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arXiv · 2406.12464

Conformal `anomalies' and renormalized stress-tensor correlators for non-conformal theories

Tommaso Bertolini·Lorenzo Casarin
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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.

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Tommaso Bertolini, Lorenzo Casarin. 2024-06-18. Conformal `anomalies' and renormalized stress-tensor correlators for non-conformal theories. https://arxiv.org/abs/2406.12464

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