Nontriviality of Abelian gauged Nambu–Jona-Lasinio models in four dimensions

We study a particular class of Abelian gauged Nambu--Jona-Lasinio models with global UL(N)×UR(N) symmetry, where N is the number of fermion flavors. We show, by treating the gauge interaction in the ladder approximation and four-fermion interactions in the leading order of the $1/N$ expansion, that the renormalization-group {β} function of the U(1) gauge coupling has ultraviolet stable fixed points for sufficiently large N. This implies the existence of a nontrivial continuum limit.