What's Wrong with Anomalous Chiral Gauge Theory?

TL;DR

This paper argues that apparent anomalies in chiral gauge theories are not fundamental issues and that, with proper quantization, such theories are consistent, renormalizable, and can generate mass terms without breaking gauge invariance.

Contribution

It demonstrates through the Chiral Schwinger Model that anomalous chiral gauge theories are consistent and can be correctly quantized to avoid gauge anomalies.

Findings

No gauge anomaly when quantized properly

Chiral gauge theories are renormalizable and unitary

Mass terms can be generated without breaking gauge invariance

Abstract

It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger Model that there is nothing wrong with apparently anomalous chiral gauge theory. If quantised correctly, there should be no gauge anomaly and chiral gauge theory should be renormalisable and unitary, even in higher dimensions and with non-abelian gauge groups. Furthermore, mass terms for gauge bosons and chiral fermions can be generated without spoiling the gauge invariance.