Resurgence and Riemann-Hilbert problems for elliptic Calabi-Yau threefolds

TL;DR

This paper explores the connection between Riemann-Hilbert problems and the topological string theory on elliptic Calabi-Yau threefolds, revealing new insights into their mathematical and physical structures.

Contribution

It establishes a link between non-linear Riemann-Hilbert problems and the Borel summation of topological string free energy for elliptic Calabi-Yau threefolds.

Findings

Relation between Riemann-Hilbert problems and topological string free energy.

Identification of Borel summability in the context of Calabi-Yau threefolds.

New mathematical structures connecting Donaldson-Thomas theory and string theory.

Abstract

Let $X$ be a Calabi-Yau threefold with an elliptic fibration. We investigate the non-linear Riemann-Hilbert problems associated to the Donaldson-Thomas theory of fibre classes, and relate them to the Borel sum of the $A$-model topological string free energy for such classes.