Resurgence and Topological Strings

TL;DR

This paper explores how resurgence theory can be combined with the holomorphic anomaly equation to extract nonperturbative insights from the asymptotic perturbative expansion of topological string theory, extending its definition beyond perturbation.

Contribution

It introduces a novel approach to incorporate resurgence with the holomorphic anomaly equation, providing a model-independent method to access nonperturbative data in topological strings.

Findings

Resurgence combined with the holomorphic anomaly yields nonperturbative information.

The method extends the perturbative definition of topological string theory.

It provides a model-independent framework for nonperturbative analysis.

Abstract

The mathematical idea of resurgence allows one to obtain nonperturbative information from the large-order behavior of perturbative expansions. This idea can be very fruitful in physics applications, in particular if one does not have access to such nonperturbative information from first principles. An important example is topological string theory, which is a priori only defined as an asymptotic perturbative expansion in the coupling constant g_s. We show how the idea of resurgence can be combined with the holomorphic anomaly equation to extend the perturbative definition of the topological string and obtain, in a model-independent way, a large amount of information about its nonperturbative structure.