Dual Projection and Selfduality in Three Dimensions

TL;DR

This paper explores duality and selfduality in three-dimensional theories using a novel dual projection method, revealing new symmetry structures and extending duality concepts beyond traditional algebraic approaches.

Contribution

It introduces a dual projection technique applicable to all dimensions, clarifies the role of parity in duality, and constructs duality symmetric actions in 3D with enhanced symmetry properties.

Findings

Dual projection method applicable to both even and odd dimensions.

Derived invariant actions exhibiting SO(2) and Z2 symmetries.

Detailed analysis of duality symmetry in (2+1)D Maxwell theory.

Abstract

We discuss the notion of duality and selfduality in the context of the dual projection operation that creates an internal space of potentials. Contrary to the prevailing algebraic or group theoretical methods, this technique is applicable to both even and odd dimensions. The role of parity in the kernel of the Gauss law to determine the dimensional dependence is clarified. We derive the appropriate invariant actions, discuss the symmetry groups and their proper generators. In particular, the novel concept of duality symmetry and selfduality in Maxwell theory in (2+1) dimensions is analysed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and $Z_2$ symmetries, contrary to conventional results.