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Abstract

We analyse the proposal of defining the Weyl anomaly for classically
non-conformal theories as $g^{mn} \langle T_{mn}\rangle - \langle g^{mn} T_{mn}
\rangle$, originally put forward by M. 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 non-local contributions.