Noncommutative D=4 gravity coupled to fermions

Details Noncommutative D=4 gravity coupled to fermions Noncommutative D=4 gravity coupled to fermions

2009-02-23

arxiv.org/abs/0902.3817v1

JHEP 0906:086,2009

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX

Scientific paper

10.1088/1126-6708/2009/06/086

We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-deformed space-time, with a $\star$-product associated to a quite general triangular Drinfeld twist. In particular the $\star$-product can be chosen to be the usual Groenewald-Moyal product. The action is geometric, invariant under diffeomorphisms and centrally extended Lorentz $\star$-gauge transformations. In the commutative limit it reduces to ordinary gravity, with local Lorentz invariance and usual real vielbein. This we achieve by imposing a charge conjugation condition on the noncommutative vielbein. The theory is coupled to fermions, by adding the analog of the Dirac action in curved space. A noncommutative Majorana condition can be imposed, consistent with the $\star$-gauge transformations. Finally, we discuss the noncommutative version of the Mac-Dowell Mansouri action, quadratic in curvatures.

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