N=1 Supergravity and Maxwell superalgebras

TL;DR

This paper constructs N=1 supergravity in four dimensions using the Maxwell superalgebra derived from osp(4|1), presenting a new algebraic approach and extending it to a family of minimal Maxwell superalgebras.

Contribution

It introduces a novel construction of 4D N=1 supergravity from Maxwell superalgebras via the semigroup expansion, extending previous algebraic frameworks.

Findings

Supergravity action derived from Maxwell superalgebra.

Extension to all minimal Maxwell superalgebras sM_{m+2}.

Supersymmetry invariance confirmed.

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.