Lorentz-violating Yang-Mills theory: discussing the Chern-Simons-like term generation

TL;DR

This paper investigates the generation of Chern-Simons-like terms in Lorentz-violating Yang-Mills theories with fermions, demonstrating that such terms are not radiatively generated and the model remains anomaly-free and quantum stable.

Contribution

It provides a scheme-independent proof that Chern-Simons-like terms are not generated radiatively in Lorentz-violating Yang-Mills theories, ensuring their quantum stability.

Findings

Chern-Simons-like term is not generated by radiative corrections.

The model is free of gauge anomalies.

The theory is quantum stable.

Abstract

We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.