N=1 Supergravity and Maxwell superalgebras

Abstract

We present the construction of the $D=4$ supergravity action from the minimal Maxwell superalgebra $s{\mathcal{M}}_4$, which can be derived from the $\mathfrak{osp}\left(4|1\right)$ superalgebra by applying the abelian semigroup expansion procedure. We show that $N=1$, $D=4$ pure supergravity can be obtained alternatively as the MacDowell-Mansouri like action built from the curvatures of the Maxwell superalgebra $s{\mathcal{M}}_4$. We extend this result to all minimal Maxwell superalgebras type $s{\mathcal{M}}_{m+2}$. The invariance under supersymmetry transformations is also analized.

22 pages, published version

References in corpus (6)

• Expanding Lie (super)algebras through abelian semigroups
• Deformations of Maxwell algebra and their Dynamical Realizations
• N=1 and N=2 pure supergravities on a manifold with boundary
• Maxwell Superalgebras and Abelian Semigroup Expansion
• Generalized Poincare algebras and Lovelock-Cartan gravity theory
• Minimal D=4 supergravity from the superMaxwell algebra