Four loop wave function renormalization in the non-abelian Thirring model

TL;DR

This paper calculates the four-loop anomalous dimension of fermions in the non-abelian Thirring model, revealing new group-theoretic structures and discussing implications for related conformal field theories.

Contribution

It provides the first four-loop computation of the fermion anomalous dimension in the non-abelian Thirring model, including the effects of evanescent operators and scheme adjustments.

Findings

Appearance of a new colour group Casimir, d_F^{abcd} d_F^{abcd.

Loss of multiplicative renormalizability due to evanescent operators.

Restoration of Fierz symmetry through scheme changes.

Abstract

We compute the anomalous dimension of the fermion field with N_f flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Green's function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, d_F^{abcd} d_F^{abcd}, in the final four loop result and discuss its consequences for the relation of the Knizhnik-Zamolodchikov critical exponents in the Wess Zumino Witten Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored.