Superconformal Partition Functions and Non-perturbative Topological Strings

TL;DR

This paper introduces a non-perturbative framework for refined topological strings, enabling computation of superconformal partition functions and indices for various 5D and 6D theories, highlighting the role of SL(3,Z) modularity.

Contribution

It provides the first non-perturbative definition of refined topological strings and connects it to superconformal theory computations, incorporating SL(3,Z) symmetry.

Findings

Derived a non-perturbative partition function expression.

Applied the framework to compute superconformal indices.

Highlighted the significance of SL(3,Z) modular transformations.

Abstract

We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S^5 and the superconformal index of a large number of 6 dimensional (2,0) and (1,0) theories, including that of N coincident M5 branes. The result can be expressed as an integral over the product of three combinations of topological string amplitudes. SL(3,Z) modular transformations acting by inverting the coupling constants of the refined topological string play a key role.