Noncommutative supergravity in D=3 and D=4
Abstract
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.
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