On the dimensional dependence of the electromagnetic duality groups

TL;DR

This paper investigates how electromagnetic duality groups depend on spacetime dimensions, introducing a dual projection method that unifies duality concepts across all even dimensions and reveals a duality between internal and external spaces.

Contribution

It introduces the dual projection operation and a new external duality space that unify duality groups across all even dimensions, extending the concept of selfduality.

Findings

Dual projection systematically reveals internal potential spaces.

Unification of Z2 and SO(2) duality groups in all even dimensions.

Discovery of a duality between internal and external duality spaces.

Abstract

We study the two-fold dimensional dependence of the electromagnetic duality groups. We introduce the dual projection operation that systematically discloses the presence of an internal space of potentials where the group operation is defined. A two-fold property of the kernel in the projection is shown to define the dimensional dependence of the duality groups. The dual projection is then generalized to reveal another hidden two-dimensional structure. The new unifying concept of the external duality space remove the dimensional dependence of the kernel, allowing the presence of both $Z_2$ and SO(2) duality groups in all even dimensions. This result, ultimately unifies the notion of selfduality to all D=2k+2 dimensions. Finally, we show the presence of an unexpected duality between the internal and external spaces leading to a duality of the duality groups.