Generalized cosmological term in $$D=4$$ D = 4 supergravity from a new AdS–Lorentz superalgebra

A new supersymmetrization of the so-called AdS–Lorentz algebra is presented. It involves two fermionic generators and is obtained by performing an abelian semigroup expansion of the superalgebra $$\mathfrak {osp}(4|1)$$ . The peculiar properties of the aforesaid expansion method are then exploited to construct a $$D=4$$ supergravity action involving a generalized supersymmetric cosmological term in a geometric way, only from the curvatures of the novel superalgebra. The action obtained with this procedure is a MacDowell–Mansouri like action. Gauge invariance and supersymmetry of the action are also analyzed.

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