I will discuss a new renormalisation group flow equation based on a gauge invariant regularisation of gauge theories and gravity.
The regularisation consists of a combination of covariant higher derivative terms in the action and determinants of Pauli-Villars operators in the path integral measure.
This approach has the advantages that no background field is introduced and the action remains gauge invariant along the flow without needing to fix a gauge.
This provides a new background independent formalism to investigate theories of quantum gravity.