Quantum Fields and Strings

I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime. In 2+1 dimensions with a dynamical critical exponent of z=2, the absence of a foliation structure allows for an A-type anomaly in the Galilean case, but also introduces the possibility of an infinite set of B-type anomalies.

I will also derive Ward identities for flat space correlation functions in Lifshitz field theories, and develop a method for calculating Lifshitz anomaly coefficients from these correlation functions using split dimensional regularization.

We study the effective twisted superpotential of 3d N=2 gauge theories compactified on a circle.  This is a rich object which encodes much of the protected information in these theories.  We review its properties, and survey some applications, including the algebra of Wilson loops, computation of supersymmetric partition functions on S^1 bundles, and the reduction of 3d dualities to two dimensions.

Abstract: We present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural operators associated with CFT bilocals whose duals are simple, diffeomorphism-invariant bulk operators.  These objects admit a description as fields in kinematic space, a phase space for such probes.  The framework of kinematic space allows for conceptually simple derivations of many results known in the literature, including linearized Einstein’s equations, the relationship between conformal blocks and geodesic Witten diagrams, and the CFT representation of bulk local operators.   Reference: https://arxiv.org/abs/1604.03110

The space of causal diamonds recently brought to attention by de Boer et al. and Czech et al. provides an organizing principle for the dependence of entanglement entropy in conformal field theories on the spatial subregion considered. I will show that the inclusion relation of causal diamonds does not give rise to a consistent notion of a causal structure and thus does not provide an alternate metric on this space. I will also show that the entanglement entropy of ball shaped regions is not enough to reconstruct the areas of higher dimensional bulk surfaces in a static geometry. Instead, I will provide a new direction for the reconstruction of the areas of bulk surfaces from boundary data in holography, using the shape derivatives of the entanglement entropy of nearly ball shaped regions.

We consider conformal blocks of two heavy operators and an arbitrary  number of light operators in a 1+1 dimensional CFT with large central charge. Using the monodromy method, these higher-point  conformal blocks are shown to factorize into products of 4-point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of  disjoint intervals for heavy states. The corresponding holographic entanglement entropy calculated via the minimal area prescription precisely matches these results from CFT.

What natural CFT quantities can “see” in the interior of the bulk AdS in a diffeomorphism invariant way? And how can we use them to learn about the emergence of local bulk physics? Inspired by the Ryu-Takayanagi relation, we construct a class of simple non-local operators on both sides of the duality and demonstrate their equivalence. Integrals of free bulk fields along geodesics/minimal surfaces are dual to what we will call “OPE blocks”: Individual conformal family contributions to the OPE of local operators. Our findings can be utilized to reconstruct local bulk operators and unify a number of previously disconnected AdS/CFT results. We extend this kinematic correspondence to incorporate gravitational interactions in AdS3 by relating geodesic operators to the Virasoro OPE blocks, hence providing a natural CFT prescription for “gravitational dressing”. We conclude with discussion of preliminary results on an interesting CFT structure that generalizes our dictionary to include arbitrary local bulk interactions. 

Painlevé equations can be obtained both from time-dependent classical Hamiltonian systems and from isomonodromic deformation problems. These realizations lead to a precise matching between Painlevé equations and Hitchin systems associated to four-dimensional N=2 SQCD as well as Argyres-Douglas theories. Long-time analysis of the Painlevé Hamiltonians dynamics allows to extract the unrefined "instanton" partition function for these theories at all strong-coupling points

We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d (2,0) type J theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of JJ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of JJ type. We can obtain the Schur and Hall-Littlewood index of these theories by computing the vacua character of the corresponding chiral algebra.

In my talk I will consider resurgence properties of Chern-Simons
theory on compact 3-manifolds. I will also describe what role
resurgence plays in the problem of categorification of Chern-Simons
theory, that is the problem of generalizing Khovanov homology of knots
to compact 3-manifolds.

We discuss information loss from black hole physics in AdS3, focusing on two sharp signatures infecting CFT2 correlators at large central charge c: `forbidden singularities' arising from Euclidean-time periodicity due to the effective Hawking temperature, and late-time exponential decay in the Lorentzian region. We show that these signatures can be derived from the behavior of the Virasoro conformal blocks at large central charge.  At finite c, we compute non-perturbative effects that resolve the unitarity-violation from forbidden singularities.  Finally, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all `saddles’ that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit, and discuss their potential to resolve the problem of late-time decay in the Lorentzian regime.