THE GAUGED VECTOR MODEL IN 4 DIMENSIONS - RESOLUTION OF AN OLD PROBLEM

A calculation of the renormalization group improved effective potentia l for the gauged U(N) vector model, coupled to N-f fermions in the fun damental representation, computed to leading order in 1/N, all orders in the scalar self-coupling lambda, and lowest order in gauge coupling g(2), with N-f 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 < lambda/g(2) < 4/3[ (N-f/N)-1], and N-f/N < 11/2. In the asymptotically free phase, the ef fective potential behaves qualitatively like the tree-level potential. In the other phase, the theory exhibits all the difficulties of the u ngauged (g(2) = 0) vector model. Therefore the theory appears to be co nsistent (only) in the asymptotically free phase. (C) 1998 Published b y Elsevier Science B.V.