String Theoretical Interpretation for Finite N Yang-Mills Theory in Two-Dimensions

TL;DR

This paper explores the string theory interpretation of two-dimensional SU(N) Yang-Mills theory at finite N, revealing a sector related to covering maps and discussing non-perturbative corrections to the expansion.

Contribution

It establishes a finite N string-theoretic interpretation of 2D Yang-Mills theory, extending the large N results to finite N and analyzing non-perturbative effects.

Findings

Identifies a sector as a sum of covering maps with covering number less than N

Provides an asymptotic 1/N expansion matching the large N chiral sector

Discusses non-perturbative corrections to the perturbative expansion

Abstract

We discuss the equivalence between a string theory and the two-dimensional Yang-Mills theory with SU(N) gauge group for finite N. We find a sector which can be interpreted as a sum of covering maps from closed string world-sheets to the target space, whose covering number is less than N. This gives an asymptotic expansion of 1/N whose large N limit becomes the chiral sector defined by D.Gross and W.Taylor. We also discuss that the residual part of the partition function provides the non-perturbative corrections to the perturbative expansion.