussed.
Action-angle variables for dihedral systems on the circle: A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N. For such `dihedral systems' we construct the action-angle variables and establish a local equivalence with a free particle on the circle. We perform the quantization of these systems in the action-angle variables and discuss the supersymmetric extension of this procedure. By allowing radial motion one obtains related two-dimensional systems, including A_2, BC_2 and G_2 three-particle rational Calogero models on R, which we also analyze.
K-field kinks in two-dimensional dilaton gravity: In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions, and the stability criteria are obtained. As an explicit example, a model with cuscuton term is studied. After rewriting the equations of motion into simpler first-order formalism and choosing a polynomial superpotential, an exact self-gravitating kink solution is obtained. The impacts of the cuscuton term are discussed.
To Half--Be or Not To Be?: It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving $D-1$ degrees of freedom in $D$ spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.
Higher-Derivative Gravitation in Bosonic and Superstring Theories and a New Mechanism for Supersymmetry Breaking: A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of auxiliary fields. As a by-product we present a consistent non-linear coupling of a spin-2 tensor to gravitation. It is shown that non-vanishing $(C_{\mu\nu\alpha\beta})^{2}$ terms arise in $N=1$, $D=4$ superstring Lagrangians due to one-loop radiative corrections with light field internal lines. We discuss the general form of quadratic $(1,1)$ supergravity in two dimensions, and show that this theory is equivalent to two scalar supermultiplets coupled to the usual Einstein supergravity. It is demonstrated that the theory possesses stable vacua with vanishing cosmological constant which spontaneously break supersymmetry.
Dilaton tadpoles and D-brane interactions in compact spaces: We analyse some physical consequences when supersymmetry is broken by a set of D-branes and/or orientifold planes in Type II string theories. Generically, there are global dilaton tadpoles at the disk level when the transverse space is compact. By taking the toy model of a set of electric charges in a compact space, we discuss two different effects appearing when global tadpoles are not cancelled. On the compact directions a constant term appears that allows to solve the equations of motion. On the non-compact directions Poincar\'e invariance is broken. We analyse some examples where the Poincar\'e invariance is broken along the time direction (cosmological models).After that, we discuss how to obtain a finite interaction between D-branes and orientifold planes in the compact space at the supergravity level.
Effective Matter Cosmologies of Massive Gravity I: Non-Physical Fluids: For the massive gravity, after decoupling from the metric equation we find a broad class of solutions of the Stuckelberg sector by solving the background metric in the presence of a diagonal physical metric. We then construct the dynamics of the corresponding FLRW cosmologies which inherit effective matter contribution through the decoupling solution mechanism of the scalar sector.
Quantum field theory on a discrete space and noncommutative geometry: We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied without being spoiled by technical complications due to the absence of divergencies.
Constrained Dynamics in the Hamiltonian formalism: These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the infinite dimensional phase space of field theory is tackled. Holonomic constraints in configuration space are considered first and Dirac brackets introduced for such systems. It is shown that Dirac brackets are a projection of Poisson brackets onto the constrained phase space and the projection operator is constructed explicitly. More general constraints on phase space are then considered and exemplified by a particle in a strong magnetic field. First class constraints on phases are introduced using the example of motion on the complex projective space ${\mathbf{C P}}^{n-1}$. Motion of a relativistic particle in Minkowski space with a reparameterisation invariant world-line is also discussed. These notes are based on a short lecture course given at Bhubaneswar Indian Institute of Technology in November 2021.
Functional RG flow of the effective Hamiltonian action: After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also of theories with bare Hamiltonians which are not quadratic in the momenta. As an example the vacuum energy and gap of quantum mechanical models are computed. Extensions of this framework to quantum field theories are discussed. In particular one possible Lorentz covariant approach for simple scalar field theories is developed. Fermionic degrees of freedom, being naturally described by a first order formulation, can be easily accommodated in this approach.
Holographic anatomy of fuzzballs: We present a comprehensive analysis of 2-charge fuzzball solutions, that is, horizon-free non-singular solutions of IIB supergravity characterized by a curve on R^4. We propose a precise map that relates any given curve to a specific superposition of R ground states of the D1-D5 system. To test this proposal we compute the holographic 1-point functions associated with these solutions, namely the conserved charges and the vacuum expectation values of chiral primary operators of the boundary theory, and find perfect agreement within the approximations used. In particular, all kinematical constraints are satisfied and the proposal is compatible with dynamical constraints although detailed quantitative tests would require going beyond the leading supergravity approximation. We also discuss which geometries may be dual to a given R ground state. We present the general asymptotic form that such solutions must have and present exact solutions which have such asymptotics and therefore pass all kinematical constraints. Dynamical constraints would again require going beyond the leading supergravity approximation.
On the phase structure of extra-dimensional gauge theories with fermions: We study the phase structure of five-dimensional Yang-Mills theories coupled to Dirac fermions. In order to tackle their non-perturbative character, we derive the flow equations for the gauge coupling and the effective potential for the Aharonov-Bohm phases employing the Functional Renormalisation Group. We analyse the infrared and ultraviolet fixed-point solutions in the flow of the gauge coupling as a function of the compactification radius of the fifth dimension. We discuss various types of trajectories which smoothly connect both dimensional limits. Last, we investigate the phase diagram and vacuum structure of the gauge potential for different fermion content.
The timbre of Hawking gravitons: an effective description of energy transport from holography: Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index (3-d) for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.
Integrable deformations of AdS/CFT: In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS$_{2,3}$ integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the $\rm AdS_3 \times S^3 \times M^4$ string sigma model.
Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings: We propose an electric-magnetic duality and conjecture an exact conformal window for a class of non-supersymmetric U(N_c) gauge theories with fermions in the (anti)symmetric representation of the gauge group and N_f additional scalar and fermion flavors. The duality exchanges N_c with N_f -N_c \mp 4 leaving N_f invariant, and has common features with Seiberg duality in N=1 SQCD with SU or SO/Sp gauge group. At large N the duality holds due to planar equivalence with N=1 SQCD. At finite N we embed these gauge theories in a setup with D-branes and orientifolds in a non-supersymmetric, but tachyon-free, non-critical type 0B string theory and argue in favor of the duality in terms of boundary and crosscap state monodromies as in analogous supersymmetric situations. One can verify explicitly that the resulting duals have matching global anomalies. Finally, we comment on the moduli space of these gauge theories and discuss other potential non-supersymmetric examples that could exhibit similar dualities.
Unitary Representations of Some Infinite Dimensional Lie Algebras Motivated by String Theory on AdS_3: We consider some unitary representations of infinite dimensional Lie algebras motivated by string theory on AdS_3. These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS_3 exists.
Six-loop divergences in the supersymmetric Kahler sigma model: The two-dimensional supersymmetric $\s$-model on a K\"ahler manifold has a non-vanishing $\b$-function at four loops, but the $\b$-function at five loops can be made to vanish by a specific choice of renormalisation scheme. We investigate whether this phenomenon persists at six loops, and conclude that it does not; there is a non-vanishing six-loop $\b$-function irrespective of renormalisation scheme ambiguities.
w(1+infinity) Algebra with a Cosmological Constant and the Celestial Sphere: It is shown that in the presence of a nonvanishing cosmological constant, Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ algebra of soft graviton symmetries is modified in a simple way. The deformed algebra contains a subalgebra generating $ SO(1,4)$ or $SO(2,3)$ symmetry groups of $\text{dS}_4$ or $\text{AdS}_4$, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed $\mathrm{w_{1+\infty}}$ are also discussed.
Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains: The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices -representations of the underlying quadratic algebra- that physically describe the interaction between the various particle-like excitations displayed by these models and the spin impurity.
Casimir effect, loop corrections and topological mass generation for interacting real and complex scalar fields in Minkowski spacetime with different conditions: In this paper the Casimir energy density, loop corrections, and generation of topological mass are investigated for a system consisting of two interacting real and complex scalar fields. The interaction considered is the quartic interaction in the form of a product of the modulus square of the complex field and the square of the real field. In addition, it is also considered the self-interaction associated with each field. In this theory, the scalar field is constrained to always obey periodic condition while the complex field obeys in one case a quasiperiodic condition and in other case mixed boundary conditions. The Casimir energy density, loop corrections, and topological mass are evaluated analytically for the massive and massless scalar fields considered. An analysis of possible different stable vacuum states and the corresponding stability condition is also provided. In order to better understand our investigation, some graphs are also presented. The formalism we use here to perform such investigation is the effective potential, which is written as loop expansions via path integral in quantum field theory.
Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T \bar T$, $T \bar J$ and Yang-Baxter deformations: In this paper we study generic features of nonlocal charges obtained from marginal deformations of WZNW models. Using free-fields representations of CFTs based on simply laced Lie algebras, one can use simple arguments to build the nonlocal charges; but for more general Lie algebras these methods are not strong enough to be generally used. We propose a brute force calculation where the nonlocality is associated to a new Lie algebra valued field, and from this prescription we impose several constraints on the algebra of nonlocal charges. Possible applications for Yang-Baxter and holographic \(T\bar{T}\) and \(T\bar{J}\) deformations are also discussed.
Hamiltonian reduction of the $U_{EM}(1)$ gauged three flavour WZW model: The three-flavour Wess-Zumino model coupled to electromagnetism is treated as a constraint system using the Faddeev-Jackiw method. Expanding into series of powers of the Goldstone boson fields and keeping terms up to second and third order we obtain Coulomb-gauge hamiltonian densities.
Proper time method in de Sitter space: We use the proper time formalism to study a (non-self-interacting) massive Klein-Gordon theory in the two dimensional de Sitter space. We determine the exact Green's function of the theory by solving the DeWitt-Schwinger equation as well as by calculating the operator matrix element. We point out how the one parameter family of arbitrariness in the Green's function arises in this method.
Double Metric, Generalized Metric and $α'$-Geometry: We relate the unconstrained `double metric' of the `$\alpha'$-geometry' formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b-field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application we prove that, to first order in $\alpha'$ and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in $\alpha'$ the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops: We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as ancillary files. This work has been updated to take into account the results of [arXiv:1911.09106], which leads to a simpler and more uniform representation of these amplitudes.
Motion of a Particle with Isospin in the Presence of a Monopole: From a consistent expression for the quadriforce describing the interaction between a coloured particle and gauge fields, we investigate the relativistic motion of a particle with isospin interacting with a BPS monopole and with a Julia-Zee dyon. The analysis of such systems reveals the existence of unidimensional unbounded motion and asymptotic trajectories restricted to conical surfaces, which resembles the equivalent case of Electromagnetism.
A Note on the Swampland Distance Conjecture: We discuss the Swampland Distance Conjecture in the framework of black hole thermodynamics. In particular, we consider black holes in de Sitter space and we show that the Swampland Distance Conjecture is a consequence of the fact that apparent horizons are always inside cosmic event horizons whenever they exist in the case of fast-roll inflation. In addition, we show that the Bekenstein and the Hubble entropy bounds for the entropy in a region of spacetime lead similarly to the same conjecture.
Hawking Radiation from Elko Particles Tunnelling across Black Strings Horizon: We apply the tunnelling method for the emission and absorption of Elko particles in the event horizon of a black string solution. We show that Elko particles are emitted at the expected Hawking temperature from black strings, but with a quite different signature with respect to the Dirac particles. We employ the Hamilton-Jacobi technique to black hole tunnelling, by applying the WKB approximation to the coupled system of Dirac-like equations governing the Elko particle dynamics. As a typical signature, different Elko particles are shown to produce the same standard Hawking temperature for black strings. However we prove that they present the same probability irrespective of outgoing or ingoing the black hole horizon. It provides a typical signature for mass dimension one fermions, that is different from the mass dimension three halves fermions inherent to Dirac particles, as different Dirac spinor fields have distinct inward and outward probability of tunnelling.
Yang-Baxter $σ$-models and dS/AdS T-duality: We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic principal chiral model and the $SL(2,C)/SU(2)$ WZW model. The latter has the de Sitter space as its (conformal) non-Abelian dual.
A Pure Spinor Twistor Description of Ambitwistor Strings: We present a novel ten-dimensional description of ambitwistor strings. This formulation is based on a set of supertwistor variables involving pure spinors and a set of constraints previously introduced in the context of the $D=10$ superparticle following a ten-dimensional twistor-like construction introduced by Berkovits. We perform a detailed quantum-mechanical analysis of the constraint algebra, we show that the corresponding central charges vanish, and after considering a convenient gauge fixing procedure, physical states are found. Vertex operators are explicitly constructed and, by noticing a relation with the standard pure spinor formalism, scattering amplitudes are shown to correctly describe $D=10$ super-Yang-Mills interactions. As in other ambitwistor string models, amplitudes are found to be localized on the support of the scattering equations, and thus this work provides a bridge between Berkovits' construction and the Cachazo-He-Yuan formulae. After extending the pure spinor twistor transform to include an additional supersymmetry, our results are immediately generalized to Type IIB supergravity.
Operator lifetime and the force-free electrodynamic limit of magnetised holographic plasma: Using the framework of higher-form global symmetries, we examine the regime of validity of force-free electrodynamics by evaluating the lifetime of the electric field operator, which is non-conserved due to screening effects. We focus on a holographic model which has the same global symmetry as that of low energy plasma and obtain the lifetime of (non-conserved) electric flux in a strong magnetic field regime. The lifetime is inversely correlated to the magnetic field strength and thus suppressed in the strong field regime.
Phase Transition of Charged-AdS Black Holes and Quasinormal Modes : a Time Domain Analysis: In this work we use the quasinormal mode of a massless scalar perturbation to probe the phase transition of the charged-AdS black hole in time profile. The signature of the critical behavior of this black hole solution is detected in the isobaric process. This paper is a natural extension of [1, 2] to the time domain analysis. More precisely, our study shows a clear signal in term of the damping rate and the oscillation frequencies of the scalar field perturbation. We conclude that the quasinormal modes can be an efficient tool to detect the signature of thermodynamic phase transition in the isobaric process far from the critical temperature, but fail to disclose this signature at the critical temperature
On the renormalization of a generalized supersymmetric version of the maximal Abelian gauge: In this work we present an algebraic proof of the renormazibility of the super-Yang-Mills action quantized in a generalized supersymmetric version of the maximal Abelian gauge. The main point stated here is that the generalized gauge depends on a set of infinity gauge parameters in order to take into account all possible composite operators emerging from the dimensionless character of the vector superfield. At the end, after the removal of all ultraviolet divergences, it is possible to specify values to the gauge parameters in order to return to the original supersymmetric maximal Abelian gauge, first presented in Phys. Rev. D91, no. 12, 125017 (2015), Ref. [1].
Spinor-vector supersymmetry algebra in three dimensions: We focus on a spin-3/2 supersymmetry (SUSY) algebra of Baaklini in D = 3 and explicitly show a nonlinear realization of the SUSY algebra. The unitary representation of the spin-3/2 SUSY algebra is discussed and compared with the ordinary (spin-1/2) SUSY algebra.
Prescriptive Unitarity: We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory, where we construct closed-form representations of all ($n$-point N$^k$MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.
Quantum fluctuations of topological ${\mathbb S}^3$-kinks: The kink Casimir effect in the massive non-linear $S^3$-sigma model is analyzed.
Brane-worlds and theta-vacua: Reductions from odd to even dimensionalities ($5\to 4$ or $3\to 2$), for which the effective low-energy theory contains chiral fermions, present us with a mismatch between ultraviolet and infrared anomalies. This applies to both local (gauge) and global currents; here we consider the latter case. We show that the mismatch can be explained by taking into account a change in the spectral asymmetry of the massive modes--an odd-dimensional analog of the phenomenon described by the Atiyah-Patodi-Singer theorem in even dimensionalities. The result has phenomenological implications: we present a scenario in which a QCD-like $\theta$-angle relaxes to zero on a certain (possibly, cosmological) timescale, despite the absence of any light axion-like particle.
Seeking the Ground State of String Theory: Recently, a number of authors have challenged the conventional assumption that the string scale, Planck mass, and unification scale are roughly comparable. It has been suggested that the string scale could be as low as a TeV. The greatest obstacle to developing a string phenomenology is our lack of understanding of the ground state. We explain why the dynamics which determines this state is not likely to be accessible to any systematic approximation. We note that the racetrack scheme, often cited as a counterexample, suffers from similar difficulties. We stress that the weakness of the gauge couplings, the gauge hierarchy, and coupling unification suggest that it may be possible to extract some information in a systematic approximation. We review the ideas of Kahler stabilization, an attempt to reconcile these facts. We consider whether the system is likely to sit at extremes of the moduli space, as in recent proposals for a low string scale. Finally we discuss the idea of Maximally Enhanced Symmetry, a hypothesis which is technically natural, compatible with basic facts about cosmology, and potentially predictive.
Topics on the geometry of D-brane charges and Ramond-Ramond fields: In this paper we discuss some topics on the geometry of type II superstring backgrounds with D-branes, in particular on the geometrical meaning of the D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see that, depending on the behaviour of the D-brane on the four non-compact space-time directions, we need different notions of homology and cohomology to discuss the associated fields and charge: we give a mathematical definition of such notions and show their physical applications. We then discuss the problem of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally, we recall the so-called *-problem and make some brief remarks about it.
Degenerations of K3, Orientifolds and Exotic Branes: A recently constructed limit of K3 has a long neck consisting of segments, each of which is a nilfold fibred over a line, that are joined together with Kaluza-Klein monopoles. The neck is capped at either end by a Tian-Yau space, which is non-compact, hyperkahler and asymptotic to a nilfold fibred over a line. We show that the type IIA string on this degeneration of K3 is dual to the type I$'$ string, with the Kaluza-Klein monopoles dual to the D8-branes and the Tian-Yau spaces providing a geometric dual to the O8 orientifold planes. At strong coupling, each O8-plane can emit a D8-brane to give an O8$^*$ plane, so that there can be up to 18 D8-branes in the type I$'$ string. In the IIA dual, this phenomenon occurs at weak coupling and there can be up to 18 Kaluza-Klein monopoles in the dual geometry. We consider further duals in which the Kaluza-Klein monopoles are dualised to NS5-branes or exotic branes. A 3-torus with $H$-flux can be realised in string theory as an NS5-brane wrapped on $T^3$, with the 3-torus fibred over a line. T-dualising gives a 4-dimensional hyperkahler manifold which is a nilfold fibred over a line, which can be viewed as a Kaluza-Klein monopole wrapped on $T^2$. Further T-dualities then give non-geometric spaces fibred over a line and can be regarded as wrapped exotic branes. These are all domain wall configurations, dual to the D8-brane. Type I$'$ string theory is the natural home for D8-branes, and we dualise this to find string theory homes for each of these branes. The Kaluza-Klein monopoles arise in the IIA string on the degenerate K3. T-duals of this give exotic branes on non-geometric spaces.
Energy radiated from a fluctuating selfdual string: We compute the energy that is radiated from a fluctuating selfdual string in the large $N$ limit of $A_{N-1}$ theory using the AdS-CFT correspondence. We find that the radiated energy is given by a non-local expression integrated over the string world-sheet. We also make the corresponding computation for a charged string in six-dimensional classical electrodynamics, thereby generalizing the Larmor formula for the radiated energy from an accelerated point particle.
Gravity-Matter Couplings from Liouville Theory: The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its $U_q(sl(2))$ quantum group structure. The result is shown to agree with matrix-model calculations on the sphere. The precise definition of the corresponding cosmological constant is given in the operator solution of the quantum Liouville theory. It is shown that the symmetry between quantum-group spins $J$ and $-J-1$ previously put forward by the author is the explanation of the continuation in the number of screening operators discovered by Goulian and Li. Contrary to the previous discussions of this problem, the present approach clearly separates the emission operators for each leg. This clarifies the structure of the dressing by gravity. It is shown, in particular that the end points are not treated on the same footing as the mid point. Since the outcome is completely symmetric this suggests the existence of a picture-changing mechanism in two dimensional gravity.
Axion-Dilaton Black Holes: In this talk some essential features of stringy black holes are described. We consider charged four-dimensional axion-dilaton black holes. The Hawking temperature and the entropy of all solutions are shown to be simple functions of the squares of supercharges, defining the positivity bounds. Spherically symmetric and multi black hole solutions are presented. The extreme solutions have some unbroken supersymmetries. Axion-dilaton black holes with zero entropy and zero area of the horizon form a family of stable particle-like objects, which we call holons. We discuss the possibility of splitting of nearly extreme black holes into holons.
The correspondence between rotating black holes and fundamental strings: The correspondence principle between strings and black holes is a general framework for matching black holes and massive states of fundamental strings at a point where their physical properties (such as mass, entropy and temperature) smoothly agree with each other. This correspondence becomes puzzling when attempting to include rotation: At large enough spins, there exist degenerate string states that seemingly cannot be matched to any black hole. Conversely, there exist black holes with arbitrarily large spins that cannot correspond to any single-string state. We discuss in detail the properties of both types of objects and find that a correspondence that resolves the puzzles is possible by adding dynamical features and non-stationary configurations to the picture. Our scheme incorporates all black hole and string phases as part of the correspondence, save for one outlier which remains enigmatic: the near-extremal Kerr black hole. Along the way, we elaborate on general aspects of the correspondence that have not been emphasized before.
On the duality of massive Kalb-Ramond and Proca fields: We compare the massive Kalb-Ramond and Proca fields with a quartic self-interaction and show that the same strong coupling scale is present in both theories. In the Proca theory, the longitudinal mode enters the strongly coupled regime beyond this scale, while the two transverse modes propagate further and survive in the massless limit. In contrast, in case of the massive Kalb-Ramond field, the two transverse modes become strongly coupled beyond the Vainshtein scale, while the pseudo-scalar mode remains in the weak coupling regime and survives in the massless limit. This indicates a contradiction with the numerous claims in the literature that these theories are dual to each other.
Noncompact Symmetries in String Theory: Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's, have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by noncompact groups modded out by their maximal compact subgroups and discrete duality groups. Then it was found that many other moduli spaces have analogous descriptions. More recently, noncompact group symmetries have turned up in effective actions used to study string cosmology and other classical configurations. This paper explores these noncompact groups in the case of toroidal compactification both from the viewpoint of low-energy effective field theory, using the method of dimensional reduction, and from the viewpoint of the string theory world sheet. The conclusion is that all these symmetries are intimately related. In particular, we find that Chern--Simons terms in the three-form field strength $H_{\mu\nu\rho}$ play a crucial role.
Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics: We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the context of generalized fractional derivatives. For this purpose, it was solved the Schr\"odinger equation in phase space with the linear potential. The solution (ground state) is obtained, analyzed through the Wigner function comparing with the original solution, the Airy function for the meson $c\overline{c}$. The identified eigenfunctions are connected to the Wigner function via the Weyl product and the Galilei group representation theory in phase space. In some ways, compared to the wave function, the Wigner function makes it simpler to see how the meson system is non-classical.
Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras: We examine a strong/weak duality between a Heisenberg coset of a theory with $\mathfrak{sl}_n$ subregular $\mathcal{W}$-algebra symmetry and a theory with a $\mathfrak{sl}_{n|1}$-structure. In a previous work, two of the current authors provided a path integral derivation of correlator correspondences for a series of generalized Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality. In this paper, we derive correlator correspondences in a similar way but for a different series of generalized duality. This work is a part of the project to realize the duality of corner vertex operator algebras proposed by Gaiotto and Rap\v{c}\'ak and partly proven by Linshaw and one of us in terms of two dimensional conformal field theory. We also examine another type of duality involving an additional pair of fermions, which is a natural generalization of the fermionic FZZ-duality. The generalization should be important since a principal $\mathcal{W}$-superalgebra appears as its symmetry and the properties of the superalgebra are less understood than bosonic counterparts.
Physicists' $d=3+1$, $N=1$ superspace-time and supersymmetric QFTs from a tower construction in complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic Geometry and a purge-evaluation/index-contracting map: The complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic Geometry aspect of a superspace(-time) $\widehat{X}$ in Sec.\,1 of D(14.1) (arXiv:1808.05011 [math.DG]) together with the Spin-Statistics Theorem in Quantum Field Theory, which requires fermionic components of a superfield be anticommuting, lead us to the notion of towered superspace(-time) $\widehat{X}^{\widehat{\boxplus}}$ and the built-in purely even physics sector $X^{\mbox{physics}}$ from $\widehat{X}^{\widehat{\boxplus}}$. We use this to reproduce the $d=3+1$, $N=1$ Wess-Zumino model and the $d=3+1$, $N=1$ supersymmetric $U(1)$ gauge theory with matter --- as in, e.g., Chap.\,V and Chap.\,VI \& part of Chap.\,VII of the classical Supersymmetry \& Supergravity textbook by Julius Wess and Jonathan Bagger --- and, hence, recast physicists' two most basic supersymmetric quantum field theories solidly into the realm of (complexified ${\Bbb Z}/2$-graded) $C^\infty$-Algebraic Geometry. Some traditional differential geometers' ways of understanding supersymmetric quantum field theories are incorporated into the notion of a purge-evaluation/index-contracting map ${\cal P}:C^\infty(X^{\mbox{physics}})\rightarrow C^\infty(\widehat{X})$ in the setting. This completes for the current case a $C^\infty$-Algebraic Geometry language we sought for in D(14.1), footnote 2, that can directly link to the study of supersymmetry in particle physics. Once generalized to the nonabelian case in all dimensions and extended $N\ge 2$, this prepares us for a fundamental (as opposed to solitonic) description of super D-branes parallel to Ramond-Neveu-Schwarz fundamental superstrings
Super-Zeeman Embedding Models on N-Supersymmetric World-Lines: We construct a model of an electrically charged magnetic dipole with arbitrary N-extended world-line supersymmetry, which exhibits a supersymmetric Zeeman effect. By including supersymmetric constraint terms, the ambient space of the dipole may be tailored into an algebraic variety, and the supersymmetry broken for almost all parameter values. The so exhibited obstruction to supersymmetry breaking refines the standard one, based on the Witten index alone.
Fractional Branes and N=1 Gauge Theories: We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group with matter in the bifundamental. In particular, when only one type of brane is present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes to the bulk fields and present the corresponding supergravity solution, valid at large distances. By using a probe analysis, we are able to obtain the Wilsonian beta-function for those gauge theories that possess some chiral multiplet. Although, due to the lack of moduli, the probe technique is not directly applicable to the case of pure N=1 Yang-Mills, we point out that the same formula gives the correct result also for this case.
Back-door fine-tuning in supersymmetric low scale inflation: Low scale inflation has many virtues and it has been claimed that its natural realisation in supersymmetric standard model can be achieved rather easily. In this letter we have demonstrated that also in this case the dynamics of the hidden sector responsible for supersymmetry breakdown and the structure of the soft terms affects significantly, and in fact often spoils, the would-be inflationary dynamics. Also, we point out that the issue if the cosmological constant cancellation in the post-inflationary vacuum strongly affects supersymmetric inflation. It is important to note the crucial difference between freezing of the modulus and actually stabilising it - the first approach misses parts of the scalar potential which turn out to be relevant for inflation. We argue, that it is more likely that the low scale supersymmetric inflation occurs at a critical point at the origin in the field space than at an inflection point away from the origin, as the necessary fine-tuning in the second case is typically larger.
Linear Models for Flux Vacua: We construct worldsheet descriptions of heterotic flux vacua as the IR limits of N=2 gauge theories. Spacetime torsion is incorporated via a 2d Green-Schwarz mechanism in which a doublet of axions cancels a one-loop gauge anomaly. Manifest (0,2) supersymmetry and the compactness of the gauge theory instanton moduli space suggest that these models, which include Fu-Yau models, are stable against worldsheet instanton effects, implying that they, like Calabi-Yaus, may be smoothly extended to solutions of the exact beta functions. Since Fu-Yau compactifications are dual to KST-type flux compactifications, this provides a microscopic description of these IIB RR-flux vacua.
Weak cosmic censorship conjecture with pressure and volume in the Gauss-Bonnet AdS black hole: With the Hamilton-Jacobi equation, we obtain the energy-momentum relation of a charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On the basis of the energy-momentum relation at the event horizon, we investigate the first law, second law, and weak cosmic censorship conjecture in both the normal phase space and extended phase space. Our results show that the first law, second law as well as the weak cosmic censorship conjecture are valid in the normal phase space for all the initial states are black holes. However, in the extended phase space, the second law is violated for the extremal and near-extremal black holes, and the weak cosmic censorship conjecture is violable for the near-extremal black hole, though the first law is still valid. In addition, in both the the normal and extended phase spaces, we find the absorbed particle changes the configuration of the near-extremal black hole, while don't change that of the extremal black hole.
Smooth tensionful higher-codimensional brane worlds with bulk and brane form fields: Completely regular tensionful codimension-n brane world solutions are discussed, where the core of the brane is chosen to be a thin codimension-(n-1) shell in an infinite volume flat bulk, and an Einstein-Hilbert term localized on the brane is included (Dvali-Gabadadze-Porrati models). In order to support such localized sources we enrich the vacuum structure of the brane by the inclusion of localized form fields. We find that phenomenological constraints on the size of the internal core seem to impose an upper bound to the brane tension. Finite transverse-volume smooth solutions are also discussed.
Two-dimensional gauge anomalies and $p$-adic numbers: We show how methods of number theory can be used to study anomalies in gauge quantum field theories in spacetime dimension two. To wit, the anomaly cancellation conditions for the abelian part of the local anomaly admit solutions if and only if they admit solutions in the reals and in the $p$-adics for every prime $p$ and we use this to build an algorithm to find all solutions.
Vector-Tensor multiplet in N=2 superspace with central charge: We use the four-dimensional N=2 central charge superspace to give a geometrical construction of the Abelian vector-tensor multiplet consisting, under N=1 supersymmetry, of one vector and one linear multiplet. We derive the component field supersymmetry and central charge transformations, and show that there is a super-Lagrangian, the higher components of which are all total derivatives, allowing us to construct superfield and component actions.
Supersymmetry of IIA warped flux AdS and flat backgrounds: We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that $AdS_n\times_w M^{10-n}$ preserve $2^{[{n\over2}]} k$ for $n\leq 4$ and $2^{[{n\over2}]+1} k$ for $4<n\leq 7$ supersymmetries, $k\in \bN_{>0}$. In addition we show that, for suitably restricted fields and $M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on $M^{10-n}$. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to $\bR^{1,n-1}\times_w M^{10-n}$ backgrounds which underpin flux compactifications to $\bR^{1,n-1}$ and show that these preserve $2^{[{n\over2}]} k$ for $2<n\leq 4$, $2^{[{n+1\over2}]} k$ for $4<n\leq 8$, and $2^{[{n\over2}]} k$ for $n=9, 10$ supersymmetries.
Low Energy Gauge Unification Theory: Because of the problems arising from the fermion unification in the traditional Grand Unified Theory and the mass hierarchy between the 4-dimensional Planck scale and weak scale, we suggest the low energy gauge unification theory with low high-dimensional Planck scale. We discuss the non-supersymmetric SU(5) model on $M^4\times S^1/Z_2 \times S^1/Z_2$ and the supersymmetric SU(5) model on $M^4\times S^1/(Z_2\times Z_2') \times S^1/(Z_2\times Z_2')$. The SU(5) gauge symmetry is broken by the orbifold projection for the zero modes, and the gauge unification is accelerated due to the SU(5) asymmetric light KK states. In our models, we forbid the proton decay, still keep the charge quantization, and automatically solve the fermion mass problem. We also comment on the anomaly cancellation and other possible scenarios for low energy gauge unification.
The Spectral Action Principle: We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space, $\Lb$ is a scale and $\chi$ a positive function. When this principle is applied to the noncommutative space defined by the spectrum of the standard model one obtains the standard model action coupled to Einstein plus Weyl gravity. There are relations between the gauge coupling constants identical to those of $SU(5)$ as well as the Higgs self-coupling, to be taken at a fixed high energy scale.
Dielectric-Branes: We extend the usual world-volume action for a Dp-brane to the case of N coincident Dp-branes where the world-volume theory involves a U(N) gauge theory. The guiding principle in our construction is that the action should be consistent with the familiar rules of T-duality. The resulting action involves a variety of potential terms, i.e., nonderivative interactions, for the nonabelian scalar fields. This action also shows that Dp-branes naturally couple to RR potentials of all form degrees, including both larger and smaller than p+1. We consider the dynamics resulting from this action for Dp-branes moving in nontrivial background fields, and illustrate how the Dp-branes are ``polarized'' by external fields. In a simple example, we show that a system of D0-branes in an external RR four-form field expands into a noncommutative two-sphere, which is interpreted as the formation of a spherical D2-D0 bound state.
Schrödinger Fields on the Plane with $[U(1)]^N$ Chern-Simons Interactions and Generalized Self-dual Solitons: A general non-relativistic field theory on the plane with couplings to an arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We identify the self-dual systems for which certain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the general self-dual system with two Chern-Simons gauge fields (and non-vanishing mutual statistics parameter), we present a systematic analysis for the static vortexlike classical solutions, with or without uniform background magnetic field. Relativistic generalizations are also discussed briefly.
BRST, Ward identities, gauge dependence, and a functional renormalization group: Basic properties of gauge theories in the framework of Faddeev-Popov (FP) method, Batalin-Vilkovisky (BV) formalism, functional renormalization group (FRG) approach are considered. The FP and BV quantizations are characterized by the Becchi-Rouet-Stora-Tyutin (BRST) symmetry while the BRST symmetry is broken in the FRG approach. It is shown that the FP method, the BV formalism and the FRG approach can be provided with the Slavnov-Taylor identity, the Ward identity and the modified Slavnov-Taylor identity, respectively. It is proven that using the background field method the background gauge invariance of effective action within the FP and FRG quantization procedures can be achieved in nonlinear gauges. The gauge-dependence problem within the FP, BV and FRG quantizations is studied. Arguments allowing us to state the existence of principal problems of the FRG in the case of gauge theories are given.
Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model in Curved Spacetime with Non-Trivial Topology: We discuss the phase structure (in the $1/N$-expansion) of the Nambu-Jona-Lasinio model in curved spacetime with non-trivial topology ${\cal M}^3 \times {\rm S}^1$. The evaluation of the effective potential of the composite field $\bar{\psi} \psi$ is presented in the linear curvature approximation (topology is treated exactly) and in the leading order of the $1/N$-expansion. The combined influence of topology and curvature to the phase transitions is investigated. It is shown, in particular, that at zero curvature and for small radius of the torus there is a second order phase transition from the chiral symmetric to the chiral non-symmetric phase. When the curvature grows and (or) the radius of ${\rm S}^1$ decreases, then the phase transition is in general of first order. The dynamical fermionic mass is also calculated in a number of different situations.
Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly: We regulate in Euclidean space the Jacobian under scale transformations for two-dimensional nonrelativistic fermions and bosons interacting via contact interactions and compare the resulting scaling anomalies. For fermions, Grassmannian integration inverts the Jacobian: however, this effect is cancelled by the regularization procedure and a result similar to that of bosons is attained. We show the independence of the result with respect to the regulating function, and show the robustness of our methods by comparing the procedure with an effective potential method using both cutoff and $\zeta$-function regularization.
Complexity Geometry and Schwarzian Dynamics: A celebrated feature of SYK-like models is that at low energies, their dynamics reduces to that of a single variable. In many setups, this "Schwarzian" variable can be interpreted as the extremal volume of the dual black hole, and the resulting dynamics is simply that of a 1D Newtonian particle in an exponential potential. On the complexity side, geodesics on a simplified version of Nielsen's complexity geometry also behave like a 1D particle in a potential given by the angular momentum barrier. The agreement between the effective actions of volume and complexity succinctly summarizes various strands of evidence that complexity is closely related to the dynamics of black holes.
Perturbations on a moving D3-brane and mirage cosmology: We study the evolution of perturbations on a moving probe D3-brane coupled to a 4-form field in an AdS$_5$-Schwarzschild bulk. The unperturbed dynamics are parametrised by a conserved energy $E$ and lead to Friedmann-Robertson-Walker `mirage' cosmology on the brane with scale factor $a(\tau)$. The fluctuations about the unperturbed worldsheet are then described by a scalar field $\phi(\tau,\vec{x})$. We derive an equation of motion for $\phi$, and find that in certain regimes of $a$ the effective mass squared is negative. On an expanding BPS brane with E=0 superhorizon modes grow as $a^4$ whilst subhorizon modes are stable. When the brane contracts, all modes grow. We also briefly discuss the case when $E>0$, BPS anti-branes as well as non-BPS branes. Finally, the perturbed brane embedding gives rise to scalar perturbations in the FRW universe. We show that $\phi$ is proportional to the gauge invariant Bardeen potentials on the brane.
First Order Description of Black Holes in Moduli Space: We show that the second order field equations characterizing extremal solutions for spherically symmetric, stationary black holes are in fact implied by a system of first order equations given in terms of a prepotential W. This confirms and generalizes the results in [14]. Moreover we prove that the squared prepotential function shares the same properties of a c-function and that it interpolates between M^2_{ADM} and M^2_{BR}, the parameter of the near-horizon Bertotti-Robinson geometry. When the black holes are solutions of extended supergravities we are able to find an explicit expression for the prepotentials, valid at any radial distance from the horizon, which reproduces all the attractors of the four dimensional N>2 theories. Far from the horizon, however, for N-even our ansatz poses a constraint on one of the U-duality invariants for the non-BPS solutions with Z \neq 0. We discuss a possible extension of our considerations to the non extremal case.
Bosonization of Nonrelativistic Fermions and W-infinity Algebra: We discuss the bosonization of non-relativistic fermions in one space dimension in terms of bilocal operators which are naturally related to the generators of $W$-infinity algebra. The resulting system is analogous to the problem of a spin in a magnetic field for the group $W$-infinity. The new dynamical variables turn out to be $W$-infinity group elements valued in the coset $W$-infinity/$H$ where $H$ is a Cartan subalgebra. A classical action with an $H$ gauge invariance is presented. This action is three-dimensional. It turns out to be similiar to the action that describes the colour degrees of freedom of a Yang-Mills particle in a fixed external field. We also discuss the relation of this action with the one we recently arrived at in the Euclidean continuation of the theory using different coordinates.
Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity: The Effective One-Body formalism of the gravitational two-body problem in general relativity is reconsidered in the light of recent scattering amplitude calculations. Based on the kinematic relationship between momenta and the effective potential, we consider an energy-dependent effective metric describing the scattering in terms of an Effective One-Body problem for the reduced mass. The identification of the effective metric simplifies considerably in isotropic coordinates when combined with a redefined angular momentum map. While the effective energy-dependent metric as expected is not unique, solutions can be chosen perturbatively in the Post-Minkowskian expansion without the need to introduce non-metric corrections. By a canonical transformation, our condition maps to the one based on the standard angular momentum map. Expanding our metric around the Schwarzschild solution we recover the solution based on additional non-metric contributions.
Holographic reconstruction of asymptotically flat spacetimes: We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime $\mathcal{M}$ and those of another massless field living in three-dimensional null boundary $\mathscr{I}^+$. The idea is to first reconstruct the bulk metric $g_{\mu\nu}$ by "inverting" the bulk correlation functions and re-express the latter in terms of boundary correlators via the correspondence. This effectively allows asymptotic observers close to $\mathscr{I}^+$ to reconstruct the deep interior of the spacetime using only correlation functions localized near $\mathscr{I}^+$.
Multidimensional Residues for Feynman Integrals with Generic Power of Propagators: We propose that the concept of multidimensional residues can be used to directly extracting the coefficients of scalar master integrals (with single propagators only) from one-loop Feynman integrals with generic power of propagators. Unlike the usual integration-by-parts (IBP) technique, where one has to solve iteratively a complicated set of equations to carry out the reduction and determine the coefficients of scalar master integrals, using multidimensional residues provides the possibility of directly extracting the coefficients of the master integrals. As the first application of this idea, we show how to directly extract the scalar box integral coefficients.
Action, entropy and pair creation rate of charged black holes in de Sitter space: We compute and clarify the interpretation of the on-shell Euclidean action for Reissner-Nordstr\"{o}m black holes in de Sitter space. We show the on-shell action is minus the sum of the black hole and cosmological horizon entropy for arbitrary mass and charge in any number of dimensions. This unifying expression helps to clear up a confusion about the Euclidean actions of extremal and ultracold black holes in de Sitter, as they can be understood as special cases of the general expression. We then use this result to estimate the probability for the pair creation of black holes with arbitrary mass and charge in an empty de Sitter background, by employing the formalism of constrained instantons. Finally, we suggest that the decay of charged de Sitter black holes is governed by the gradient flow of the entropy function and that, as a consequence, the regime of light, superradiant, rapid charge emission should describe the potential decay of extreme charged Nariai black holes to singular geometries.
Gribov horizon and BRST symmetry: a few remarks: The issue of the BRST symmetry in presence of the Gribov horizon is addressed in Euclidean Yang-Mills theories in the Landau gauge. The positivity of the Faddeev-Popov operator within the Gribov region enables us to convert the soft breaking of the BRST invariance exhibited by the Gribov-Zwanziger action into a non-local exact symmetry, displaying explicit dependence from the non-perturbative Gribov parameter. Despite its non-locality, this symmetry turns out to be useful in order to establish non-perturbative Ward identities, allowing us to evaluate the vacuum expectation value of quantities which are BRST exact. These results are generalized to the refined Gribov-Zwanziger action introduced in [1], which yields a gluon propagator which is non-vanishing at the origin in momentum space, and a ghost propagator which is not enhanced in the infrared.
Three-BMN Correlation Functions: Integrability vs. String Field Theory One-Loop Mismatch: We compare calculations of the three-point correlation functions of BMN operators at the one-loop (next-to-leading) order in the scalar SU(2) sector from the integrability expression recently suggested by Gromov and Vieira, and from the string field theory expression based on the effective interaction vertex by Dobashi and Yoneya. A disagreement is found between the form-factors of the correlation functions in the one-loop contributions. The order-of-limits problem is suggested as a possible explanation of this discrepancy.
Thermodynamics of noncommutative high-dimensional AdS black holes with non-Gaussian smeared matter distributions: Considering non-Gaussian smeared matter distributions, we investigate thermodynamic behaviors of the noncommutative high-dimensional Schwarzschild-Tangherlini anti-de Sitter black hole, and obtain the condition for the existence of extreme black holes. We indicate that the Gaussian smeared matter distribution, which is a special case of non-Gaussian smeared matter distributions, is not applicable for the 6- and higher-dimensional black holes due to the hoop conjecture. In particular, the phase transition is analyzed in detail. Moreover, we point out that the Maxwell equal area law maintains for the noncommutative black hole whose Hawking temperature is within a specific range, but fails for that whose the Hawking temperature is beyond this range.
Supersymmetry and Attractors: We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the Bertotti-Robinson-type geometry. These results provide an explicit model independent expression for the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropy-area formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge.
Quaternionic Formulation of the Exact Parity Model: The exact parity model (EPM) is a simple extension of the Standard Model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In this paper we show that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory.
Massless scalar particle on AdS spacetime: Hamiltonian reduction and quantization: We investigate the massless scalar particle dynamics on $AdS_{N+1} ~ (N>1)$ by the method of Hamiltonian reduction. Using the dynamical integrals of the conformal symmetry we construct the physical phase space of the system as a $SO(2,N+1)$ orbit in the space of symmetry generators. The symmetry generators themselves are represented in terms of $(N+1)$-dimensional oscillator variables. The physical phase space establishes a correspondence between the $AdS_{N+1}$ null-geodesics and the dynamics at the boundary of $AdS_{N+2}$. The quantum theory is described by a UIR of $SO(2,N+1)$ obtained at the unitarity bound. This representation contains a pair of UIR's of the isometry subgroup SO(2,N) with the Casimir number corresponding to the Weyl invariant mass value. The whole discussion includes the globally well-defined realization of the conformal group via the conformal embedding of $AdS_{N+1}$ in the ESU $\rr\times S^N$.
From U(1) Maxwell Chern-Simons to Azbel-Hofstadter: Testing Magnetic Monopoles and Gravity to $\sim 10^{-15}$\textit{m}?: It is built a map between an Abelian Topological Quantum Field Theory, $2+1D$ compact U(1) gauge Maxwell Chern-Simons Theory and the nonrelativistic quantum mechanics Azbel-Hofstadter model of Bloch electrons. The $U_q(sl_2)$ quantum group and the magnetic translations group of the Azbel-Hofstadter model correspond to discretized subgroups of U(1) with linear gauge parameters. The magnetic monopole confining and condensate phases in the Topological Quantum Field Theory are identified with the extended (energy bands) and localized (gaps) phases of the Bloch electron. The magnetic monopole condensate is associated, at the nonrelativistic level, with gravitational white holes due to deformed classical gauge fields. These gravitational solutions render the existence of finite energy pure magnetic monopoles possible. This mechanism constitutes a dynamical symmetry breaking which regularizes the solutions on those localized phases allowing physical solutions of the Shr\"odinger equation which are chains of electron filaments connecting several monopole-white holes.To test these results would be necessary a strong external magnetic field $B\sim 5 T$ at low temperature $T<1 K$. To be accomplished, it would test the existence of magnetic monopoles and classical gravity to a scale of $\sim 10^{-15}$ \textit{meters}, the dimension of the monopole-white hole. A proper discussion of such experiment is out of the scope of this theoretical work.
Casimir Energy of the Universe and the Dark Energy Problem: We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function ($\be$-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.
Monodromy of an Inhomogeneous Picard-Fuchs Equation: The global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard-Fuchs equation, the series expansions around large complex structure, conifold, and around the open string discriminant are obtained. The monodromies are explicitly calculated from this data and checked to be integral. The limiting value of the normal function at large complex structure is an irrational number expressible in terms of the di-logarithm.
UV cancelations in gravity loop integrands: In this work we explore the properties of four-dimensional gravity integrands at large loop momenta. This analysis can not be done directly for the full off-shell integrand but only becomes well-defined on cuts that allow us to unambiguously specify labels for the loop variables. The ultraviolet region of scattering amplitudes originates from poles at infinity of the loop integrands and we show that in gravity these integcrands conceal a number of surprising features. In particular, certain poles at infinity are absent which requires a conspiracy between individual Feynman integrals contributing to the amplitude. We suspect that this non-trivial behavior is a consequence of yet-to-be found symmetry or hidden property of gravity amplitudes. We discuss mainly amplitudes in $\mathcal{N}=8$ supergravity but most of the statements are valid for pure gravity as well.
Holography of Wrapped M5-branes and Chern-Simons theory: We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N^3 scaling with precise coefficients.
Two-dimensional SUSY-pseudo-Hermiticity without separation of variables: We study SUSY-intertwining for non-Hermitian Hamiltonians with special emphasis to the two-dimensional generalized Morse potential, which does not allow for separation of variables. The complexified methods of SUSY-separation of variables and two-dimensional shape invariance are used to construct particular solutions - both for complex conjugated energy pairs and for non-paired complex energies.
Magnetic monopole - domain wall collisions: Interactions of different types of topological defects can play an important role in the aftermath of a phase transition. We study interactions of fundamental magnetic monopoles and stable domain walls in a Grand Unified theory in which $SU(5) \times Z_2$ symmetry is spontaneously broken to $SU(3)\times SU(2)\times U(1)/Z_6$. We find that there are only two distinct outcomes depending on the relative orientation of the monopole and the wall in internal space. In one case, the monopole passes through the wall, while in the other it unwinds on hitting the wall.
Quantum Theory, Noncommutativity and Heuristics: Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts. Firstly as field theories on noncommutative spacetimes they come with natural regularization parameters. Secondly they are related in a natural way to theories of quantum gravity which typically give rise to noncommutative spacetimes. Therefore noncommutative field theories can shed light on the problem of quantizing gravity. An attractive aspect of noncommutative field theories is that they can be formulated so as to preserve spacetime symmetries and to avoid the introduction of irrelevant degrees freedom and so they provide models of consistent fundamental theories. In these notes we review the formulation of symmetry aspects of noncommutative field theories on the simplest type of noncommutative spacetime, the Moyal plane. We discuss violations of Lorentz, P, CP, PT and CPT symmetries as well as causality. Some experimentally detectable signatures of these violations involving Planck scale physics of the early universe and linear response finite temperature field theory are also presented.
De Sitter Uplift with Dynamical Susy Breaking: We propose the use of D-brane realizations of Dynamical Supersymmetry Breaking (DSB) gauge sectors as sources of uplift in compactifications with moduli stabilization onto de Sitter vacua. This construction is fairly different from the introduction of anti D-branes, yet allows for tunably small contributions to the vacuum energy via their embedding into warped throats. The idea is explicitly exemplified by the embedding of the 1-family $SU(5)$ DSB model in a local warped throat with fluxes, which we discuss in detail in terms of orientifolds of dimer diagrams.
Massless Charged Particles Tunneling Radiation from a RN-dS Horizon and the Linear and Quadratic GUP: In this paper, we investigate the massless Reissner-Nordstrom de Sitter metric in the context of minimal length scenarios. We prove not only the confinement of the energy density of massless charged particles, both fermions and bosons, but also their ability to tunnel through the cosmological horizon. These massless particles might be interacting with Dirac sea and in this case they will appear outside the cosmological horizon in the context of dS/CFT holography. This result may formulate a fundamental reason for the expansion of the Dirac sea. Therefore, a spacetime Big Crunch may occur.
Superselection Sectors of $\son$ Wess-Zumino-Witten Models: The superselection structure of $\son$ WZW models is investigated from the point of view of algebraic quantum field theory. At level $1$ it turns out that the observable algebras of the WZW theory can be constructed in terms of even CAR algebras. This fact allows to give a formulation of these models close to the DHR framework. Localized endomorphisms are constructed explicitly in terms of Bogoliubov transformations, and the WZW fusion rules are proven using the DHR sector product. At level $2$ it is shown that most of the sectors are realized in $\HNSh=\HNS\otimes\HNS$ where $\HNS$ is the Neveu-Schwarz sector of the level $1$ theory. The level $2$ characters are derived and $\HNSh$ is decomposed completely into tensor products of the sectors of the WZW chiral algebra and irreducible representation spaces of the coset Virasoro algebra. Crucial for this analysis is the DHR decomposition of $\HNSh$ into sectors of a gauge invariant fermion algebra since the WZW chiral algebra as well as the coset Virasoro algebra are invariant under the gauge group $\Oz$.
Flowing from relativistic to non-relativistic string vacua in AdS$_5 \times$S$^5$: We find the connection between relativistic and non-relativistic string vacua in AdS$_5 \times$S$^5$ in terms of a free parameter $c$ flow. First, we show that the famous relativistic BMN vacuum flows in the large $c$ parameter to an unphysical solution of the non-relativistic theory. Then, we consider the simplest non-relativistic vacuum, found in arXiv:2109.13240 (called BMN-like), and we identify its relativistic origin, namely a non-compact version of the folded string with zero spin, ignored in the past due to its infinite energy. We show that, once the critical closed B-field required by the non-relativistic limit is included, the total energy of such relativistic solution is finite, and in the large $c$ parameter it precisely matches the one of the BMN-like string. We also analyse the case with spin in the transverse AdS directions.
Three-dimensional BF Theories and the Alexander-Conway Invariant of Knots: We study 3-dimensional BF theories and define observables related to knots and links. The quantum expectation values of these observables give the coefficients of the Alexander-Conway polynomial.
Dimensional continuation without perturbation theory: A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is motivated by studying the strong coupling expansion, but the end result makes no reference to any perturbation theory. It is shown that the formula leads to the correct dimension dependence in weak coupling perturbation theory at one loop.
M5-branes in ABJM theory and Nahm equation: We construct BPS solutions representing M2-M5 bound state in the ABJM action explicitly. They include the funnel type solutions and 't Hooft Polyakov monopole solutions. Furthermore, we give a one to one correspondence between the solutions of the BPS equation and the ones of an extended Nahm equation which includes the Nahm equation. This enables us to construct infinitely many conserved quantities from the Lax form of the Nahm equation.
θ-angle monodromy in two dimensions: "\theta-angle monodromy" occurs when a theory possesses a landscape of metastable vacua which reshuffle as one shifts a periodic coupling \theta by a single period. "Axion monodromy" models arise when this parameter is promoted to a dynamical pseudoscalar field. This paper studies the phenomenon in two-dimensional gauge theories which possess a U(1) factor at low energies: the massive Schwinger and gauged massive Thirring models, the U(N) 't Hooft model, and the {\mathbb CP}^N model. In all of these models, the energy dependence of a given metastable false vacuum deviates significantly from quadratic dependence on \theta just as the branch becomes completely unstable (distinct from some four-dimensional axion monodromy models). In the Schwinger, Thirring, and 't Hooft models, the meson masses decrease as a function of \theta. In the U(N) models, the landscape is enriched by sectors with nonabelian \theta terms. In the {\mathbb CP}^N model, we compute the effective action and the size of the mass gap is computed along a metastable branch.
Toward getting finite results from N=4 SYM with alpha'-corrections: We take our first step toward getting finite results from the alpha'-corrected D=4 N=4 SYM theory with emphasis on the field theory techniques. Starting with the classical action of N=4 SYM with the leading alpha'-corrections, we examine new divergence at one loop due to the presence of the alpha'-terms. The new vertices do not introduce additional divergence to the propagators or to the three-point correlators. However they do introduce new divergence, e.g., to the scalar four-point function which should be canceled by extra counter-terms. We expect that the counter-terms will appear in the 1PI effective action that is obtained by considering the string annulus diagram. We work out the structure of the divergence and comment on an application to the anomalous dimension of the SYM operators in the context of AdS/CFT.
Lagrangian Formulation for Free Mixed-Symmetry Bosonic Gauge Fields in (A)dS(d): Covariant Lagrangian formulation for free bosonic massless fields of arbitrary mixed-symmetry type in (A)dS(d) space-time is presented. The analysis is based on the frame-like formulation of higher-spin field dynamics [1] with higher-spin fields described as p-forms taking values in appropriate modules of the (A)dS(d). The problem of finding free field action is reduced to the analysis of an appropriate differential complex, with the derivation Q associated with the variation of the action. The constructed action exhibits additional gauge symmetries in the flat limit in agreement with the general structure of gauge symmetries for mixed-symmetry fields in Minkowski and (A)dS(d) spaces.
Biharmonic Superspace for N=4 Mechanics: We develop a new superfield approach to N=4 supersymmetric mechanics based on the concept of biharmonic superspace (bi-HSS). It is an extension of the N=4,d=1 superspace by two sets of harmonic variables associated with the two SU(2) factors of the R-symmetry group SO(4) of the N=4, d=1 super Poincar\'e algebra. There are three analytic subspaces in it: two of the Grassmann dimension 2 and one of the dimension 3. They are closed under the infinite-dimensional "large" N=4 superconformal group, as well as under the finite-dimensional superconformal group D(2,1;\alpha). The main advantage of the bi-HSS approach is that it gives an opportunity to treat N=4 supermultiplets with finite numbers of off-shell components on equal footing with their ``mirror'' counterparts. We show how such multiplets and their superconformal properties are described in this approach. We also define nonpropagating gauge multiplets which can be used to gauge various isometries of the bi-HSS actions. We present an example of nontrivial N=4 mechanics model with a seven-dimensional target manifold obtained by gauging an U(1) isometry in a sum of the free actions of the multiplet (4,4,0) and its mirror counterpart.
Neutrino mixing and mass hierarchy in Gaussian landscapes: The flavor structure of the Standard Model may arise from random selection on a landscape. In a class of simple models, called "Gaussian landscapes," Yukawa couplings derive from overlap integrals of Gaussian zero-mode wavefunctions on an extra-dimensional space. Statistics of vacua are generated by scanning the peak positions of these wavefunctions, giving probability distributions for all flavor observables. Gaussian landscapes can account for all of the major features of flavor, including both the small electroweak mixing in the quark sector and the large mixing observed in the lepton sector. We find that large lepton mixing stems directly from lepton doublets having broad wavefunctions on the internal manifold. Assuming the seesaw mechanism, we find the mass hierarchy among neutrinos is sensitive to the number of right-handed neutrinos, and can provide a good fit to neutrino oscillation measurements.
Horava-Lifshitz Gravity And Ghost Condensation: In this paper we formulate RFDiff invariant f(R) Horava-Lifshitz gravity and we show that it is related to the ghost condensation in the projectable version of Horava-Lifshitz gravity.
Quotient Stacks and String Orbifolds: In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather are literally sigma models on objects called quotient stacks, which are closely related to (but not quite the same as) quotient spaces. We show how this is an immediate consequence of definitions, and also how this explains a number of features of string orbifolds, from the fact that the CFT is well-behaved to orbifold Euler characteristics. Put another way, many features of string orbifolds previously considered ``stringy'' are now understood as coming from the target-space geometry; one merely needs to identify the correct target-space geometry.
Renormalizability of the Dynamical Two-Form: A proof of renormalizability of the theory of the dynamical non-Abelian two-form is given using the Zinn-Justin equation. Two previously unknown symmetries of the quantum action, different from the BRST symmetry, are needed for the proof. One of these is a gauge fermion dependent nilpotent symmetry, while the other mixes different fields with the same transformation properties. The BRST symmetry itself is extended to include a shift transformation by use of an anticommuting constant. These three symmetries restrict the form of the quantum action up to arbitrary order in perturbation theory. The results show that it is possible to have a renormalizable theory of massive vector bosons in four dimensions without a residual Higgs boson.
Arithmetic Spacetime Geometry from String Theory: An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic characters can be derived from the geometry of spacetime, and that the geometry is uniquely determined by the two-dimensional field theory on the world sheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay-Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.
Ultra-violet Behavior of Bosonic Quantum Membranes: We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $\beta = 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.
Perturbative Expansion around the Gaussian Effective Action: The Background Field Method: We develop a systematic method of the perturbative expansion around the Gaussian effective action based on the background field method. We show, by applying the method to the quantum mechanical anharmonic oscillator problem, that even the first non-trivial correction terms greatly improve the Gaussian approximation.
Three-quark clusters at finite temperatures and densities: We present a relativistic three-body equation to study correlations in a medium of finite temperatures and densities. This equation is derived within a systematic Dyson equation approach and includes the dominant medium effects due to Pauli blocking and self energy corrections. Relativity is implemented utilizing the light front form. The equation is solved for a zero-range force for parameters close to the confinement-deconfinement transition of QCD. We present correlations between two- and three-particle binding energies and calculate the three-body Mott transition.
Exact renormalization flow and domain walls from holography: The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in N=2 supergravity background are interpreted as the exact renormalization group flow equations in two dimensions. Our geometrical description of the renormalization flow is manifestly covariant under general reparametrization of the 2d coupling constants. An explicit exact solution to the 2d renormalization flow, based on its dual holographic description in terms of the Zamolodchikov metric, is considered in the particular case of the four-dimensional NLSM target space described by the SU(2)-invariant (Weyl) anti-self-dual Einstein metrics. The exact regular (Tod-Hitchin) solutions to these metrics are governed by the Painlev'e VI equation, and describe domain walls.
Closed universes can satisfy the holographic principle in three dimensions: We examine in details Friedmann-Robertson-Walker models in 2+1 dimensions in order to investigate the cosmic holographic principle suggested by Fischler and Susskind. Our results are rigorously derived differing from the previous one found by Wang and Abdalla. We discuss the erroneous assumptions done in this work. The matter content of the models is composed of a perfect fluid, with a $\gamma$-law equation of state. We found that closed universes satisfy the holographic principle only for exotic matter with a negative pressure. We also analyze the case of a collapsing flat universe.
Superfluid properties of BPS monopoles: This paper is devoted to demonstrating manifest superfluid properties of the Minkowskian Higgs model with vacuum BPS monopole solutions at assuming the "continuous" $\sim S^2$ vacuum geometry in that model. It will be also argued that point hedgehog topological defects are present in the Minkowskian Higgs model with BPS monopoles. It turns out, and we show this, that the enumerated phenomena are compatible with the Faddeev-Popov "heuristic" quantization of the Minkowskian Higgs model with vacuum BPS monopoles, coming to fixing the Weyl (temporal) gauge $A_0=0$ for gauge fields $A$ in the Faddeev-Popov path integral.
S-confinements from deconfinements: We consider four dimensional $\mathcal{N}=1$ gauge theories that are S-confining, that is they are dual to a Wess-Zumino model. S-confining theories with a simple gauge group have been classified. We prove all the S-confining dualities in the list, when the matter fields transform in rank-$1$ and/or rank-$2$ representations. Our only assumptions are the S-confining dualities for $SU(N)$ with $N+1$ flavors and for $Usp(2N)$ with $2N+4$ fundamentals. The strategy consists in a sequence of deconfinements and re-confinements. We pay special attention to the explicit superpotential at each step.
Twisted holography without conformal symmetry: We discuss the notion of translation-invariant vacua for 2d chiral algebras and relate it to the notion of the associated variety. The two-dimensional chiral algebra associated to four-dimensional ${\cal N}=4$ $U(N)$ SYM has a conjectural holographic dual involving the B-model topological string theory. We study the effect of non-zero vacuum expectation values on the chiral algebra correlation functions and derive a holographic dual Calabi-Yau geometry. We test our proposal by a large $N$ analysis of correlation functions of determinant operators, whose saddles can be matched with semi-classical configurations of "Giant Graviton" D-branes in the bulk
Killing-Yano equations with torsion, worldline actions and G-structures: We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for $G= U(n), SU(n), Sp(n), Sp(n)\cdot Sp(1), G_2$ and $Spin(7)$. We find that the Killing-Yano equation, which arises as a condition for the invariance of the worldline action, does not always determine the torsion coupling uniquely in terms of the metric and fundamental forms. We show that there are several connections with skew-symmetric torsion for $G=U(n), SU(n)$ and $G_2$ that solve the invariance conditions. We describe all these compatible connections for each of the $G$-structures and explain the geometric nature of the couplings.
Quantum Corrections in Collective Field Theory: We review and extend the computation of scattering amplitudes of tachyons in the $c=1$ matrix model using a manifestly finite prescription for the collective field hamiltonian. We give further arguments for the exactness of the cubic hamiltonian by demonstrating the equality of the loop corrections in the collective field theory with those calculated in the fermionic picture.
Instanton Effects in Matrix Models and String Effective Lagrangians: We perform an explicit calculation of the lowest order effects of single eigenvalue instantons on the continuous sector of the collective field theory derived from a $d=1$ bosonic matrix model. These effects consist of certain induced operators whose exact form we exhibit.
About Symmetries in Physics: The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of a lecture presented at the fifth ``Seminaire Rhodanien de Physique: Sur les Symetries en Physique" held at Dolomieu (France), 17-21 March 1997. Up to the appendix and the graphics, it is to be published in "Symmetries in Physics", F.Gieres, M.Kibler,C.Lucchesi and O.Piguet, eds. (Editions Frontieres, 1998).]
BPS Quantization of the Five-Brane: We give a unified description of all BPS states of M-theory compactified on $T^5$ in terms of the five-brane. We compute the mass spectrum and degeneracies and find that the $SO(5,5,Z)$ U-duality symmetry naturally arises as a T-duality by assuming that the world-volume theory of the five-brane itself is described by a string theory. We also consider the compactification on $S^1/Z_2 \times T^4$, and give a new explanation for its correspondence with heterotic string theory by exhibiting its dual equivalence to M-theory on $K3\times S^1$.
Tunnelling Effects in a Brane System and Quantum Hall Physics: We argue that a system of interacting D-branes, generalizing a recent proposal, can be modelled as a Quantum Hall fluid. We show that tachyon condensation in such a system is equivalent to one particle tunnelling. In a conformal field theory effective description, that induces a transition from a theory with central charge c=2 to a theory with c=3/2, with a corresponding symmetry enhancement.
Tensor and Vector Multiplets in Six-Dimensional Supergravity: We construct the complete coupling of $(1,0)$ supergravity in six dimensions to $n$ tensor multiplets, extending previous results to all orders in the fermi fields. We then add couplings to vector multiplets, as dictated by the generalized Green-Schwarz mechanism. The resulting theory embodies factorized gauge and supersymmetry anomalies, to be disposed of by fermion loops, and is determined by corresponding Wess-Zumino consistency conditions, aside from a quartic coupling for the gaugini. The supersymmetry algebra contains a corresponding extension that plays a crucial role for the consistency of the construction. We leave aside gravitational and mixed anomalies, that would only contribute to higher-derivative couplings.
Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory: We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime}$. In an axial gauge, a regularized version of the Hamiltonian of this gauge theory is $H_{0}+{e^{\prime}}^{2}H_{1}$, where $H_{0}$ is the Hamiltonian of a set of (1+1)-dimensional principal chiral nonlinear sigma models. We treat $H_{1}$ as the interaction Hamiltonian. For gauge group SU(2), we use form factors of the currents of the principal chiral sigma models to compute the string tension for small $e^{\prime}$, after reviewing exact S-matrix and form-factor methods. In the anisotropic regime, the dependence of the string tension on the coupling constant is not in accord with generally-accepted dimensional arguments.
Matrix Gravity and Massive Colored Gravitons: We formulate a theory of gravity with a matrix-valued complex vierbein based on the SL(2N,C)xSL(2N,C) gauge symmetry. The theory is metric independent, and before symmetry breaking all fields are massless. The symmetry is broken spontaneously and all gravitons corresponding to the broken generators acquire masses. If the symmetry is broken to SL(2,C) then the spectrum would correspond to one massless graviton coupled to $2N^2 -1$ massive gravitons. A novel feature is the way the fields corresponding to non-compact generators acquire kinetic energies with correct signs. Equally surprising is the way Yang-Mills gauge fields acquire their correct kinetic energies through the coupling to the non-dynamical antisymmetric components of the vierbeins.
Algebro-geometric approach to a fermion self-consistent field theory on coset space SU(m+n)/S(U(m) x U(n)): The integrability-condition method is regarded as a mathematical tool to describe the symmetry of collective sub-manifold. We here adopt the particle-hole representation. In the conventional time-dependent (TD) self-consistent field (SCF) theory, we take the one-form linearly composed of the TD SCF Hamiltonian and the infinitesimal generator induced by the collective-variable differential of canonical transformation on a group. Standing on the differential geometrical viewpoint, we introduce a Lagrange-like manner familiar to fluid dynamics to describe collective coordinate systems. We construct a geometric equation, noticing the structure of coset space SU(m+n)/S(U(m) x U(n)). To develop a perturbative method with the use of the collective variables, we aim at constructing a new fermion SCF theory, i.e., renewal of TD Hartree-Fock (TDHF) theory by using the canonicity condition under the existence of invariant subspace in the whole HF space. This is due to a natural consequence of the maximally decoupled theory because there exists an invariant subspace, if the invariance principle of Schredinger equation is realized. The integrability condition of the TDHF equation determining a collective sub-manifold is studied, standing again on the differential geometric viewpoint. A geometric equation works well over a wide range of physics beyond the random phase approximation.
Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes: In this paper, we derive generalized Bern-Carrasco-Johansson relations for color-ordered Yang-Mills amplitudes by imposing gauge invariance conditions and dimensional reduction appropriately on the new discovered graphic expansion of Einstein-Yang-Mills amplitudes. These relations are also satisfied by color-ordered amplitudes in other theories such as color-scalar theory, bi-scalar theory and nonlinear sigma model (NLSM). As an application of the gauge invariance induced relations, we further prove that the three types of BCJ numerators in NLSM , which are derived from Feynman rules, Abelian Z-theory and Cachazo-He- Yuan formula respectively, produce the same total amplitudes. In other words, the three distinct approaches to NLSM amplitudes are equivalent to each other.
On the Unlikeliness of Multi-Field Inflation: Bounded Random Potentials and our Vacuum: Based on random matrix theory, we compute the likelihood of saddles and minima in a class of random potentials that are softly bounded from above and below, as required for the validity of low energy effective theories. Imposing this bound leads to a random mass matrix with non-zero mean of its entries. If the dimensionality of field-space is large, inflation is rare, taking place near a saddle point (if at all), since saddles are more likely than minima or maxima for common values of the potential. Due to the boundedness of the potential, the latter become more ubiquitous for rare low/large values respectively. Based on the observation of a positive cosmological constant, we conclude that the dimensionality of field-space after (and most likely during) inflation has to be low if no anthropic arguments are invoked, since the alternative, encountering a metastable deSitter vacuum by chance, is extremely unlikely.
Is There Scale Invariance in N=1 Supersymmetric Field Theories ?: In two dimensions, it is well known that the scale invariance can be considered as conformal invariance. However, there is no solid proof of this equivalence in four or higher dimensions. We address this issue in the context of 4d $\mathcal{N}=1$ SUSY theories. The SUSY version of dilatation current for theories without conserved $R$ symmetry is constructed through the FZ-multiplet. We discover that the scale-invariant SUSY theory is also conformal when the real superfield in the dilatation current multiplet is conserved. Otherwise, it is only scale-invariant, despite of the transformation of improvement.
Proving the Absence of the Perturbative Corrections to the N=2 U(1) Kähler Potential Using the N=1 Supergraph Techniques: Perturbative N=2 non-renormalization theorem states that there is no perturbative correction to the Kahler potential \int d^4\theta K(\Phi,\bar{\Phi}). We prove this statement by using the N=1 supergraph techniques. We consider the N=2 supersymmetric U(1) gauge theory which possesses general prepotential F(\Psi).
Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect: We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We make a transformation from the noncommutative coordinates to a set of commuting coordinates and then we write the Hamiltonian for this system. The energy spectrum and the expectation value of the current can then be calculated and the Hall conductivity can be extracted. We use the same method to calculate the phase shift for the Aharonov-Bohm effect. Precession measurements could allow strong upper limits to be imposed on the noncommutativity coordinate and momentum parameters $\Theta$ and $\Xi$.
Magnetic Mass in 4D AdS Gravity: We provide a fully-covariant expression for the diffeomorphic charge in 4D anti-de Sitter gravity, when the Gauss-Bonnet and Pontryagin terms are added to the action. The couplings of these topological invariants are such that the Weyl tensor and its dual appear in the on-shell variation of the action, and such that the action is stationary for asymptotic (anti) self-dual solutions in the Weyl tensor. In analogy with Euclidean electromagnetism, whenever the self-duality condition is global, both the action and the total charge are identically vanishing. Therefore, for such configurations the magnetic mass equals the Ashtekhar-Magnon-Das definition.
Graph duality as an instrument of Gauge-String correspondence: We explore an identity between two branching graphs and propose a physical meaning in the context of the gauge-gravity correspondence. From the mathematical point of view, the identity equates probabilities associated with $\mathbb{GT}$, the branching graph of the unitary groups, with probabilities associated with $\mathbb{Y}$, the branching graph of the symmetric groups. In order to furnish the identity with physical meaning, we exactly reproduce these probabilities as the square of three point functions involving certain hook-shaped backgrounds. We study these backgrounds in the context of LLM geometries and discover that they are domain walls interpolating two AdS spaces with different radii. We also find that, in certain cases, the probabilities match the eigenvalues of some observables, the embedding chain charges. We finally discuss a holographic interpretation of the mathematical identity through our results.
Shifting Spin on the Celestial Sphere: We explore conformal primary wavefunctions for all half integer spins up to the graviton. Half steps are related by supersymmetry, integer steps by the classical double copy. The main results are as follows: we 1) introduce a convenient spin frame and null tetrad to organize all radiative modes of varying spin; 2) identify the massless spin-3/2 conformal primary wavefunction as well as the conformally soft Goldstone mode corresponding to large supersymmetry transformations; 3) indicate how to express a conformal primary of arbitrary spin in terms of differential operators acting on a scalar primary; 4) demonstrate that conformal primary metrics satisfy the double copy in a variety of forms -- operator, Weyl, and Kerr-Schild -- and are exact, albeit complex, solutions to the fully non-linear Einstein equations of Petrov type N; 5) propose a novel generalization of conformal primary wavefunctions; and 6) show that this generalization includes a large class of physically interesting metrics corresponding to ultra-boosted black holes, shockwaves and more.
Casimir force between Chern-Simons surfaces: We calculate the Casimir force between two parallel plates if the boundary conditions for the photons are modified due to presence of the Chern-Simons term. We show that this effect should be measurable within the present experimental technique.
Compact T-branes: We analyse global aspects of 7-brane backgrounds with a non-commuting profile for their worldvolume scalars, also known as T-branes. In particular, we consider configurations with no poles and globally well-defined over a compact K\"ahler surface. We find that such T-branes cannot be constructed on surfaces of positive or vanishing Ricci curvature. For the existing T-branes, we discuss their stability as we move in K\"ahler moduli space at large volume and provide examples of T-branes splitting into non-mutually-supersymmetric constituents as they cross a stability wall.
Polarized Dirac fermions in de Sitter spacetime: The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions of the Dirac equation with given momentum and helicity are derived and the final form of the quantum Dirac field is established. It is shown that the canonical quantization leads to a correct physical interpretation of the massive or massless fermion quantum fields.
The 1/2 BPS 't Hooft loops in N=4 SYM as instantons in 2d Yang-Mills: We extend the recent conjecture on the relation between a certain 1/8 BPS subsector of 4d N=4 SYM on S^2 and 2d Yang-Mills theory by turning on circular 1/2 BPS 't Hooft operators linked with S^2. We show that localization predicts that these 't Hooft operators and their correlation functions with Wilson operators on S^2 are captured by instanton contributions to the partition function of the 2d Yang-Mills theory. Based on this prediction, we compute explicitly correlation functions involving the 't Hooft operator, and observe precise agreement with S-duality predictions.
Holographic entanglement entropy and thermodynamic instability of planar R-charged black holes: The holographic entanglement entropy of an infinite strip subsystem on the asymptotic AdS boundary is used as a probe to study the thermodynamic instabilities of planar R-charged black holes (or their dual field theories). We focus on the single-charge AdS black holes in $D=5$, which correspond to spinning D3-branes with one non-vanishing angular momentum. Our results show that the holographic entanglement entropy indeed exhibits the thermodynamic instability associated with the divergence of the specific heat. When the width of the strip is large enough, the finite part of the holographic entanglement entropy as a function of the temperature resembles the thermal entropy, as is expected. As the width becomes smaller, however, the two entropies behave differently. In particular, there exists a critical value for the width of the strip, below which the finite part of the holographic entanglement entropy as a function of the temperature develops a self-intersection. We also find similar behavior in the single-charge black holes in $D=4$ and $7$.
Gauge-Invariant Operators for Singular Knots in Chern-Simons Gauge Theory: We construct gauge invariant operators for singular knots in the context of Chern-Simons gauge theory. These new operators provide polynomial invariants and Vassiliev invariants for singular knots. As an application we present the form of the Kontsevich integral for the case of singular knots.
Spinning strings and correlation functions in the AdS/CFT correspondence: In this thesis we present some computations made in both sides of the AdS/CFT holographic correspondence using the integrability of both theories. Regarding the string theory side, this thesis is focused in the computation of the dispersion relation of closed spinning strings in some deformed $AdS_3 \times S^3$ backgrounds. In particular we are going to focus in the deformation provided by the mixing of R-R and NS-NS fluxes and the so-called $\eta$-deformation. These computations are made using the classical integrability of these two deformed string theories, which is provided by the presence of a set of conserved quantities called "Uhlenbeck constants". The existence of the Uhlenbeck constants is central for the method used to derive the dispersion relations. Regarding the gauge theory side, we are interested in the computation of two and three-point correlation functions. Concerning the two-point function a computation of correlation functions involving different operators and different number of excitations is performed using the Algebraic Bethe Ansatz and the Quantum Inverse Scattering Method. These results are compared with computations done with the Coordinate Bethe Ansatz and with Zamolodchikov-Faddeev operators. Concerning the three-point functions, we will explore the novel construction given by the hexagon framework. In particular we are going to start from the already proposed hexagon form factor and rewrite it in a language more resembling of the Algebraic Bethe Ansatz. For this intent we construct an invariant vertex using Zamolodchikov-Faddeev operators, which is checked for some simple cases.
Rigid open membrane and non-abelian non-commutative Chern-Simons theory: In the Berkooz-Douglas matrix model of M theory in the presence of longitudinal $M5$-brane, we investigate the effective dynamics of the system by considering the longitudinal $M5$-brane as the background and the spherical $M5$-brane related with the other space dimensions as the probe brane. Due to there exists the background field strength provided by the source of the longitudinal $M5$-brane, an open membrane should be ended on the spherical $M5$-brane based on the topological reason. The formation of the bound brane configuration for the open membrane ending on the 5-branes in the background of longitudinal 5-brane can be used to model the 4-dimensional quantum Hall system proposed recently by Zhang and Hu. The description of the excitations of the quantum Hall soliton brane configuration is established by investigating the fluctuations of $D0$-branes living on the bound brane around their classical solution derived by the transformations of area preserving diffeomorphisms of the open membrane. We find that this effective field theory for the fluctuations is an SO(4) non-commutative Chern-Simons field theory. The matrix regularized version of this effective field theory is given in order to allow the finite $D0$-branes to live on the bound brane. We also discuss some possible applications of our results to the related topics in M-theory and to the 4-dimensional quantum Hall system.
A note on C-Parity Conservation and the Validity of Orientifold Planar Equivalence: We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like - but otherwise generic - representations of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang-Mills theory and orientifold field theory on R4, since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.
Operator Mixing and the AdS/CFT correspondence: We provide a direct prescription for computing the mixing among gauge invariant operators in N=4 SYM. Our approach is based on the action of the superalgebra on the states of the theory and thus it can be also applied to resolve the mixing in the dual string description. As an example, we focus on the supermultiplet containing the BMN operators with two impurities. On the field theory side, we derive the leading planar quantum corrections to the naive expression of the highest weight state. Then we use the same prescription in the BMN limit of the AdS5xS5 string theory and derive the form of the 2-impurity highest weight state. The string expression matches nicely the SYM result and provides a prediction for the mixing due to higher order quantum corrections in field theory.
Classification and a toolbox for orientifold models: We provide the general tadpole conditions for a class of supersymmetric orientifold models by studing the general properties of the elements included in the orientifold group. In this talk, we concentrate on orientifold models of the type $T^6/Z_M\times Z_N$.
Higher-order field theories: $φ^6$, $φ^8$ and beyond: The $\phi^4$ model has been the "workhorse" of the classical Ginzburg--Landau phenomenological theory of phase transitions and, furthermore, the foundation for a large amount of the now-classical developments in nonlinear science. However, the $\phi^4$ model, in its usual variant (symmetric double-well potential), can only possess two equilibria. Many complex physical systems possess more than two equilibria and, furthermore, the number of equilibria can change as a system parameter (e.g., the temperature in condensed matter physics) is varied. Thus, "higher-order field theories" come into play. This chapter discusses recent developments of higher-order field theories, specifically the $\phi^6$, $\phi^8$ models and beyond. We first establish their context in the Ginzburg--Landau theory of successive phase transitions, including a detailed discussion of the symmetric triple well $\phi^6$ potential and its properties. We also note connections between field theories in high-energy physics (e.g., "bag models" of quarks within hadrons) and parametric (deformed) $\phi^6$ models. We briefly mention a few salient points about even-higher-order field theories of the $\phi^8$, $\phi^{10}$, etc.\ varieties, including the existence of kinks with power-law tail asymptotics that give rise to long-range interactions. Finally, we conclude with a set of open problems in the context of higher-order scalar fields theories.
Hidden symmetries and Large N factorisation for permutation invariant matrix observables: Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under $S_N$, the symmetric group of all permutations of $N$ objects. In this paper, the permutation invariant matrix observables (PIMOs) of degree $k$ are shown to be in one-to-one correspondence with equivalence classes of elements in the diagrammatic partition algebra $P_k(N)$. On a 4-dimensional subspace of the 13-parameter space of $S_N$ invariant Gaussian models, there is an enhanced $O(N)$ symmetry. At a special point in this subspace, is the simplest $O(N)$ invariant action. This is used to define an inner product on the PIMOs which is expressible as a trace of a product of elements in the partition algebra. The diagram algebra $P_k(N)$ is used to prove the large $N$ factorisation property of this inner product, which generalizes a familiar large $N$ factorisation for inner products of matrix traces invariant under continuous symmetries.
A Solution of the Randall-Sundrum Model and the Mass Hierarchy Problem: A solution of the Randall-Sundrum model for a simplified case (one wall) is obtained. It is given by the $1/k^2$-expansion (thin wall expansion) where $1/k$ is the {\it thickness} of the domain wall. The vacuum setting is done by the 5D Higgs potential and the solution is for a {\it family} of the Higgs parameters. The mass hierarchy problem is examined. Some physical quantities in 4D world such as the Planck mass, the cosmological constant, and fermion masses are focussed. Similarity to the domain wall regularization used in the chiral fermion problem is explained. We examine the possibility that the 4D massless chiral fermion bound to the domain wall in the 5D world can be regarded as the real 4D fermions such as neutrinos, quarks and other leptons.
Quantum causal histories: Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum history as conditions on the evolution operators. A quantum causal history in which transitivity holds can be treated as ``directed'' topological quantum field theory. Two examples of such histories are described.
Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit: In this paper, the finite temperature Casimir force acting on a two-dimensional Casimir piston due to electromagnetic field is computed. It was found that if mixed boundary conditions are assumed on the piston and its opposite wall, then the Casimir force always tends to restore the piston towards the equilibrium position, regardless of the boundary conditions assumed on the walls transverse to the piston. In contrary, if pure boundary conditions are assumed on the piston and the opposite wall, then the Casimir force always tend to pull the piston towards the closer wall and away from the equilibrium position. The nature of the force is not affected by temperature. However, in the high temperature regime, the magnitude of the Casimir force grows linearly with respect to temperature. This shows that the Casimir effect has a classical limit as has been observed in other literatures.
Deconstructing Scalar QED at Zero and Finite Temperature: We calculate the effective potential for the WLPNGB in a world with a circular latticized extra dimension. The mass of the WLPNGB is calculated from the one-loop quantum effect of scalar fields at zero and finite temperature. We show that a series expansion by the modified Bessel functions is useful to calculate the one-loop effective potentials.
Gauge/Gravity Duals with Holomorphic Dilaton: We consider configurations of D7-branes and whole and fractional D3-branes with N=2 supersymmetry. On the supergravity side these have a warp factor, three-form flux and a nonconstant dilaton. We discuss general IIB solutions of this type and then obtain the specific solutions for the D7/D3 system. On the gauge side the D7-branes add matter in the fundamental representation of the D3-brane gauge theory. We find that the gauge and supergravity metrics on moduli space agree. However, in many cases the supergravity curvature is large even when the gauge theory is strongly coupled. In these cases we argue that the useful supergravity dual must be a IIA configuration.
Duality, Monodromy and Integrability of Two Dimensional String Effective Action: The monodromy matrix, ${\hat{\cal M}}$, is constructed for two dimensional tree level string effective action. The pole structure of ${\hat{\cal M}}$ is derived using its factorizability property. It is found that the monodromy matrix transforms non-trivially under the non-compact T-duality group, which leaves the effective action invariant and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, ${\hat{\cal M}}$ for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$, where these ideas can be directly checked. We consider well known charged black hole solutions in the heterotic string theory which can be generated by T-duality transformations from a spherically symmetric `seed' Schwarzschild solution. We construct the monodromy matrix for the Schwarzschild black hole background of the heterotic string theory.
Isoperimetric Inequalities and Magnetic Fields at CERN: We discuss the generalization of the classical isoperimetric inequality to asymptotically hyperbolic Riemannian manifolds. It has been discovered that the AdS/CFT correspondence in string theory requires that such an inequality hold in order to be internally consistent. In a particular application, to the systems formed in collisions of heavy ions in particle colliders, we show how to formulate this inequality in terms of measurable physical quantities, the magnetic field and the temperature. Experiments under way at CERN in Geneva can thus be said to be testing an isoperimetric inequality.
On the Scattering Phase for AdS_5 x S^5 Strings: We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x S^5 apparently solving Janik's crossing relation.
All 4-dimensional static, spherically symmetric, 2-charge abelian Kaluza-Klein black holes and their CFT duals: We derive the dual CFT Virasoro algebras from the algebra of conserved diffeomorphism charges, for a large class of abelian Kaluza-Klein black holes. Under certain conditions, such as non-vanishing electric and magnetic monopole charges, the Kaluza-Klein black holes have a Reissner-Nordstrom space-time structure. For the non-extremal charged Kaluza-Klein black holes, we use the uplifted 6d pure gravity solutions to construct a set of Killing horizon preserving diffeomorphisms. For the (non-supersymmetric) extremal black holes, we take the NENH limit, and construct a one-parameter family of diffeomorphisms which preserve the Hamiltonian constraints at spatial infinity. In each case we evaluate the algebra of conserved diffeomorphism charges following Barnich, Brandt and Compere, who used a cohomological approach, and Silva, who employed a covariant-Lagrangian formalism. At the Killing horizon, it is only Silva's algebra which acquires a central charge extension, and which enables us to recover the Bekenstein-Hawking black hole entropy from the Cardy formula. For the NENH geometry, the extremal black hole entropy is obtained only when the free parameter of the diffeomorphism generating vector fields is chosen such that the central terms of the two algebras are in agreement.
Quantum Groups on Fibre Bundles: It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of quantum spaces noncommutative principal and vector bundles are defined and their properties are studied. Important constructions in the classical theory of principal fibre bundles like associated bundles and differential calculi are carried over to the quantum case. At the end $q$-deformed instanton models are introduced for every integral index.
Revisiting Schwarzschild black hole singularity through string theory: The resolution of black hole singularities represents an essential problem in the realm of quantum gravity. Due to the Belinskii, Khalatnikov and Lifshitz (BKL) proposal, the structure of the black hole interior in vacuum Einstein's equations can be described by the Kasner universe, which possesses the $O\left(d,d\right)$ symmetry. It motivates us to use the anisotropic Hohm-Zwiebach action, known as the string effective action with all orders $\alpha^{\prime}$ corrections for the $O\left(d,d\right)$ symmetric background, to study the singularity problem of black hole. In this letter, we obtain the singular condition for black holes and demonstrate that it is possible to resolve the Schwarzschild black hole singularity through the non-perturbative $\alpha^{\prime}$ corrections of string theory.