Study of Wilson loop functionals in 2D Yang-Mills theories

TL;DR

This paper derives explicit formulas for Wilson loop expectation values in 2D Yang-Mills theories on various manifolds, analyzing contributions from invariant connections and monopoles in both continuum and lattice frameworks.

Contribution

It provides a general explicit formula for Wilson loop expectations in 2D Yang-Mills theories on arbitrary manifolds, including analysis of invariant connection contributions.

Findings

Explicit formulas for Wilson loop expectations on arbitrary manifolds.

Identification of invariant connection contributions similar to monopoles.

Comparison between continuum and lattice formulations.

Abstract

The derivation of the explicit formula for the vacuum expectation value of the Wilson loop functional for an arbitrary gauge group on an arbitrary orientable two-dimensional manifold is considered both in the continuum case and on the lattice. A contribution to this quantity, coming from the space of invariant connections, is also analyzed and is shown to be similar to the contribution of monopoles.