Renormalisation group flows for gauge theories in axial gauges

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. We discuss the absence of spurious singularities and the finiteness of the flow. It is shown how heat-kernel methods can be used to obtain approximate solutions to the flow and the corresponding Ward identities. New 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 β-function for arbitrary regulator.