N=1 supergravity and Maxwell superalgebras

We present the construction of the D = 4 supergravity action from the minimal Maxwell superalgebra sℳ4, which can be derived from the $$ \mathfrak{osp}\ \left(4\Big|1\right) $$ 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 sℳ4. We extend this result to all minimal Maxwell superalgebras type sℳ m + 2. The invariance under supersymmetry transformations is also analized.

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