OSp(1|4) supergravity and its noncommutative extension

We review the OSp(1|4)-invariant formulation of N=1, D=4 supergravity and present its noncommutative extension, based on a product originating from an Abelian twist with deformation parameter θ. After the use of a geometric generalization of the Seiberg-Witten map, we obtain an extended (higher-derivative) supergravity theory, invariant under usual OSp(1|4) gauge transformations. Gauge fixing breaks the OSp(1|4) symmetry to its Lorentz subgroup and yields a Lorentz-invariant extended theory for which the classical limit θ→0 is the usual N=1, D=4 anti-de Sitter supergravity.