Abstract
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.
Highlights
General Relativity emerges as a limit of a Born-Infeld like theory invariant under a certain subalgebra of the Lie algebra Mm [10,11,12,13]
We present the construction of the D = 4 supergravity action from the minimal Maxwell superalgebra sM4, which can be derived from the osp (4|1) 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
Summary
General Relativity emerges as a limit of a Born-Infeld like theory invariant under a certain subalgebra of the Lie algebra Mm [10,11,12,13]. This action, describing N = 1, D = 4 supergravity, is not invariant under the osp (4|1) gauge transformations. This new superalgebra obtained after a reduced resonant S-expansion of osp (4|1) superalgebra corresponds to a minimal superMaxwell algebra sM4 in D = 4 which contains the Maxwell algebra M4 = {Jab, Pa, Zab} and the Lorentz type subalgebra LM4 = {Jab, Zab} as subalgebras.
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