Large-N Reduction, Master Field and Loop Equations in Kazakov-Migdal Model

TL;DR

This paper investigates the large-N reduction in the Kazakov-Migdal model, deriving loop equations and solutions, demonstrating the equivalence of reduced and unreduced models in certain regimes, and extending solutions to general potentials.

Contribution

It derives loop equations for the Kazakov-Migdal model at large N and finds exact solutions, advancing understanding of large-N reduction and master fields in lattice gauge theories.

Findings

Loop equations reduce to two equations for quadratic potentials.

Exact strong coupling solutions are obtained for any dimension D.

Reduced and unreduced models' loop averages coincide in the large mass expansion.

Abstract

I study the large-N reduction a la Eguchi--Kawai in the Kazakov--Migdal lattice gauge model. I show that both quenching and twisting prescriptions lead to the coordinate-independent master field. I discuss properties of loop averages in reduced as well as unreduced models and demonstrate those coincide in the large mass expansion. I derive loop equations for the Kazakov--Migdal model at large N and show they are reduced for the quadratic potential to a closed set of two equations. I find an exact strong coupling solution of these equations for any D and extend the result to a more general interacting potential.