Noncommutative supergravity in D = 3 and D = 4

We present a noncommutative D = 3, N = 1 supergravity, invariant under diffeomorphisms, local U(1,1) noncommutative *-gauge transformations and local *-supersymmetry. Its commutative limit is the usual D = 3 pure supergravity, without extra fields. A noncommutative deformation of D = 4, N = 1 supergravity is also obtained, reducing to the usual simple supergravity in the commutative limit. Its action is invariant under diffeomorphisms and local GL(2,C) *-gauge symmetry. The supersymmetry of the commutative action is broken by noncommutativity. Local *-supersymmetry invariance can be implemented in a noncommutative D = 4, N = 1 supergravity with chiral gravitino and complex vierbein.