On Duality Symmetry in Charged P-Form Theories

TL;DR

This paper investigates duality symmetry in charged p-form theories across all dimensions, revealing that duality groups are either Z_2 or SO(2), depending on the fields' ranks and spacetime dimensions, with origins linked to operator parity.

Contribution

It demonstrates that duality groups in charged p-form theories are universally either Z_2 or SO(2), determined by the rank and dimension, and explains their physical origin through operator parity analysis.

Findings

Duality groups are Z_2 or SO(2) in all dimensions.

Duality group depends on field rank and spacetime dimension.

Parity of certain operators explains duality symmetry properties.

Abstract

We study duality transformation and duality symmetry in the the electromagnetic-like charged p-form theories. It is shown that the dichotomic characterization of duality groups as $Z_2$ or SO(2) remains as the only possibilities but are now present in all dimensions even and odd. This is a property defined in the symplectic sector of the theory both for massive and massless tensors. It is shown that the duality groups depend, in general, both on the ranks of the fields and on the dimension of the spacetime. We search for the physical origin of this two-fold property and show that it is traceable to the dimensional and rank dependence of the parity of certain operator (a generalized-curl) that naturally decomposes the symplectic sector of the action. These operators are only slightly different in the massive and in the massless cases but their physical origin are quite distinct.