Large-N Reduction, Master Field and Loop Equations in Kazakov-Migdal Model

I study the large-N reduction a la Eguchi--Kawai in the Kazakov--Migdal lattice gauge model. I show that both quenching and twisting prescriptions lead to the coordinate-independent master field. I discuss properties of loop averages in reduced as well as unreduced models and demonstrate those coincide in the large mass expansion. I derive loop equations for the Kazakov--Migdal model at large N and show they are reduced for the quadratic potential to a closed set of two equations. I find an exact strong coupling solution of these equations for any D and extend the result to a more general interacting potential.Comment: 17 pages (1 Latex figure), ITEP-YM-6-92 The figure is replaced by printable on

Critical Scaling and Continuum Limits in the D>1 Kazakov-Migdal Model

I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find critical lines associated with gamma_{string}=-1/2 and gamma_{string}=0 as well as a tri-critical point associated with a Kosterlitz-Thouless phase transition. The continuum theories are constructed expanding around the critical points. The one associated with gamma_{string}=0 coincides with the standard d=1 string while the Kosterlitz-Thouless phase transition separates it from that with gamma_{string}=-1/2 which is indistinguishable from pure 2D gravity for local observables but has a continuum limit for correlators of extended Wilson loops at large distances due to a singular behavior of the Itzykson-Zuber correlator of the gauge fields. I reexamine the KM model with an arbitrary potential in the large-D limit and show that it reduces at large N to a one-matrix model whose potential is determined self-consistently. A relation with discretized random surfaces is established via the gauged Potts model which is equivalent to the KM model at large N providing the coordination numbers coincide.Comment: 45pp., Latex, YM-4-9

Adjoint Fermions Induce QCD

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 Kazakov--Migdal model with the quadratic potential. We discuss the possibility for the adjoint fermion model to be solvable at N_c=\infty in the weak coupling region where the Wilson loops obey normal area law.Comment: 16 pages (1 Latex figure), ITEP-YM-7-92 (signs revised