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 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.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- June 2009
- DOI:
- 10.1088/1126-6708/2009/06/087
- arXiv:
- arXiv:0902.3823
- Bibcode:
- 2009JHEP...06..087A
- Keywords:
-
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Mathematical Physics
- E-Print:
- 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