Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials

TL;DR

This paper analyzes a special double scaling limit of large N two-dimensional Yang-Mills theory on a torus, revealing exact relations to Hurwitz numbers, moduli spaces of holomorphic differentials, and string theory.

Contribution

It introduces a novel double scaling limit that isolates the chiral sector and connects gauge theory coefficients to volumes of moduli spaces of holomorphic differentials.

Findings

Exact strong-coupling expansion derived

Hurwitz numbers computed from gauge theory

Volumes of moduli spaces shown to coincide with gauge theory coefficients

Abstract

We describe and solve a double scaling limit of large N Yang-Mills theory on a two-dimensional torus. We find the exact strong-coupling expansion in this limit and describe its relation to the conventional Gross-Taylor series. The limit retains only the chiral sector of the full gauge theory and the coefficients of the expansion determine the asymptotic Hurwitz numbers, in the limit of infinite winding number, for simple branched coverings of a torus. These numbers are computed exactly from the gauge theory vacuum amplitude and shown to coincide with the volumes of the principal moduli spaces of holomorphic differentials. The string theory interpretation of the double scaling limit is also described.