# Planned seminars

## 06/12/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Nathan Benjamin, Princeton University

We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space $H/SL(2,\mathbb{Z})$, and of target space moduli space $O(c, c; \mathbb{Z})\backslash O(c, c; \mathbb{R})/O(c) × O(c)$. This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to $AdS_3$ gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

## 13/12/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Sourav Roychowdhury, Chennai Mathematical Institute

In this talk I will discuss Klebanov-Tseytlin background and its non-Abelian T-dual geometry. In particular I will show that the T-dual background admits pp-wave geometry in the neighbourhood of appropriate null geodesic. I will make comments on possible dual gauge theory for our pp-wave background.

## 10/01/2022, Monday, 15:00–16:00 Europe/Lisbon — Online

Kiril Hristov, Sofia University

We reinterpret the OSV formula for the on-shell action/entropy function of asymptotically flat BPS black holes as a fixed point formula that is formally equivalent to a recent gluing proposal for asymptotically AdS$_4$ black holes. This prompts a conjecture that the complete perturbative answer for the most general gravitational building block of 4d $N = 2$ supergravity at a single fixed point takes the form of a Nekrasov-like partition function with equivariant parameters related to the higher-derivative expansion of the prepotential. In turn this leads to a simple localization-like proposal for a set of supersymmetric partition functions in (UV completed) 4d $N = 2$ supergravity theories. The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. In particular, it follows that the OSV formula comes from the unrefined limit of the general expression including only the so-called $\mathbb{W}$ tower of higher derivatives, while the on-shell action of pure (Euclidean) AdS$_4$ with round $S^3$ boundary comes from the NS limit that includes only the $\mathbb{T}$ tower.