On the dimensional dependence of duality groups for massive p-forms

TL;DR

This paper explores the duality properties of massive p-form theories using soldering formalism, comparing mass generation mechanisms and classifying duality groups based on operator parity in various spacetime dimensions.

Contribution

It develops a formalism for duality analysis of massive p-forms, connecting soldering mass generation with Higgs and Julia-Toulouse mechanisms, and classifies duality groups based on operator parity.

Findings

Soldering formalism interpolates between Higgs and Julia-Toulouse mechanisms in even dimensions.

Duality group classification depends on the parity of the symplectic operator.

Explicit duality actions are derived for different cases.

Abstract

We study the soldering formalism in the context of abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger \cite{QT} a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.