Nonperturbative Renormalization Group and Renormalizability of Gauged NJL Model

TL;DR

This paper investigates the non-perturbative renormalizability of the gauged NJL model in four dimensions using the exact renormalization group, demonstrating conditions under which the model remains renormalizable and discussing extensions.

Contribution

It provides a non-perturbative analysis of the gauged NJL model's renormalizability, including the existence of renormalized trajectories and fixed points, extending previous perturbative studies.

Findings

Existence of a two-dimensional renormalized trajectory for certain gauge couplings.

Renormalizability guaranteed by UV fixed points in fixed gauge coupling scenarios.

Extension to higher-dimensional operators and relation to gauge-Higgs-Yukawa systems.

Abstract

Non-perturbative renormalizability, or non-triviality, of the gauged Nambu-Jona-Lasinio (NJL) model in four dimensions is examined by using non-perturbative (exact) renormalization group in large $N_c$ limit. When running of the gauge coupling is asymptotically free and slow enough, the two dimensional renormalized trajectory (subspace) spanned by the four fermi coupling and the gauge coupling is found to exist, which implies renormalizability of the gauged NJL model. In the case of fixed gauge coupling, renormalizability of the model turns out to be guaranteed by the line of the UV fixed points. We discuss also non-triviality of the gauged NJL model extended to include higher dimensional operators and correspondence with the gauge-Higgs-Yukawa system.