Weyl Anomaly Induced Stress Tensors in General Manifolds

TL;DR

This paper derives stress tensors from Weyl anomalies in general manifolds using dimensional regularization, extending previous results and discussing ambiguities in anomaly types.

Contribution

It generalizes anomaly-induced stress tensor calculations to non-conformally flat backgrounds and addresses regularization and ambiguity issues.

Findings

Type A anomaly-induced stress tensors are extended to 4 and 6 dimensions.

Regulators are necessary for well-defined Type B anomaly stress tensors.

Ambiguities in Type D anomalies and Weyl invariants are discussed.

Abstract

Considering arbitrary conformal field theories in general (non-conformally flat) backgrounds, we adopt a dimensional regularization approach to obtain stress tensors from Weyl anomalies. The results of type A anomaly-induced stress tensors in four and six-dimensions generalize the previous results calculated in a conformally flat background. On the other hand, regulators are needed to have well-defined type B anomaly-induced stress tensors. We also discuss ambiguities related to type D anomalies, Weyl invariants and order of limit issues.