On Exponential corrections to the 1/N expansion in two-dimensional Yang Mills theory

TL;DR

This paper calculates exponential corrections to the 1/N expansion in 2D Yang-Mills theory, revealing non-perturbative effects possibly related to D-strings and fuzzy geometries, thus deepening understanding of non-perturbative phenomena in gauge theories.

Contribution

It introduces explicit calculations of exponential corrections to the 1/N expansion in 2D Yang-Mills, highlighting non-perturbative effects and their geometric interpretations.

Findings

Exponential $e^{-AN}$ corrections are computed.

Mixing between holomorphic and anti-holomorphic sectors is observed.

Non-perturbative terms suggest D-string configurations and fuzzy geometries.

Abstract

We compute $e^{-AN}$ corrections to the Gross-Taylor 1/N expansion of the paritition function of two-dimensional SU(N) and U(N) Yang Mills theory. We find a very similar structure of mixing between holomorphic and anti-holomorphic sectors as that described by Vafa for the 1/N expansion. Some of the non-perturbative terms are suggestive of D-strings wrapping the $T^2$ of the 2dYM but blowing up into a fuzzy geometry by the Myers effect in the directions transverse to the $T^2$.