This week

We describe a powerful new technique for computing various physical observables in supergravity, without solving any supergravity equations. Applications include gravitational free energies, black hole entropies, and central charges and other CFT quantities of interest in holography. In the talk I will aim to describe the general idea, and give a flavour of some applications.

In a very general setting, entropy quantifies the amount of information about a system that an observer has access to. However, in contrast to quantum mechanics, in quantum field theory naive measures of entropy are divergent. To obtain finite results, one needs to consider measures such as relative entropy, which can be computed from the modular Hamiltonian using Tomita--Takesaki theory. In this talk, I will give a short introduction to Tomita--Takesaki modular theory and present examples of modular Hamiltonians. Using these, I will give results for therelative entropy between the de Sitter vacuum state and a coherent excitation thereof in diamond and wedge regions, and show explicitly that the result satisfies the expected properties for a relative entropy. Finally, I will use local thermodynamic laws to determine the local temperature that is measured by an observer, and consider the backreaction of the quantum state on the geometry to prove an entropy-area law for de Sitter spacetime. Based on arXiv:arXiv:2308.14797, 2310.12185, 2311.13990 and 2312.04629.

Topological orders in 2+1 dimensions are captured by modular tensor categories (MTCs). We propose a correspondence that assigns a fusion category to a pair (M,G), where M is a Seifert 3-manifold and G is an ADE Lie group. We conjecture that the fusion category associated to (M,G) is an MTC if and only if M has trivial first homology group with coefficients in the center of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to access the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realizing all MTCs (unitary or non-unitary) with rank at most 5.

It has recently been recognized that various observables in different four-dimensional supersymmetric gauge theories can be computed for an arbitrary 't Hooft coupling as determinants of certain semi-infinite matrices. It turns out that these quantities can be expressed as Fredholm determinants of the so-called Bessel kernel and they are closely related to celebrated Tracy-Widom distribution (more precisely, its finite temperature generalization) describing level-spacing distributions in matrix models. We exploit this relation to determine their dependence on the ’t Hooft coupling constant. Unlike the weak coupling expansion, which has a finite radius of convergence, the strong coupling expansion is factorially divergent, necessitating the inclusion of nonperturbative, exponentially small corrections. We develop a method to systematically compute these corrections and discuss the resurgent properties of the resulting transseries.