On the 2D Yang-Mills/Hurwitz Correspondence

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 $1\mathrm{/}N$ expansion of the chiral partition function receives contributions from both classical and monotone Hurwitz theory for all but finitely many compact orientable spacetimes.