A New Gravitational Action For The Trace Anomaly

TL;DR

This paper proposes a scalar-tensor extension of General Relativity to construct a local, diff-invariant effective action for the trace anomaly, addressing inconsistencies in previous approaches and revealing potential physical implications.

Contribution

It introduces a novel scalar-tensor theory that preserves the trace anomaly equation and includes a new mass scale, improving the effective gravitational action for the trace anomaly.

Findings

Maintains two-derivative equations of motion.

Reduces to the conformal Galileon in a certain approximation.

Addresses inconsistency in previous trace anomaly actions.

Abstract

The question of building a local diff-invariant effective gravitational action for the trace anomaly is reconsidered. General Relativity (GR) combined with the existing action for the trace anomaly is an inconsistent low energy effective field theory. This issue is addressed by extending GR into a certain scalar-tensor theory, which preserves the GR trace anomaly equation, up to higher order corrections. The extension introduces a new mass scale -- assumed to be below the Planck scale -- that governs four high dimensional terms in a local diff-invariant trace anomaly action. Such terms can be kept, while an infinite number of Planck-suppressed invariants are neglected. The resulting theory maintains two derivative equations of motion. In a certain approximation it reduces to the conformal Gallileon, which could have physical consequences.