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

TL;DR

This paper investigates Abelian gauged Nambu-Jona-Lasinio models with a focus on their renormalization-group behavior, revealing ultraviolet stable fixed points and the potential for a nontrivial continuum limit in four dimensions.

Contribution

It demonstrates the existence of ultraviolet stable fixed points in Abelian gauged Nambu-Jona-Lasinio models using ladder approximation and 1/N expansion, indicating a nontrivial continuum limit.

Findings

Ultraviolet stable fixed points exist for large N.

The models admit a nontrivial continuum limit.

Renormalization-group beta function analysis supports these results.

Abstract

We study a particular class of Abelian gauged Nambu-Jona-Lasinio models with global U_L(N)xU_R(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 beta 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.