Renormalization Ambiguities and Conformal Anomaly in Metric-Scalar Backgrounds

TL;DR

This paper investigates the ambiguities in the conformal anomaly for scalar field theories in curved backgrounds, highlighting their relation to finite renormalizations and providing a method to identify such ambiguities.

Contribution

It introduces a general approach to identify theories with conformal anomaly ambiguities due to finite renormalizations of non-minimal terms.

Findings

Ambiguities are linked to finite renormalizations of local non-minimal terms.

The analysis applies to scalar and Yukawa models in the conformal limit.

A general method to detect potential anomaly ambiguities is proposed.

Abstract

We analyze the problem of the existing ambiguities in the conformal anomaly in theories with external scalar field in curved backgrounds. In particular, we consider the anomaly of self-interacting massive scalar field theory and of Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of a local non-minimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise.