# On the induction of the four-dimensional Lorentz-breaking non-Abelian Chern-Simons action

## TL;DR

This paper demonstrates how a Lorentz-breaking non-Abelian Chern-Simons action in four dimensions can be generated through one-loop quantum corrections, showing its regularization dependence but consistent emergence across schemes.

## Contribution

It introduces a method to generate a Lorentz-breaking non-Abelian Chern-Simons term via one-loop corrections with a specific Lorentz-breaking coupling.

## Key findings

- The Chern-Simons term is regularization dependent.
- It appears unambiguously in different regularization schemes.
- The term is consistent at both zero and finite temperature.

## Abstract

A four-dimensional Lorentz-breaking non-Abelian Chern-Simons like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the non-Abelian gauge field to the spinor field. This term is shown to be regularization dependent but nevertheless it can be found unambiguously in different regularization schemes at zero and finite temperature.