Functional equation for pure Yang–Mills Wilson-loop two-point correlator from Schwinger–Dyson equations

Abstract

The physics of pure Yang–Mills can be described gauge-invariantly using n-point functions of Wilson loops. These n-point functions must obey functional Schwinger–Dyson equations, which highly simplify in the limit of large number of colors N. These equations have remained unsolved for several decades (except for trivial spacetimes).In this paper, I study the Schwinger–Dyson equations for the Wilson-loop two-point function in large-N U(N) pure Yang–Mills theory with a lattice regulator. I recast the equation in a form that makes it suitable for extraction of the Wilson-loop propagator (and thus the large-N glueball spectrum) using path integral techniques.