Application of Non-Perturbative Renormalization Group to Nambu-Jona-Lasinio/Gross-Neveu model at Finite Temperature and Chemical Potential

TL;DR

This paper applies the Non-Perturbative Renormalization Group to study the phase structure of the Nambu-Jona-Lasinio/Gross-Neveu model at finite temperature and chemical potential, incorporating mesonic fluctuations and analyzing N_c dependence.

Contribution

It extends NPRG analysis of the NJL/Gross-Neveu model by including mesonic fluctuations and exploring N_c dependence beyond leading order.

Findings

NPRG results match Schwinger-Dyson equations at large cutoff.

Inclusion of mesonic fluctuations affects the phase diagram.

N_c dependence of the chiral phase structure is characterized.

Abstract

The chiral phase structure of the Nambu-Jona-Lasinio/Gross-Neveu model at finite temperature T and finite chemical potential \mu is investigated using (Wilsonian) Non-Perturbative Renormalization Group (NPRG). In the large N_c limit, the solutions of NPRG with various cutoff schemes are shown. For a sufficiently large ultra-violet cutoff, NPRG results coincide with those of Schwinger-Dyson equation and have little cutoff scheme dependence. Next, to improve the approximation, we incorporate the mesonic fluctuations. We introduce the auxiliary fields for mesons, and then derive NPRG equation for finite N_c. The chiral phase structure on (T,\mu) plane beyond the leading of 1/N_c expansion is investigated in the sharp cutoff limit. N_c dependence of chiral phase diagram is obtained.