Non-perturbative effects and wall-crossing from topological strings

TL;DR

This paper demonstrates how topological string theory can be used to compute and resum non-perturbative brane instanton effects in type II Calabi-Yau compactifications, revealing their continuity across BPS stability lines.

Contribution

It establishes a connection between topological strings and non-perturbative effects, including brane instantons, and explores their behavior under wall-crossing and in various compactification scenarios.

Findings

Topological string encodes non-perturbative D-brane instanton corrections.

Wall-crossing effects are consistent with topological string predictions.

Mirror matrix models relate instantons to non-perturbative effects.

Abstract

We argue that the Gopakumar-Vafa interpretation of the topological string partition function can be used to compute and resum certain non-perturbative brane instanton effects of type II CY compactifications. In particular the topological string A-model encodes the non-perturbative corrections to the hypermultiplet moduli space metric from general D1/D(-1)-brane instantons in 4d N=2 IIB models. We also discuss the reduction to 4d N=1 by fluxes and/or orientifolds and/or D-branes, and the prospects to resum brane instanton contributions to non-perturbative superpotentials. We argue that the connection between non-perturbative effects and the topological string underlies the continuity of non-perturbative effects across lines of BPS stability. We also confirm this statement in mirror B-model matrix model examples, relating matrix model instantons to non-perturbative D-brane instantons. The computation of non-perturbative effects from the topological string requires a 3d circle compactification and T-duality, relating effects from particles and instantons, reminiscent of that involved in the physical derivation of the Kontsevich-Soibelmann wall-crossing formula.