Electro-Magnetic Space-Time Duality for 2+1-Dimensional Stationary Classical Solutions

TL;DR

This paper explores a web of space-time dualities in 2+1-dimensional theories that relate electric and magnetic solutions, extending previous static dualities to rotating cases and discussing higher-dimensional generalizations.

Contribution

It extends the known static electric-magnetic duality to stationary rotating solutions and introduces two new duality maps, completing a comprehensive duality web in 2+1 dimensions.

Findings

Extended duality to rotating solutions.

Identified limitations in 3+1 dimensions.

Discussed generalization to higher forms.

Abstract

In this paper it is studied a space-time duality web that maps electric into magnetic (and magnetic into electric) charged classical stationary rotating solutions for $2+1$-dimensional Abelian Einstein Maxwell Chern-Simons theories. A first duality map originally suggested by Kogan for static charged solutions is extended to stationary rotating space-times and are suggested two new space-time dualities maps. The three dualities complete a close duality web. It is also shown that in $3+1$-dimensions these dualities are only possible for systems which exhibit non-projected cylindrical symmetry and are not related to the standard electromagnetic duality of Maxwell equations which acts on the physical fields and charges. Generalization to $N$-form theories in higher dimensional space-times is briefly discussed.