Resummations and Non-Perturbative Corrections

TL;DR

This paper introduces a generalized Borel resummation method, applies it to large N duality in Chern-Simons theory and topological strings, and uncovers non-perturbative corrections consistent with membrane instanton proposals.

Contribution

It develops a generalized Borel resummation technique and demonstrates its effectiveness in capturing non-perturbative effects in topological string theory.

Findings

Derived a simple integral formula for free energy in large N duality.

Identified non-perturbative corrections matching membrane instanton predictions.

Validated the approach with multiple examples.

Abstract

We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and find a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling gs, we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in gs. Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:1306.1734. Various other examples are also presented.