Nonperturbative refined topological string

TL;DR

This paper extends a recent nonperturbative formula for topological string free energy to the refined case, demonstrating it captures the trans-series structure and Stokes automorphisms, revealing resurgent properties.

Contribution

It introduces a nonperturbative formula for refined topological string free energy, advancing understanding of its resurgent structure and automorphisms.

Findings

The formula reproduces the trans-series structure of the refined topological string.

It captures the Stokes automorphisms related to resurgent properties.

The approach confirms the nonperturbative completion of the refined topological string.

Abstract

A formula for the full nonperturbative topological string free energy was recently proposed by Hattab and Palti \cite{HP24a}. In this work, we extend their result to the refined topological string theory. We demonstrate that the proposed formula for the full nonperturbative refined topological string free energy correctly reproduces the trans-series structure of the refined topological string and captures the Stokes automorphisms associated with its resurgent properties.