Anomalies From the Covariant Derivative Expansion

We revisit the calculation of chiral anomalies for global and gauge symmetries in the framework of the covariant derivative expansion (CDE). Due to the presence of UV divergences, the result is an ambiguous quantity that depends on the regularization procedure and the renormalization scheme. We introduce a class of regulators that facilitate a straightforward evaluation of the anomaly exclusively in <math display="inline"><mi>d</mi><mo>=</mo><mn>4</mn></math> spacetime dimensions using the CDE methodology. We derive a master formula for the anomaly that integrates various known results into a unified framework.