M. Asorey, E.V. Gorbar, I.L. Shapiro
Universality and Ambiguities of the Conformal Anomaly
Preprint series: ESI preprints

MSC:

81T50 Anomalies

83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories

83C47 Quantum field theory aspects, See also {81T20}

81T17 Renormalization group methods

PACS: 04.62.+v,11.10.Gh,11.10.Hi
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.

Keywords: Conformal Anomaly, Regularization Methods, Renormalization Group, Universality