Conformal anomalies and renormalized stress tensor correlators for nonconformal theories

We analyze the proposal of defining the Weyl anomaly for classically nonconformal theories as gmn⟨Tmn⟩−⟨gmnTmn⟩, originally put forward by Duff, in the case of a scalar field with quartic self-interaction in 4d. We work in the context of dimensional regularization in curved background to two loops (first order in the coupling). We review the original regularized but not renormalized prescription and its ambiguities; we argue that it cannot be extended to the interacting theory as it fails to provide a finite result. We then propose an alternative prescription via renormalized expectation values. At one loop, our candidate reproduces the local heat kernel result, while its extension to interacting theories contains nonlocal contributions. Published by the American Physical Society 2024