Covariant and background independent functional RG flow for the effective average action

TL;DR

This paper develops a covariant, background-independent functional renormalization group approach for scalar quantum field theories, ensuring symmetry preservation and enabling simplified truncations based on the total field.

Contribution

It introduces a new IR cutoff scheme that maintains covariance and background independence, allowing for single-field dependent truncations in the RG flow.

Findings

Exact solvability of Ward identities with the new cutoff

Background independence at all scales

Conditions for symmetry preservation along RG flow

Abstract

We extend our prescription for the construction of a covariant and background-independent effective action for scalar quantum field theories to the case where momentum modes below a certain scale are suppressed by the presence of an infrared regulator. The key step is an appropriate choice of the infrared cutoff for which the Ward identity, capturing the information from single-field dependence of the ultraviolet action, continues to be exactly solvable, and therefore, in addition to covariance, manifest background independence of the effective action is guaranteed at any scale. A practical consequence is that in this framework one can adopt truncations dependent on the single total field. Furthermore we discuss the necessary and sufficient conditions for the preservation of symmetries along the renormalization group flow.