The Problem of Large-N Phase Transition in Kazakov-Migdal Model of Induced QCD

We study the lattice gauge model proposed recently by Kazakov and Migdal for inducing QCD. We discuss an extra local Z_N which is a symmetry of the model and propose of how to construct observables. We discuss the role of the large-N phase transition which should occur before the one associated with the continuum limit in order that the model describes continuum QCD. We formulate the mean field approach to study the large-N phase transition for an arbitrary potential and show that no first order phase transition occurs for the quadratic potential.