An Exact Solution of Induced Large-N Lattice Gauge Theory at Strong Coupling

TL;DR

This paper demonstrates that the strong coupling solution of the Kazakov--Migdal lattice gauge model at large N matches that of a known hermitean one-matrix model, providing an exact analytical solution.

Contribution

It establishes an exact correspondence between the Kazakov--Migdal model and a hermitean one-matrix model at strong coupling for general potentials.

Findings

Strong coupling solution matches hermitean one-matrix model

Derived explicit relation between potentials in the models

Provided proof via loop equations for even potentials

Abstract

I show that the strong coupling solution of the Kazakov--Migdal model with a general interaction potential $V(\Phi)$ in $D$ dimensions coincides at large $N$ with that of the hermitean one-matrix model with the potential $\tilde{V}(\Phi)$: $$ (2D-1)\tilde{V}'= (D-1)V'+ D\sqrt{(V')^2+4(1-2D)\Phi^2}, $$ whose solution is known. The proof is given for an even potential $V(\Phi)=V(-\Phi)$ by solving loop equations.