Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions

TL;DR

This paper computes a light-like Wilson loop in 1+1 dimensional Yang--Mills theory, demonstrating gauge invariance and revealing that the theory is not free, contrary to common beliefs, with implications for understanding gauge invariance and topological effects.

Contribution

It provides a perturbative calculation of a light-like Wilson loop in 1+1D Yang--Mills theory, showing gauge invariance and challenging the notion that the theory is free.

Findings

Finite gauge-invariant result obtained

Does not exhibit abelian exponentiation

Contradicts the belief that the theory is free

Abstract

A light-like Wilson loop is computed in perturbation theory up to ${\cal O} (g^4)$ for pure Yang--Mills theory in 1+1 dimensions, using Feynman and light--cone gauges to check its gauge invariance. After dimensional regularization in intermediate steps, a finite gauge invariant result is obtained, which however does not exhibit abelian exponentiation. Our result is at variance with the common belief that pure Yang--Mills theory is free in 1+1 dimensions, apart perhaps from topological effects.