Perturbative renormalisation of the chiral Gross-Neveu model

TL;DR

This paper investigates the renormalization of the chiral Gross-Neveu model with Wilson fermions, highlighting the need to tune multiple parameters to restore chiral symmetry in the continuum limit.

Contribution

It introduces a perturbative approach to fixing parameters in the chiral Gross-Neveu model, accounting for chirally non-invariant terms, and confirms results in the infinite flavor limit.

Findings

Bare mass and coupling constants must be tuned for chiral symmetry restoration.

Perturbative calculations agree with the infinite flavor limit.

Strategy outlined for parameter fixing in lattice simulations.

Abstract

We study the chiral Gross-Neveu model with Wilson fermions. In the framework of the Schroedinger functional we show that in general not only the bare mass has to be tuned to achieve chiral symmetry in the continuum, but also coupling constants multiplying chirally non-invariant four fermion terms. The strategy for fixing the parameters of the theory is explained in perturbation theory and the results of a first order calculation are presented. The results are shown to agree with the infinite flavour limit.