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In the leading order of a modified 1/Nc expansion, we show that a class ofgauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-definedtheories in the continuum limit. The renormalized Yukawa coupling y and thequartic scalar coupling \lambda have to lie on a certain line in the(y,\lambda) plane and the line terminates at an upper bound. The gaugedNambu--Jona-Lasinio (NJL) model in the limit of its ultraviolet cutoff going toinfinity, is shown to become equivalent to the gauge-Higgs-Yukawa system withthe coupling constants just on that terminating point. This proves therenormalizability of the gauged NJL model in four dimensions. The effectivepotential for the gauged NJL model is calculated by using renormalization grouptechnique and confirmed to be consistent with the previous result by Kondo,Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation.Comment: 32 pages, LaTeX, 3 Postscript Figures are included as uuencoded files  (need `epsf.tex'), KUNS-1278, HE(TH) 94/10 / NIIG-DP-94-2. (Several  corrections in the introduction and references.

Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged NJL Model