Non-perturbative topological strings from resurgence

TL;DR

This paper develops a non-perturbative formulation of topological string theory on Calabi-Yau threefolds using resurgence techniques, expressing the partition function as a product of Borel sums and analyzing Stokes phenomena.

Contribution

It provides a novel non-perturbative expression for topological string partition functions in the holomorphic limit, connecting them to resolved conifold invariants and resurgence theory.

Findings

Partition function expressed as a product over resolved conifold functions.

Derived Borel sums and Stokes jumps for the asymptotic series.

Non-perturbative corrections depend only on genus zero Gopakumar-Vafa invariants.

Abstract

The partition function of topological string theory on any family of Calabi-Yau threefolds is defined perturbatively as an asymptotic series in the topological string coupling and encodes, in a holomorphic limit, higher genus Gromov-Witten as well as Gopakumar-Vafa invariants. We prove that the partition function of topological strings of any CY in this limit can be written as a product, where each factor is given by the partition function of the resolved conifold with shifted arguments, raised to the power of certain sheaf invariants. We use this result to put forward an expression for the non-perturbative topological string partition function in this limit, as a product over analytic functions in the topological string coupling which correspond to the Borel sums for the resolved conifold found previously. We furthermore find an expression for the Borel transform of the full asymptotic series in this limit expressed in terms of the sheaf invariants. We use this to define the Borel sums and compute the corresponding Stokes jumps which constitute non-perturbative corrections to the partition function. The jumps depend only on genus zero GV invariants and their sum can be expressed entirely in terms of a single function which is introduced as a deformation of the prepotential.