Induction of the four-dimensional Lorentz-breaking non-Abelian Chern-Simons action

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 a spinor field. This term is shown to be regularization dependent, but nevertheless it can be found unambiguously in different regularization schemes at zero and at finite temperature.