Conformal Decomposition of the Effective Action and Covariant Curvature Expansion

TL;DR

This paper analyzes a class of effective actions in four-dimensional quantum field theory that reproduce the conformal anomaly, introducing a new conformal basis for the covariant curvature expansion and discussing potential applications.

Contribution

It introduces a conformal basis for the covariant curvature expansion of effective actions that reproduce the conformal anomaly in 4D, fixing gauge freedom within this class.

Findings

Rewritten the conformal invariant part of the effective action in a new basis.

Expanded the effective action up to third order in curvature.

Discussed potential applications of the conformal decomposition.

Abstract

The class of effective actions exactly reproducing the conformal anomaly in 4D is considered. It is demonstrated that the freedom within this class can be fixed by the choice of the conformal gauge. The conformal invariant part of the generic one-loop effective action expanded in the covariant series up to third order in the curvature is rewritten in the new conformal basis. The possible applications of the obtained results are discussed.