Maxwell-Chern-Simons Vortices and Holographic Superconductors

TL;DR

This paper explores vortex solutions in a holographic superconductor model with an axionic coupling, revealing how the effective Chern-Simons term influences magnetic vortex configurations in the boundary theory.

Contribution

It introduces a novel holographic setup with axionic coupling that induces an effective Chern-Simons term, leading to new vortex solutions in the boundary theory.

Findings

Effective Chern-Simons term modifies magnetic vortex profiles.

Axion field remains non-condensed at infinity.

Numerical solutions demonstrate Chern-Simons-like vortices.

Abstract

We investigate probe limit vortex solutions of a charged scalar field in Einstein-Maxwell theory in 3+1 dimensions, for an asymptotically AdS Schwarzschild black hole metric 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 but does not condense at spatial infinity.