Resurgent structure of 2d Yang-Mills theory on a torus

TL;DR

This paper investigates the resurgent structure of the topological string dual to 2d U(N) Yang-Mills on a torus, deriving formulas for instanton amplitudes and proposing a non-perturbative partition function that includes all instanton contributions.

Contribution

It provides closed-form formulas for instanton amplitudes at all orders and introduces a non-perturbative partition function incorporating all real instantons, advancing understanding of non-perturbative effects in 2d Yang-Mills.

Findings

Derived formulas for instanton amplitudes up to high orders

Proposed a real, non-perturbative partition function including all real instantons

Identified infinite towers of complex instantons potentially related to BPS states

Abstract

We study the resurgent structure of the topological string dual to 2d $U(N)$ Yang-Mills on torus. We find closed form formulas for instanton amplitudes up to arbitrarily high instanton orders, based on which we propose the non-perturbative partition function including contributions from all the real instantons, which is real for positive modulus and string coupling. We also explore complex instantons and find two infinite towers of them. We expect them to correspond to BPS states in type II string.