Correlators of the Kazakov-Migdal Model

TL;DR

This paper derives and solves loop equations for one-link correlators in the Kazakov-Migdal model, providing explicit solutions for Gaussian potentials and reducing non-Gaussian cases to algebraic equations.

Contribution

It introduces explicit loop equations for the model's correlators and solves them for Gaussian potentials, extending to non-Gaussian cases.

Findings

Explicit solutions for Gaussian potential case

Reduction of non-Gaussian cases to algebraic equations

Loop equations analogous to Hermitean two-matrix model

Abstract

We derive loop equations for the one-link correlators of gauge and scalar fields in the Kazakov-Migdal model. These equations determine the solution of the model in the large N limit and are similar to analogous equations for the Hermitean two-matrix model. We give an explicit solution of the equations for the case of a Gaussian, quadratic potential. We also show how similar calculations in a non-Gaussian case reduce to purely algebraic equations.