BPS Wall Crossing and Topological Strings

TL;DR

This paper connects BPS state counting in N=2 gauge theories with topological string theory, demonstrating how wall crossing phenomena and spin content are naturally explained through dualities and geometric constructions.

Contribution

It provides a geometric and string-theoretic framework that explains the Kontsevich-Soibelman wall crossing conjecture and its refinement for BPS states.

Findings

Wall crossing is derived from topological string computations.

Spin content of BPS states is incorporated via a refined conjecture.

Chern-Simons theory and twistorial methods are essential tools.

Abstract

By embedding N=2 gauge theories in string theory and utilizing string dualities we map the counting of BPS states with arbitrary electric and magnetic charges to computations of an A-model topological string on an associated geometry constructed from the data of the SW curve. We show how the conjecture of Kontsevich and Soibelman regarding wall crossing, as well as a more refined version which captures the spin content of BPS states, is a natural consequence. Chern-Simons theory realized on A-branes and a twistorial construction play key roles.