Mellin-Barnes Representation of the Topological String

TL;DR

This paper uses Mellin-Barnes integrals to analytically continue topological string free energy, revealing non-perturbative effects and confirming related conjectures at tree-level.

Contribution

It introduces a Mellin-Barnes integral approach for analytic continuation of topological string free energy, uncovering non-perturbative terms and validating existing conjectures.

Findings

Identification of non-perturbative contributions

Confirmation of conjectures at tree-level

Extension to refined and Nekrasov-Shatashvili limits

Abstract

We invoke integrals of Mellin-Barnes type to analytically continue the Gopakumar-Vafa resummation of the topological string free energy in the string coupling constant, leading to additional non-perturbative terms. We also discuss in a similar manner the refined and Nekrasov-Shatashvili limit version thereof. The derivation is straight-forward and essentially boils down to taking residue. This allows us to confirm some related conjectures in the literature at tree-level.