Discontinuous behavior of perturbative Yang-Mills theories in the limit of dimensions D->2

TL;DR

This paper investigates the behavior of perturbative Yang-Mills theories as the spacetime dimension approaches two, revealing finite results for Wilson loops in light-cone gauge despite the vanishing of certain vertices.

Contribution

It provides a detailed perturbative calculation of Wilson loops in D=2+ε dimensions, highlighting discontinuous behavior as D approaches 2 and comparing light-cone and Feynman gauges.

Findings

Finite Wilson loop results as ε approaches 0

Discontinuous behavior of Yang-Mills theories at D=2

Agreement between light-cone and Feynman gauge calculations

Abstract

We calculate in dimensions $D=2+\epsilon$ and in light-cone gauge (LCG) the perturbative ${\cal O}(g^4)$ contribution to a rectangular Wilson loop in the (t,x)-plane coming from diagrams with a self-energy correction in the vector propagator. In the limit $\epsilon \to 0$ the result is finite, in spite of the vanishing of the triple vector vertex in LCG, and provides the expected agreement with the analogous calculation in Feynman gauge.