Dual projection and self-duality in three dimensions - art. no. 045005

We discuss the notion of duality and self-duality in the context of the dua l projection operation that creates an internal space of potentials. Distin ctly from the algebraic or group theoretical methods, this technique is app licable to both even and odd dimensions. The parity in the kernel of the Ga uss law is shown to play a crucial role in determining the dimensional depe ndence of the duality groups and actions, Using this novel concept, we deri ve the appropriate invariant actions and discuss the symmetry groups and th eir proper generators. In particular, the presence of a duality symmetry an d self-duality in Maxwell theory in 2+1 dimensions is analyzed 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) sym metries, contrary to conventional results.