Three loop renormalization of the SU(N_c) non-abelian Thirring model

TL;DR

This paper performs a detailed three-loop renormalization of the non-abelian Thirring model with SU(N_c) symmetry, addressing evanescent operators and comparing different renormalization schemes to ensure consistency with related models.

Contribution

It provides the first three-loop renormalization of the non-abelian Thirring model, including the treatment of evanescent operators and analysis of model equivalences.

Findings

Established three-loop MSbar renormalization group functions.

Identified non-multiplicative renormalizability of the SU(N_f) Gross Neveu model.

Explicitly computed the renormalization constant for the evanescent operator.

Abstract

We renormalize to three loops a version of the Thirring model where the fermion fields not only lie in the fundamental representation of a non-abelian colour group SU(N_c) but also depend on the number of flavours, N_f. The model is not multiplicatively renormalizable in dimensional regularization due to the generation of evanescent operators which emerge at each loop order. Their effect in the construction of the true wave function, mass and coupling constant renormalization constants is handled by considering the projection technique to a new order. Having constructed the MSbar renormalization group functions we consider other massless independent renormalization schemes to ensure that the renormalization is consistent with the equivalence of the non-abelian Thirring model with other models with a four-fermi interaction. One feature to emerge from the computation is the establishment of the fact that the SU(N_f) Gross Neveu model is not multiplicatively renormalizable in dimensional regularization. An evanescent operator arises first at three loops and we determine its associated renormalization constant explicitly.