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

Abstract

We calculate in dimensions $D=2+ε$ 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 $ε\to 0$ 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.