## Title and Abstract

### Babak Haghighat

**M5 branes and Theta functions**

We propose quantum states for Little String Theories (LSTs) arising from M5 branes probing A- and D-type singularities. This extends Witten’s picture of M5 brane partition functions as theta functions to this more general setup. Compactifying the world-volume of the five-branes on a two-torus, we find that the corresponding theta functions are sections of line bundles over complex 4-tori. This formalism allows us to derive Seiberg-Witten curves for the resulting four-dimensional theories. Along the way, we prove a duality for LSTs observed by Iqbal, Hohenegger and Rey.

### Valentin Reys

**Localization in supergravity and precision tests for AdS/CFT**

Localization techniques have proven to be a powerful tool for obtaining exact results in rigidly supersymmetric theories. In this talk, we will discuss how this framework can be used in the study of locally supersymmetric theories, i.e. in supergravity. We will discuss the BRST quantization of supergravity theories on spaces with an asymptotic boundary via a suitable background field formalism. When the background is restricted to have a residual isometry group, an equivariant BRST algebra arises as a deformation of the standard nilpotent BRST algebra. This equivariant algebra can then be used to localize supersymmetric partition functions. As an illustration of this general formalism, we will present recent results for the exact entropy of asymptotically AdS4 BPS black holes and compare with exact results previously obtained in the dual CFT3 using indices. Such exact results on both sides will pave the way for precision tests of the AdS/CFT correspondence beyond the large N limit in this context.

### Sunil Mukhi

**New Results in the Rational Modular Bootstrap**

I will present a complete construction of consistent, modular-covariant characters satisfying the basic requirements to describe two-character rational CFT. These are found as solutions of modular linear differential equations. Next I will describe partial progress on a more difficult problem, namely which of these solutions actually describes the partition function of a CFT. Several explicit examples will be constructed using even self-dual lattices in combination with the novel coset construction.

### Shuichi Yokoyama

**Anomaly, regularization and partition function on lens space**

In this talk, I will speak about how to determine a correct phase factor in the partition function on three-manifold particularly using three-sphere and lens space. Our result improves the work by D.Yokoyama and Y.Imamura on lens space partition function, and passes a couple of duality tests including the total phase.