Weyl anomaly induced stress tensors in general manifolds

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.