Non-semisimple gaugings of D = 5, \U0001d4a9 = 8supergravity and FDAs

Abstract

We reformulate maximal D = 5 supergravity in the consistent approachuniquely based on free differential algebras and the solution of theirBianchi identities (i.e. the rheonomic method). In this approach theLagrangian is unnecessary since the field equations follow from closure ofthe supersymmetry algebra. This enables us to explicitly construct thenon-compact gaugings corresponding to the non-semisimple algebrasCSO(p,q,r), irrespectively of the existence of a Lagrangian.The use of free differential algebras is essential to clarify, within acohomological set-up, the dualization mechanism between 1- and2-forms. Our theories contain 12-r self-dual 2-forms and 15 + r gauge vectors, r of which are Abelian and neutral. These theories,whose existence is proved and their supersymmetry algebra constructedhereby, have potentially interesting properties in relation to domainwall solutions and the trapping of gravity.