出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We present a noncommutative extension of first order Einstein-Hilbert gravity in the context of twist-deformed space-time, with a ?-product associated to a triangular Drinfeld twist. In particular the ?-product can be chosen to be the usual Groenewald-Moyal product. The action is geometric, invariant under diffeomorphisms and centrally extended Lorentz GL(2,C) ?-gauge transformations. By imposing a charge conjugation condition on the noncommutative vielbein, the commutative limit reduces to ordinary gravity, with local Lorentz invariance and usual real vielbein. The theory is then coupled to fermions, by adding the analog of the Dirac action in curved space. A noncommutative Majorana condition can be imposed, consistent with the ?- gauge transformations. We also discuss a noncommutative deformation of D = 4, N = 1 supergravity, 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 realized in a noncommutative D = 4, N = 1 supergravity with chiral gravitino and complex vierbein.
