Topologically massive magnetic monopoles

TL;DR

This paper demonstrates that magnetic monopoles in topologically massive electrodynamics require a curved spacetime background, specifically anti-de Sitter space, due to the topological mass, and extends this to a gravity-electrodynamics coupling.

Contribution

It reveals that magnetic monopoles in Maxwell-Chern-Simons theory necessitate curved spacetime, linking topological mass to spacetime geometry, and extends the analysis to topologically massive gravity.

Findings

Monopole Dirac string forms a cone in AdS space.

Topological mass relates to the cone's opening angle.

Pure Einstein-Maxwell-Chern-Simons gravity admits monopole solutions.

Abstract

We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, {\it a priory} completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics in the framework of the theory of Deser, Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a monopole solution.