Auxiliary Field Method in 4- and 3- dimensional Nambu--Jona-Lasinio Models

TL;DR

This paper evaluates the auxiliary field method in Nambu--Jona-Lasinio models across 3 and 4 dimensions by analyzing quantum effects on the gap equation, revealing conditions for chiral symmetry breaking and restoration.

Contribution

It demonstrates the validity of the auxiliary field method at the one-loop level in Nambu--Jona-Lasinio models with finite N, including the effects of quantum corrections on chiral symmetry.

Findings

Quantum effects can restore chiral symmetry at large coupling in 3 and 4 dimensions.

Chiral symmetry breaking is enhanced at small coupling in 3 dimensions.

An intrinsic fermion mass helps justify the loop expansion by avoiding infrared divergences.

Abstract

In order to check the validity of auxiliary field method in the Nambu--Jona-Lasinio model, the one-loop (=quantum) effects of auxiliary fields to the gap equation are considered with N-component fermion models in 4 and 3 dimensions. N is not assumed so large but regarded as a loop expansion parameter. To overcome infrared divergences caused by the Nambu-Goldstone bosons, an intrinsic fermion mass is assumed. It is shown that the loop expansion can be justified by this intrinsic mass whose lower limit is also given. It is found that due to quantum effects, chiral symmetry breaking ($\chi$SB) is restored in D=4 and D=3 when the four-Fermi coupling is large. However, $\chi$SB is enhanced in a small coupling region in D=3.