On the 2D Yang-Mills/Hurwitz Correspondence

TL;DR

This paper demonstrates that in the large N limit, 2D Yang-Mills theory with U(N) gauge group transitions into a mixed Hurwitz theory, with the partition function's expansion involving both classical and monotone Hurwitz contributions.

Contribution

It establishes a novel connection between large N 2D Yang-Mills theory and mixed Hurwitz theory, expanding understanding of gauge theory and enumerative geometry.

Findings

Large N limit of 2D Yang-Mills becomes mixed Hurwitz theory.

Partition function expansion includes classical and monotone Hurwitz contributions.

The correspondence holds for all but finitely many compact orientable spacetimes.

Abstract

In this paper, we show that in the large $N$ limit two-dimensional Yang-Mills theory with $U(N)$ gauge group becomes mixed Hurwitz theory, in the sense that the $1/N$ expansion of the chiral partition function receives contributions from both classical and monotone Hurwitz theory for all but finitely many compact orientable spacetimes.