Remarks on a Chern-Simons-like coupling

TL;DR

This paper investigates the static potential in a gauge theory with a massive vector field coupled via a Chern-Simons-like term, revealing an exact screening phase with qualitative differences from axionic electrodynamics.

Contribution

It introduces a novel analysis of a gauge theory with a Chern-Simons-like coupling, showing an exact screening phase and comparing it to axionic and hidden-sector gauge theories.

Findings

Exact screening phase obtained in the model.

Static potential similar to axionic electrodynamics.

Qualitative departure from massive axionic electrodynamics.

Abstract

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.