Wilson Loops in Two-Dimensional Yang-Mills Theories

Abstract

This Ph.D. thesis reaches two main results. The first one is represented by a detailed study, in Feynman gauge, of the perturbative ${\cal O}(g^4)$ contribution to a space-time Wilson loop, with respect to its (expected) Abelian-like time exponentiation when the temporal side goes to infinity. As soon as we are in dimensions greater than two, the expected behavior is found. But if we proceed first to the dimensional limit $D \to 2$, the exponentiation is not recovered. The limits $T \to \infty$ and $D \to 2$ do not commute. The other result is the computation in dimensions $D=2+ε$ and in light-cone gauge with Mandelstam-Leibbrandt prescription of the perturbative ${\cal O}(g^4)$ contribution to the same Wilson loop, 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 light-cone gauge, and provides the expected agreement with the analogous calculation in Feynman gauge. Consequences of these results concerning two and higher-dimensional gauge theories are pointed out.