A new gravitational action for the trace anomaly

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.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

The paper reconsiders the question of constructing a locally diffeomorphism-invariant effective gravitational action for the trace anomaly. Combining General Relativity (GR) with the existing action for the trace anomaly is inconsistent as a low energy effective field theory. The inconsistency is resolved by extending GR into a scalar-tensor theory that preserves the GR trace anomaly equation up to higher order corrections. The resulting theory introduces a new mass scale that governs high-dimensional terms in a locally diffeomorphism-invariant trace anomaly action.