The SU(N) Wilson Loop Average in 2 Dimensions

TL;DR

This paper provides explicit solutions for the Wilson loop averages in two-dimensional SU(N) gauge theories, extending known results to arbitrary contours and manifolds of genus zero, enhancing understanding of gauge invariants in 2D.

Contribution

It offers explicit solutions to the loop equations for SU(N) Wilson loops on 2D manifolds, generalizing previous results to arbitrary contours and topologies.

Findings

Explicit solution for SU(2) Wilson loop on 2D plane.

Generalization to SU(N) for arbitrary contours.

Extension to any 2D manifold of genus 0.

Abstract

We solve explicitly a closed, linear loop equation for the SU(2) Wilson loop average on a two-dimensional plane and generalize the solution to the case of the SU(N) Wilson loop average with an arbitrary closed contour. Furthermore, the flat space solution is generalized to any two-dimensional manifold for the SU(2) Wilson loop average and to any two-dimensional manifold of genus 0 for the SU(N) Wilson loop average.