Maxwell-Chern-Simons vortices and holographic superconductors

We investigate vortex solutions of a charged scalar field in Einstein-Maxwell theory in 3+1 dimensions with the addition of an axionic coupling to the Maxwell field. We show that the inclusion of such a term, together with a suitable potential for the axion field, can induce an effective Chern-Simons term on the 2+1 dimensional boundary. We obtain numerical solutions of the equations of motion and find Maxwell-Chern-Simons like magnetic vortex configurations, where the magnetic field profile varies with the size of the effective Chern-Simons coupling. The axion field has a non-trivial profile inside the AdS bulk and on the 2+1 dimensional boundary but does not condense at spatial infinity.