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.
We propose to induce QCD by fermions in the adjoint representation of the gauge group SU (N c ) on the lattice. We consider various types of lattice fermions: chiral, Kogut-Susskind and Wilson ones. Using the mean field method we show that a first order large-N phase transition occurs with decreasing fermion mass. We conclude, therefore, that adjoint fermions induce QCD. We draw the same conclusion for the adjoint scalar or fermion models at large number of flavors N f when they induce a single-plaquette lattice gauge theory. We find an exact strong coupling solution for the adjoint fermion model and show it is quite similar to that for the KazakovMigdal model with the quadratic potential. We discuss the possibility for the adjoint fermion model to be solvable as N c → ∞ in the weak coupling region where the Wilson loops obey normal area law.
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