One-loop conformal anomaly in an implicit momentum space regularization framework

TL;DR

This paper investigates the one-loop conformal anomaly in a gravitational background using a momentum space regularization method, highlighting the regularization dependence and arbitrariness in the anomaly's terms.

Contribution

It introduces a momentum space regularization framework to analyze conformal anomalies, explicitly parametrizing regularization-dependent terms and comparing with existing results.

Findings

Regularization-dependent terms are explicitly parametrized.

The anomaly term $ox R$ contains unavoidable arbitrariness.

Comparison shows consistency with previous literature but highlights regularization issues.

Abstract

In this paper we consider matter fields in a gravitational background in order to compute the breaking of the conformal current at one-loop order. Standard perturbative calculations of conformal symmetry breaking expressed by the non-zero trace of the energy-momentum tensor have shown that some violating terms are regularization dependent, which may suggest the existence of spurious breaking terms in the anomaly. Therefore, we perform the calculation in a momentum space regularization framework in which regularization dependent terms are judiciously parametrized. We compare our results with those obtained in the literature and conclude that there is an unavoidable arbitrariness in the anomalous term $\Box R$.