High Energy Physics Theory

We study the bilinear and higher-order fermion condensates in4-dimensionalSU(N)gauge theories with a single Dirac fermion in a general representation. Augmented with a mixed anomaly between the0-form discrete chiral,1-form center, and0-form baryon number symmetries (BC anomaly), we sort out theories that admit higher-order condensates and vanishing fermion bilinears. Then, the BC anomaly is utilized to prove, in the absence of a topological quantum field theory, that nonvanishing fermion bilinears are inevitable in infrared-gapped theories with2-index (anti)symmetric fermions. We also contrast the BC anomaly with the0-form anomalies and show that it is the former anomaly that determines the infrared physics; we argue that the BC anomaly lurks deep to the infrared while the0-form anomalies are just variations of local terms. We provide evidence of this assertion by studying the BC anomaly in vector-like theories compactified on a small spacial circle. These theories are weakly-coupled, under analytical control, and they admit a dual description in terms of abelian photons that determine the deep infrared dynamics. We show that the dual photons talk directly to the1-form center symmetry in order to match the BC anomaly, while the0-form anomalies are variations of local terms and are matched by fiat. Finally, we study the fate of the BC anomaly in the compactified theories when they are held at a finite temperature. The effective field theory that describes the low-energy physics is2-dimensional. We show that the BC anomaly cascades from4to2dimensions.

We study the properties {of a conformal field theory} (CFT) driven periodically with a continuous protocol characterized by a frequency?D. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operatorU. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result forUthat matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability (Pn), equal (Cn) and unequal (Gn) time two-point primary correlators, energy density(En), and themthRenyi entropy (Smn) afterndrive cycles. Our results show that below a crossover stroboscopic time scalenc,Pn,EnandGnexhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure ofCn,GnandEnfor the continuous protocol and find emergence of spatial divergences ofCnandGnin both the heating and non-heating phases. We express our results forSmnandCnin terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

We present a construction of the most general BPS black holes of STU supergravity (N=2supersymmetricD=4supergravity coupled to three vector super-multiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.

We introduce a method for finding flux vacua of type IIB string theory in which the flux superpotential is exponentially small and at the same time one or more complex structure moduli are stabilized exponentially near to conifold points.

The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. This holds both for covariantly conserved currents associated to real symmetries that leave the action invariant as well as for non-conserved Noether currents associated to extended symmetry transformations which change the action, but in a specific way. We discuss then in particular symmetries and extended symmetries associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations and local shear transformations. Together they constitute the symmetry group of the frame bundle GL(d). The corresponding non-conserved Noether currents are the dilatation or Weyl current, the spin current and the shear current for which divergence-type equations of motion are obtained from the quantum effective action.

In this paper, we discuss the Inönü-Winger contraction of the conformal algebra. We start with the light-cone form of the Poincaré algebra and extend it to write down the conformal algebra inddimensions. To contract the conformal algebra, we choose five dimensions for simplicity and compactify the third transverse direction in to a circle of radiusRfollowing Kaluza-Klein dimensional reduction method. We identify the inverse radius,1/R, as the contraction parameter. After the contraction, the resulting representation is found to be the continuous spin representation in four dimensions. Even though the scaling symmetry survives the contraction, but the special conformal translation vector changes and behaves like the four-momentum vector. We also discussed the generalization toddimensions.

We develop a truncated Hamiltonian method to study nonequilibrium real time dynamics in the Schwinger model - the quantum electrodynamics in D=1+1. This is a purely continuum method that captures reliably the invariance under local and global gauge transformations and does not require a discretisation of space-time. We use it to study a phenomenon that is expected not to be tractable using lattice methods: we show that the 1+1D quantum electrodynamics admits the dynamical horizon violation effect which was recently discovered in the case of the sine-Gordon model. Following a quench of the model, oscillatory long-range correlations develop, manifestly violating the horizon bound. We find that the oscillation frequencies of the out-of-horizon correlations correspond to twice the masses of the mesons of the model suggesting that the effect is mediated through correlated meson pairs. We also report on the cluster violation in the massive version of the model, previously known in the massless Schwinger model. The results presented here reveal a novel nonequilibrium phenomenon in 1+1D quantum electrodynamics and make a first step towards establishing that the horizon violation effect is present in gauge field theory.

We analyze to which extent the KKLT proposal for the construction of de Sitter vacua in string theory is quantitatively controlled. Our focus is on the quality of the 10d supergravity approximation. As our main finding, we uncover and quantify an issue which one may want to call the "singular-bulk problem". In particular, we show that, requiring the curvature to be small in the conifold region, one is generically forced into a regime where the warp factor becomes negative in a significant part of the Calabi-Yau orientifold. This implies true singularities, independent of the familiar, string-theoretically controlled singularities of this type in the vicinity of O-planes. We also discuss possible escape routes as well as other control issues, related to the need for a large tadpole and hence for a complicated topology.

We compute thermal 2-point correlation functions in the black braneAdS5background dual to 4d CFT's at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

We characterize the correspondence between the twistedN=2super-Yang-Mills theory and the Baulieu-Singer topological theory quantized in the self-dual Landau gauges. While the first is based on an on-shell supersymmetry, the second is based on an off-shell Becchi-Rouet-Stora-Tyutin symmetry. Because of the equivariant cohomology, the twistedN=2in the ultraviolet regime and Baulieu-Singer theories share the same observables, the Donaldson invariants for 4-manifolds. The triviality of the Gribov copies in the Baulieu-Singer theory in these gauges shows that working in the instanton moduli space on the twistedN=2side is equivalent to working in the self-dual gauges on the Baulieu-Singer one. After proving the vanishing of theβfunction in the Baulieu-Singer theory, we conclude that the twistedN=2in the ultraviolet regime, in any Riemannian manifold, is correspondent to the Baulieu-Singer theory in the self-dual Landau gauges -- a conformal gauge theory defined in Euclidean flat space.