Remarks on a Chern-Simons-like coupling
  We consider the static quantum potential for a gauge theory which includes a light massive vector field interacting with the familiar $U(1)_{QED}$ photon via a Chern-Simons- like coupling, by using the gauge-invariant, but path-dependent, variables formalism. An exactly screening phase is then obtained, which displays a marked departure of a qualitative nature from massive axionic electrodynamics. The above static potential profile is similar to that encountered in axionic electrodynamics consisting of a massless axion-like field, as well as to that encountered in the coupling between the familiar $U(1)_{QED}$ photon and a second massive gauge field living in the so-called $U(1)_h$ hidden-sector, inside a superconducting box. 
Patricio Gaete
hep-th