Gauge theory, topological strings, and S-duality

TL;DR

This paper derives a duality between topological gauge theory and the A-model on Calabi-Yau 3-folds using S-duality, and explores related mirror dualities involving B-models and Little String Theory.

Contribution

It provides a derivation of a conjectured duality between topological gauge theory and the A-model from string theory principles.

Findings

Duality between topological U(1) gauge theory and A-model established

S-duality of IIB string theory underpins the duality derivation

Mirror duality relates B-model and Little String Theory sectors

Abstract

We offer a derivation of the duality between the topological U(1) gauge theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold. This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa. We deduce it from the S-duality of the IIB superstring. We also argue that the mirror version of this duality relates the topological B-model on a Calabi-Yau 3-fold and a topological sector of the Type IIA Little String Theory on the same manifold.