The non-abelian Coulomb phase of the gauged vector model at large N Original Research Article

The renormalization group flows of the coupling constants for the gauged U(N) vector model, with Nf massless fermions in the defining representation, are studied in the large N limit, to all orders in the scalar coupling λ, leading order in 1/N, and lowest two orders in the gauge coupling g2. It is shown that the restrictions of asymptotic freedom, and the reality of the coupling constants throughout the flows, places important restrictions on Nf/N. For the case with massless mesons, these conditions are sufficiently restrictive to imply the existence of an infrared fixed point (g∗, λ∗) 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 g2) breakdown of chiral symmetry are presented.