Non-perturbative effects and the refined topological string

TL;DR

This paper demonstrates that non-perturbative membrane instanton effects in ABJM theory are fully determined by the refined topological string on local P1xP1, providing a first-principles derivation of these effects and proposing a general non-perturbative free energy framework.

Contribution

It establishes a direct link between membrane instanton corrections in ABJM theory and the refined topological string on local P1xP1, offering a novel derivation and a general proposal for non-perturbative topological string free energy.

Findings

Membrane instanton series are determined by the refined topological string.

Provides a first-principles derivation of non-perturbative effects.

Proposes a general non-perturbative free energy for local Calabi-Yau manifolds.

Abstract

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.