The gauged vector model in four dimensions: Resolution of an old problem? Original Research Article

A calculation of the renormalization group improved effective potential for the gauged U(N) vector model, coupled to Nf fermions in the fundamental representation, computed to leading order in 1N, all orders in the scalar self-coupling λ, and lowest order in gauge coupling g2, with Nf of order N, is presented. It is shown that the theory has two phases, one of which is asymptotically free, and the other not, where the asymptotically free phase occurs if 0 < λ/g2 < 43[(Nf/N) − 1], and Nf/N < 112. In the asymptotically free phase, the effective potential behaves qualitatively like the tree-level potential. In the other phase, the theory exhibits all the difficulties of the ungauged (g2 = 0) vector model. Therefore the theory appears to be consistent (only) in the asymptotically free phase.