Les Houches lectures on non-perturbative topological strings

TL;DR

This paper provides an overview of non-perturbative topological string theory, discussing resurgence, BPS invariants, and the spectral theory correspondence to define the theory on toric Calabi-Yau manifolds.

Contribution

It introduces a comprehensive review of non-perturbative aspects of topological strings, including recent results and the TS/ST correspondence for toric Calabi-Yau manifolds.

Findings

Resurgent structure relates to BPS invariants.

Non-perturbative amplitudes derived from resurgence.

Spectral theory provides a non-perturbative definition.

Abstract

In these lecture notes for the Les Houches School on Quantum Geometry I give an introductory overview of non-perturbative aspects of topological string theory. After a short summary of the perturbative aspects, I first consider the non-perturbative sectors of the theory as unveiled by the theory of resurgence. I give a self-contained derivation of recent results on non-perturbative amplitudes, and I explain the conjecture relating the resurgent structure of the topological string to BPS invariants. In the second part of the lectures I introduce the topological string/spectral theory (TS/ST) correspondence, which provides a non-perturbative definition of topological string theory on toric Calabi-Yau manifolds in terms of the spectral theory of quantum mirror curves