The local RG equation and chiral anomalies

TL;DR

This paper extends the local RG equation to include chiral anomalies, revealing a new anomaly, and discusses implications for energy-momentum tensor trace, scheme choices, non-renormalization theorems, and the theta parameter.

Contribution

It introduces a generalized local RG equation accounting for chiral anomalies, including a new anomaly, and explores its consequences for anomalies, scheme dependence, and theta parameter constraints.

Findings

A new anomaly is required by Wess-Zumino consistency.

The trace of the energy-momentum tensor is expressed in terms of covariant flavor currents.

Constraints on the perturbative running of the theta parameter are derived.

Abstract

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.