Non-Semisimple Gaugings of D=5 N=8 Supergravity and FDA.s

TL;DR

The paper proves the existence of non-semisimple CSO$(p,q,r)$ gaugings in $D=5$, ${ m N}=8$ supergravity and shows they can be constructed within the Free Differential Algebra (FDA) and rheonomy framework, independent of a conventional Lagrangian. It clarifies how the gauging reshapes field content by yielding $15+r$ gauge vectors and $12-r$ self-dual two-forms, with $r$ neutral abelian vectors, and explains the dualization mechanism that resolves consistency issues for non-semisimple gaugings. The work demonstrates that the full dynamics—DPES field equations and the scalar potential—can be derived from the closure of the supersymmetry algebra via Bianchi identities, even when a standard action is unavailable. These results have potential implications for domain-wall/QFT correspondences and gravity trapping, and they set the stage for further analysis of vacua and the scalar potential in these novel theories.

Abstract

We reformulate maximal D=5 supergravity in the consistent approach uniquely based on Free Differential Algebras and the solution of their Bianchi identities (= rheonomic method). In this approach the lagrangian is unnecessary since the field equations follow from closure of the supersymmetry algebra. This enables us to explicitly construct the non-compact gaugings corresponding to the non--semisimple algebras CSO(p,q,r), irrespectively from the existence of a lagrangian. The use of Free Differential Algebras is essential to clarify, within a cohomological set up, the dualization mechanism between one-forms and two-forms. Our theories contain 12-r self-dual two-forms and 15+r gauge vectors, r of which are abelian and neutral. These theories, whose existence is proved and their supersymmetry algebra constructed hereby, have potentially interesting properties in relation with domain wall solutions and the trapping of gravity.