OSp(1|4) supergravity and its noncommutative extension

Abstract

We review the OSp(1|4)-invariant formulation of N=1, D=4 supergravity and present its noncommutative extension, based on a star-product originating from an abelian twist with deformation parameter θ. After 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 whose classical limit θ--> 0 is the usual N=1, D=4 AdS supergravity.

20 pages, LaTeX. Added fields and curvatures at first order in θ. Matches published version in Phys. Rev. D

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