Weakly-Coupled Trace Anomaly Action for Gravity

TL;DR

This paper presents a local, diff-invariant quantum effective action for gravity that models the trace anomaly, identifies its strong coupling issues, and proposes a new sector to resolve these problems with implications for quantum gravity theories.

Contribution

It introduces a novel local effective action for the trace anomaly in gravity and demonstrates how a new sector with broken scale invariance can mitigate strong coupling issues.

Findings

Counter-term dominates among possible terms for the trace anomaly

The scattering amplitude becomes strongly coupled at low energies without modifications

Introducing a new sector with broken scale invariance alleviates the strong coupling problem

Abstract

We discuss a local, diff-invariant quantum effective action for gravity that captures the trace anomaly via a counter-term. We discuss why this counter-term is the most significant among infinitely many possible ones, and show how the counter-term leads to a scattering amplitude that is strongly coupled at arbitrarily low energies. We show how the introduction of a new sector with spontaneously broken scale invariance removes the strong coupling problem, and discuss some physical consequences due to the new sector. Three Appendices summarize quantum effective actions -- highlighting connections between their local, and seemingly non-local formulations -- for the scale anomaly in 4D QED, for the axial anomaly in 2D QED, and for the scale anomaly in a 2D sigma model.