The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge

TL;DR

This paper computes the five-loop beta function and anomalous dimensions for a general gauge group with fermions, confirming previous results and extending understanding of gauge parameter dependence in high-order quantum field theory calculations.

Contribution

It provides the five-loop beta function for a general gauge group and extends anomalous dimension calculations beyond Feynman gauge, confirming previous all-Nf results.

Findings

Confirmed all-Nf five-loop beta function results.

Derived linear gauge parameter dependence of anomalous dimensions.

Extended renormalization understanding in non-abelian gauge theories.

Abstract

We focus on a non-abelian gauge field coupled to a single (but general) representation of a family of Nf fermions. By using the same machinery that had allowed us to evaluate the sub-leading large-Nf term of the five-loop Beta function earlier, we here report on a confirmation of the all-Nf result that has in the meantime been published by another group. Furthermore, in order to push forward the 5-loop renormalization program regarding gauge parameter dependence, we present the linear terms of the complete set of anomalous dimensions, in an expansion in the covariant gauge parameter around the Feynman gauge.