The String Dual to Two-dimensional Yang-Mills Theory Revisited

TL;DR

This paper revisits the duality between two-dimensional chiral Yang-Mills theory and a deformed Gromov-Witten theory, revealing algebraic structures and geometric interpretations that deepen understanding of string dualities in low dimensions.

Contribution

It introduces a novel algebraic framework and geometric interpretation linking chiral Yang-Mills theory to a deformed Gromov-Witten theory via the Gromov-Witten/Hurwitz correspondence.

Findings

Identifies the algebraic structure as a partial permutation Frobenius algebra.

Interprets the theory as a finite deformation with area-dependent interactions.

Includes an integral over the moduli space of Riemann surfaces and relates closed string states to completed cycles.

Abstract

We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that Riemann surface. Firstly, we argue that the algebraic structure that underlies the large N limit of the chiral gauge theory is a partial permutation Frobenius algebra of observables which codes covering maps of all degrees simultaneously. Secondly, we exploit the Gromov-Witten/Hurwitz correspondence to interpret chiral Yang-Mills theory as a finite deformation of a Gromov-Witten theory by an area-dependent transposition interaction and an operator that codes a compactification of Hurwitz space. The proposed string dual manifestly includes an integral over the moduli space of Riemann surfaces as well as the identification of closed string states as completed cycles.