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

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.

final version to appear in Int. Jour. Mod. Phys. A, minor corrections, added a few comments on Wilson loops and non-abelian Stokes theorem