Non-Perturbative Real Topological Strings

TL;DR

This paper explores the resurgent structure of real topological strings on Calabi-Yau manifolds, deriving trans-series solutions and linking disk invariants to Stokes constants, with explicit formulas and evidence on local P2.

Contribution

It extends the operator formalism to real topological strings, providing explicit multi-instanton amplitude formulas and connecting invariants to Stokes phenomena.

Findings

Trans-series solutions to holomorphic anomaly equations at all orders.

Disk invariants appear as Stokes constants in the resurgent structure.

Explicit formulas for multi-instanton amplitudes.

Abstract

We study the resurgent structure of Walcher's real topological string on general Calabi-Yau manifolds. We find trans-series solutions to the corresponding holomorphic anomaly equations, at all orders in the string coupling constant, by extending the operator formalism of the closed topological string, and we obtain explicit formulae for multi-instanton amplitudes. We find that the integer invariants counting disks appear as Stokes constants in the resurgent structure, and we provide experimental evidence for our results in the case of the real topological string on local $\mathbb{P}^2$.