NONTRIVIALITY OF GAUGE-HIGGS-YUKAWA SYSTEM AND RENORMALIZABILITY OF GAUGED NJL MODEL

In the leading order of a modified 1/N-c expansion, we show that a cla ss of gauge-Higgs-Yukawa systems in four dimensions give non-trivial a nd well-defined theories in the continuum limit. The renormalized Yuka wa coupling gamma and the quartic scalar coupling lambda have to lie o n a certain line in the (gamma, lambda) plane and the line terminates at an upper bound. The gauged Nambu-Jona-Lasinio (NJL) model in the li mit of its ultraviolet cutoff going to infinity, is shown to become eq uivalent to the gauge-Higgs-Yukawa system with the coupling constants just on that terminating point. This proves the renormalizability of t he gauged NJL moder in four dimensions. The effective potential for th e gauged NJL model is calculated by using renormalization group techni que and confirmed to be consistent with the previous result by Kondo, Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation .