QCD ON A TREE

Abstract

We propose a model which can be regarded as a mean field approximation for pure lattice QCD and chiral field. It always possesses a phase transition between a strong-coupling phase (where it reduces to a one-plaquette integral) and a nontrivial weak-coupling one. For the U(N) gauge group, it is equivalent to some hermitian multi-matrix model. This analogy allows us to determine possible large-N critical regimes thus generalizing the Gross-Witten phase transition in the one-plaquette model.