Field Strength Correlators For 2D Yang-Mills Over Riemann Surfaces

TL;DR

This paper computes topological field strength correlators in 2D Yang-Mills theories on Riemann surfaces using abelianization, revealing phase transitions and applications to Wilson loops.

Contribution

It introduces a method to compute correlators via abelianization, highlighting topological obstructions and phase transitions in the large N limit.

Findings

Correlators are topological and nontrivial due to obstructions.

Second order phase transitions occur at critical points on the sphere.

Results apply to contractible Wilson loop computations.

Abstract

The path integral computation of field strength correlation functions for two dimensional Yang-Mills theories over Riemann surfaces is studied. The calculation is carried out by abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.