Functional Equation for Pure Yang–Mills Wilson-loop Two-Point Correlator from Schwinger–Dyson Equations

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.