Chiral anomalies and Poincare invariance

TL;DR

This paper investigates how different regularizations of the fermionic determinant in chiral gauge theories affect Poincare invariance, revealing that only certain regularizations preserve Lorentz and translational symmetries.

Contribution

It demonstrates that Poincare invariance can be anomalously violated depending on the regularization scheme, emphasizing the importance of consistent regularization for symmetry preservation.

Findings

Lorentz and translational invariance are violated with covariant anomalies.

Wess-Zumino regularization preserves Poincare invariance.

Regularization choice impacts the consistency of chiral anomalies.

Abstract

I study variations of the fermionic determinant for a nonabelian Dirac fermion with external vector and axial vector sources. I consider different regularizations, leading to different chiral anomalies when the variations are chiral transformations. For these different regularizations, I then consider variations associated with Poincare transformations. I find that both Lorentz and translational invariance are anomalously violated in general, but that they are respected when the variations of the determinant are regularized to give a Wess-Zumino consistent anomaly (the Bardeen anomaly). If the variations are regularized to give a covariant anomaly, then Poincare invariance is not respected. Following Manohar in an investigation of Poincare anomalies in a chiral gauge theory, this gives an alternative way to understand the need for a consistent regularization of the variations of the fermionic determinant.