The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form

TL;DR

This paper computes the 4-loop beta-function for the 2D Non-Abelian Thirring model and finds discrepancies with the conjectured exact beta-function, challenging its validity across classical groups.

Contribution

It provides an explicit 4-loop calculation of the beta-function for classical groups and tests the conjectured exact form, revealing inconsistencies.

Findings

Discovered a 4-loop contribution incompatible with the conjectured beta-function.

Identified a higher-order group-theoretical invariant affecting the beta-function.

Challenged the validity of the proposed exact beta-function for classical groups.

Abstract

Recently, B. Gerganov, A. LeClair and M. Moriconi [Phys. Rev. Lett. 86 (2001) 4753] have proposed an "exact" (all orders) beta-function for 2-dimensional conformal field theories with Kac-Moody current-algebra symmetry at any level k, based on a Lie group G, which are perturbed by a current-current interaction. This theory is also known as the Non-Abelian Thirring model. We check this conjecture with an explicit calculation of the beta-function to 4-loop order, for the classical groups G= SU(N), SO(N) and SP(N). We find a contribution at 4-loop order, proportional to a higher-order group-theoretical invariant, which is incompatible with the proposed beta-function in all possible regularization schemes.