Quantum Fields and Strings

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.