Chiral Anomalies? A Voice for Choice

TL;DR

This paper develops a gauge-invariant, renormalizable theory for gauged chiral fermions with abelian anomalies by adding specific terms, providing a novel approach akin to gauge fixing with Fadeev-Popov ghosts.

Contribution

It introduces a method to construct a gauge-invariant and renormalizable theory from anomalous chiral models using finite action modifications, similar to gauge fixing techniques.

Findings

Constructed a gauge-invariant, renormalizable theory with anomalous fermions.

Demonstrated equivalence to alternative regularization methods.

Compared models to abelian Wess-Zumino models, highlighting renormalizability.

Abstract

We consider theories with gauged chiral fermions in which there are abelian anomalies, and no nonabelian anomalies (but there may be nonabelian gauge fields present). We construct an associated theory that is gauge invariant, renormalizable, and with the same particle content, by adding a finite number of terms to the action. Alternatively one can view the new theory as arising from the original theory by using another regularization, one that is gauge invariant. The situation is reminiscent of the mechanism of adding Fadeev-Popov ghosts to an unsatisfactory gauge theory, to arrive at the usual quantization procedure. The models developed herein are much like the abelian Wess-Zumino model (an abelian effective theory with a Wess-Zumino counter term), but unlike the W-Z model are renormalizable!