The local RG equation and chiral anomalies

We generalize the local renormalization group (RG) equation to theories with chiral anomalies. We find that a new anomaly is required by the Wess-Zumino consistency conditions. Taking into account the new anomaly, the trace of the energy momentum tensor is expressed in terms of the covariant flavor currents, instead of the consistent ones. This result is used to show that a flavor rotation induced by the RG flow can be eliminated by a choice of scheme even in the presence of chiral anomalies. As part of a general discussion of chiral anomalies in the presence of background sources, we also derive non-renormalization theorems. Finally, we introduce the theta parameter as a source, and derive constraints on a perturbative running of this parameter.