The trace anomaly effective action for gravity is not a valid low-energy EFT unless a new sector with spontaneously broken scale invariance adds a kinetic term for the anomalyon scalar.
Conformal Anomaly in Weyl Theory and Anomaly Free Superconformal Theories,
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Weakly-Coupled Trace Anomaly Action for Gravity
The trace anomaly effective action for gravity is not a valid low-energy EFT unless a new sector with spontaneously broken scale invariance adds a kinetic term for the anomalyon scalar.