Noncommutative supergravity in D=3 and D=4
arXiv:0902.3823 · doi:10.1088/1126-6708/2009/06/087
Abstract
We present a noncommutative D=3, N=1 supergravity, invariant under diffeomorphisms, local U(1,1) noncommutative \star-gauge transformations and local \star-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) \star-gauge symmetry. The supersymmetry of the commutative action is broken by noncommutativity. Local \star-supersymmetry invariance can be implemented in a noncommutative D=4, N=1 supergravity with chiral gravitino and complex vierbein.
22 pages, LaTeX. We discuss in more depth the noncommutative deformation of D=4 simple supergravity, and how noncommutativity breaks the supersymmetry of the commutative action