Large-N Universality of the Two-Dimensional Yang-Mills String

TL;DR

This paper demonstrates that in large N two-dimensional Yang-Mills theory, Wilson loop expectation values are universal across different gauge groups, with implications for understanding phase transitions via string theory reformulation.

Contribution

It proves the gauge-group independence of Wilson loop expectations in large N 2D Yang-Mills theory using a string theory approach, establishing a universal behavior.

Findings

Wilson loop expectations are gauge-group independent at large N

Constructed an isomorphism between string maps for different theories

Indicated a large N phase transition between coupling phases

Abstract

We exhibit the gauge-group independence (``universality'') of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the string theory reformulation of these gauge theories. By constructing an isomorphism between the string maps contributing to normalized Wilson loop expectation values in the different theories, we prove the large N universality of these observables on any surface. The string calculation of the Wilson loop expectation value on the sphere also leads to an indication of the large N phase transition separating strong- and weak-coupling phases.