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

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.