The Non-Abelian Coulomb Phase of the Gauged Vector Model at Large N

The renormalization group flows of the coupling constants for the gauged U(N) vector model, with N_f massless fermions in the defining representation, are studied in the large N limit, to all orders in the scalar coupling lambda, leading order in 1/N, and lowest two orders in the gauge coupling g^2. It is shown that the restrictions of asymptotic freedom, and the reality of the coupling constants throughout the flows, places important restrictions on N_f/N. For the case with massless mesons, these conditions are sufficiently restrictive to imply the existence of an infrared fixed-point (g_*,lambda_*) in both couplings. Thus, the consistent massless theory is scale invariant, and in a non-abelian Coulomb phase. The case of massive mesons, and of spontaneously broken symmetry is also discussed, with similar, but not identical, conclusions. Speculations related to the possibility that there is a non-perturbative (in g^2) breakdown of chiral symmetry are presented.