Remarks on a Lorentz-breaking 4D chiral gauge theory

TL;DR

This paper explores a Lorentz-violating chiral gauge theory with fermions, scalars, and gauge fields, demonstrating how to generate a Carroll-Field-Jackiw term and cancel anomalies while maintaining renormalizability.

Contribution

It introduces a Lorentz-violating chiral model that achieves anomaly cancellation and generates a Carroll-Field-Jackiw term through parameter adjustments, with proven renormalizability.

Findings

Unambiguous generation of Carroll-Field-Jackiw term

Anomaly cancellation in the Lorentz-violating model

Renormalizability maintained in broken symmetry phase

Abstract

We investigate a Lorentz-violating chiral model composed by two fermions, a complex scalar field and a gauge field. We show that by convenientely adjusting the parameters of the model, it is possible to generate an unambiguous Carroll-Field-Jackiw term and, at the same time, provide the cancelation of the chiral anomaly. The renormalizability of the model is investigated and it is shown that the same counterterms needed in the symmetric phase also renormalize the model with broken symmetry.