Resurgence analysis of 2d Yang-Mills theory on a torus

TL;DR

This paper analyzes the large N expansion of 2D Yang-Mills theory on a torus, revealing non-perturbative effects via resurgence and connecting them to fermionic systems, highlighting the non-Borel summability of the series.

Contribution

It introduces a novel resurgence analysis of the 2D Yang-Mills partition function, including a modified recursion relation and a different analytic continuation approach.

Findings

Genus expansion is not Borel summable.

Non-perturbative corrections are linked to fermionic system continuations.

The Stokes parameter is purely imaginary.

Abstract

We study the large $N$ 't Hooft expansion of the partition function of 2d $U(N)$ Yang-Mills theory on a torus. We compute the $1/N$ genus expansion of both the chiral and the full partition function of 2d Yang-Mills using the recursion relation found by Kaneko and Zagier with a slight modification. Then we study the large order behavior of this genus expansion, from which we extract the non-perturbative correction using the resurgence relation. It turns out that the genus expansion is not Borel summable and the coefficient of 1-instanton correction, the so-called Stokes parameter, is pure imaginary. We find that the non-perturbative correction obtained from the resurgence is reproduced from a certain analytic continuation of the grand partition function of a system of non-relativistic fermions on a circle. Our analytic continuation is different from that considered in hep-th/0504221.