Renormalisation group flows for gauge theories in axial gauges

TL;DR

This paper explores the use of Exact Renormalisation Group flows in axial gauges for gauge theories, introducing a novel background field approach and employing heat-kernel methods to derive key theoretical results.

Contribution

It presents a new approach to gauge theories in axial gauges using a background field in the infrared regulator, with novel expansion schemes and derivation of the one-loop effective action and beta-function.

Findings

Derived the one-loop effective action for covariantly constant fields

Calculated the one-loop beta-function for arbitrary regulators

Developed heat-kernel methods for approximate solutions in axial gauges

Abstract

Gauge theories in axial gauges are studied using Exact Renormalisation Group flows. We introduce a background field in the infrared regulator, but not in the gauge fixing, in contrast to the usual background field gauge. It is shown how heat-kernel methods can be used to obtain approximate solutions to the flow and the corresponding Ward identities. Expansion schemes are discussed, which are not applicable in covariant gauges. As an application, we derive the one-loop effective action for covariantly constant field strength, and the one-loop beta-function for arbitrary regulator.