Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals

In Lorentz violating quantum electrodynamics (QED) it is known that a radiatively induced Chern-Simons term appears in the effective action for the gauge field, which is finite but undetermined. This ambiguity is shown to be absent in a condensed matter realization of such a theory in Weyl semi-metals due to the existence of a full microscopic model from which this effective theory emerges. Physically observable consequences such as birefringence are also discussed in this scenario.