Non-Perturbative Renormalization Group and Renormalizability of Gauged NJL Model

Abstract

Non-perturbative renormalizability, or non-triviality, of the gauged Nambu-Jona-Lasinio (NJL) model in four dimensions is examined by using the non-perturbative (exact) renormalization group in the large N c limit. When the running of the gauge coupling is asymptotically free and sufficiently slow, the two-dimensional renormalized trajectory (subspace) spanned by the four-fermi coupling and the gauge coupling is found to exist. This implies renormalizability of the gauged NJL model. In the case of a fixed gauge coupling, renormalizability of the model turns out to be guaranteed by the line of UV fixed points. We also discuss non-triviality of the gauged NJL model extended to include higher-dimensional operators and correspondence with the gauge-Higgs-Yukawa system. * ) Non-linear sigma models in less than four dimensions also are known as non-perturbatively renormalizable models with similar structure. 5)