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