Lorentz symmetry breaking in Abelian vector-field models with Wess-Zumino interaction

We consider Abelian vector-field models in the presence of the Wess-Zumino interaction with pseudoscalar matter. The occurrence of the dynamic breaking of Lorentz symmetry at classical and one-loop levels is described for massless and massive vector fields. This phenomenon appears to be the nonperturbative counterpart of the perturbative renormalizability and/or unitarity breaking in chiral gauge theories.