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

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 $\tilde{V}(\Phi )$: $$(2D-1){\tilde{V}}^{\prime }=(D-1)V^{\prime }+D\sqrt{(V^{\prime }{)}^2+4(1-2D){\Phi }^2},$$ whose solution is known. The proof is given for an even potential $V(\Phi )=V(-\Phi )$ by solving loop equations.

Comments: Latex (3 Latex figures), 13pp, ITEP-YM-2-93 [minor revising]