Universality and Ambiguities of the Conformal Anomaly

TL;DR

This paper examines the universality and ambiguities of the one-loop conformal anomaly across various regularization schemes, highlighting conditions under which certain terms are universal or ambiguous, with implications for cosmology and holography.

Contribution

It provides a comprehensive analysis of the conformal anomaly's universality and ambiguities using multiple regularization methods, clarifying when certain terms are scheme-independent or not.

Findings

Euler and Weyl terms are universally scheme-independent.

The $ox R$ term's universality depends on the regularization breaking conformal symmetry softly.

Ambiguities in the $R^2$ term arise in some regularization schemes.

Abstract

The one-loop structure of the trace anomaly is investigated using different regularizations and renormalization schemes: dimensional, proper time and Pauli-Villars. The universality of this anomaly is analyzed from a very general perspective. The Euler and Weyl terms of the anomalous trace of the stress tensor are absolutely universal. The pure derivative $ \square R$-term is shown to be universal only if the regularization breaks conformal symmetry softly. If the breaking of conformal symmetry by the regularization method is hard the coefficient of this term might become arbitrary which points out the presence of an ambiguous $ \int\sqrt{-g} R^2$-term in the effective quantum action. These ambiguities arise in some prescriptions of dimensional and Pauli-Villars regularizations. We discuss the implications of these results for anomaly-induced inflationary scenarios and AdS/CFT correspondence.