ASC Workshops

Recent developments in holography indicate that the semi-classical Euclidean path-integral of Einstein gravity is much more powerful than previously anticipated. It is capable of reproducing a unitary Page curve for black hole evaporation, and can even capture some features of the discrete nature of black hole microstates. Wormhole geometries play a key role in this context. I will propose a mechanism to explain this in the CFT: the OPE Randomness Hypothesis. This ansatz is a generalization of the Eigenstate Thermalization Hypothesis which applies to chaotic CFTs, and treats OPE coefficients of heavy operators as random variables with a given probability distribution. I will present two applications of this framework: First, it resolves a factorization puzzle in AdS_3/CFT_2 due to the genus-2 wormhole, as raised by Maoz and Maldacena. Second, it provides an argument against global symmetries in quantum gravity.

I present evidence, both from a GR and a holographic viewpoint, that Coleman's Euclidean axion wormholes do not contribute to the path integral.

Given that exact global symmetries are forbidden by quantum gravity, it is natural to expect that bounds on the quality of approximate global symmetries exist. So far, holographic arguments have only been provided for the former claim. I will discuss a classification of approximate global symmetries and describe a simple argument, based the Weak Gravity Conjecture, for a quantitative bound on the sub-class of "gauge-derived" global symmetries. This has intriguing relations to wormhole-based arguments, which I will also present. I will end with a brief discussion of the fundamental problems associated with euclidean wormholes and of some recent developments in this context.

I will review some recent progress on six-dimensional conformal field theories, highlighting applications to the

dynamics of M5-branes. On an orbifold singularity, M5s can fractionate, and they can recombine by sometimes

leaving behind a 'frozen' version of the singularity. The CFTs describing these processes also happen to be

ubiquitous building blocks for more complicated ones. There is also evidence for other processes where branes

recombine in patterns associated to nilpotent orbits of Lie groups, with precise checks obtained by anomalies and

moduli space dimensions.

The talks will focus on half-BPS boundary conditions for 3d N=2 gauge theories that preserve 2d N=(0,2)

supersymmetry. I will review (and extend) the classification of such boundary conditions and the BPS local

operators living on them, which form chiral algebras. I define a half-index that counts boundary local operators,

or equivalently computes a character of the boundary chiral algebra. With the help of the half-index and some

physical intuition, I will identify the action on boundary conditions of some basic dualities, including ``mirror

symmetries'' and level-rank dualities. This in turn leads to a definition of duality interfaces. (Work in progress

with D. Gaiotto and N. Paquette.)

As a consequence of electric-magnetic duality, partition functions of four-dimensional gauge theories can be

expressed in terms of modular forms in many cases. I will discuss new results for the modularity of topologically

twisted partition functions of N=2 and N=4 supersymmetric theories, and in particular how these partititon

functions may involve (iterated) integrals of modular forms.

The gauge origami are the statistical mechanical models which arise from supersymmetric localisation of gauge

theory path integrals. I will describe the gauge theory problems which lead to these models, and time permitting

will explain the connection to quantum algebras and integrable systems.

After recalling how some 4d N=2 gauge theories arise from reductions of 6d N=(2,0) superconformal theories on

a Riemann surface, I will discuss two discrete quotients with codimension 2 orbifold singularities. In the first

case the orbifold acts by rotations around one plane of the 4d N=2 theory; this is related to a Gukov-Witten

surface operator that imposes a monodromy around that plane. We deduce instanton partition functions in the

presence of surface operators; interestingly, instantons can fractionalize. In the second case the orbifold acts by

reflection on the 4d theory and the Riemann surface. We learn how boundaries are encoded in the AGT

correspondence. We are led to consider 4d N=2 quiver theories where some vector multiplets live on a

hemisphere and others on a projective space.