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

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.Comment: Reference [8] has been properly place

Holographic glueballs from the circle reduction of Romans supergravity

“…In higher dimensions, one might try to generalise this line of argument. For example, if the number of dimensions is D = 2p + 1, a massive p-form can be written in terms of two massless p-forms soldered together by a first-order differential operator that introduces the mass term (see for example [69] for a nicely pedagogical discussion). But the equations of motion of the p-forms involve their duals, because the mass terms are written with the completely anti-symmetric tensor µ 1 ···µ D .…”

“…We find it useful to remind the reader how the equivalence of massive 2-form and massive 1-forms in D = 4 dimensions can be made manifest, and for this purpose we follow [66] (see also [67,68]), and make explicit the role of the gauge redundancies in the two formulations, in particular in reference to the Higgs mechanism. We also comment briefly on what happens in higher dimensions, on how the dualities between forms of different order affect the Higgs and the soldering phenomena (see for instance [69]), and on some of the subtleties emerging in the context of gauged supergravities (see for instance [70] and references therein).…”

Towards top-down holographic composite Higgs: minimal coset from maximal supergravity

“…The massive vector has the same number of propagating degrees of freedom as a massless vector together with a scalar, while the massive 2-form is obtained by soldering two massless vectors (see for instance refs. [156,157]).…”

Confinement, brane symmetry and the Julia-Toulouse approach for condensation of defects

“…These considerations about duality are naturally extended to general p-forms in arbitrary dimensions D. In fact, it is easy to show that for massless p-forms described by Maxwell-like theories, the dual pair A p and Ãq obeys the relation p + q + 2 = D, where p e q are the ranks of the forms. For massive p-forms the relation is p + q + 1 = D. Detailed investigations about duality transformations and the corresponding structure of the duality groups were worked out in [28][29][30].…”