The String Calculation of Wilson Loops in Two-Dimensional Yang-Mills Theory

TL;DR

This paper shows that Wilson loop expectation values in two-dimensional Yang-Mills theory can be understood as a sum over surface covers, resembling an open string theory expansion, linking gauge theory and string theory concepts.

Contribution

It provides a natural string-theoretic description of Wilson loop expectations in SO(N) and Sp(N) Yang-Mills theories on various surfaces, connecting to branched cover classifications.

Findings

Large-N expansion expressed as a sum over surface covers

Connection established between gauge theory and open string theory

Comparison with QCD_2 chiral sectors enhances understanding

Abstract

We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum takes the form of the perturbative expansion of an open string theory. The derivation makes contact with the classification of branched covers by Gabai and Kazez. Comparison with the analogous results for the chiral sectors of QCD_2 is instructive for both cases.