CPT-violating z=3 Horava-Lifshitz QED and generation of the Carroll-Field-Jackiw term

We study the $z=3$ Horava-Lifshitz QED with a CPT-breaking term, characterized by the axial vector $b_{\mu }$, and perform the one-loop calculations. Explicitly, we demonstrate that just as in the usual Lorentz-breaking QED, in our case, the Carroll-Field-Jackiw term is finite but ambiguous.