Gauge theory, topological strings, and S-duality

TL;DR

The paper addresses a deep nonperturbative link between the all-genus A-model topological string on a Calabi–Yau 3-fold and a topological $U(1)$ gauge theory by deriving the duality from Type IIB S-duality. Through a chain of dualities starting with a D5-brane instanton on $X$, the authors map the problem to Type IIA on Taub–NUT, where gravitational F-terms are controlled by the A-model free energies $F_g$, yielding a precise correspondence between the gauge-theory partition function and the all-genus A-model partition function with $\tilde{\omega}=g_s^{-1}\omega$ in the appropriate limit. They show that the genus-$g$ contributions satisfy $R_g=(-1)^{g-1} F_g$ (and $\theta_0=\pi$ for certain cases), providing an all-genus equivalence and a parameter map that makes the duality nonperturbatively exact. The discussion also connects to mirror symmetry and Little String Theory, suggesting a B-model/LST duality via DVV and NOV, and highlights future directions for understanding RR flux effects and nonperturbative membranes in this framework.

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.