Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map

Physics – High Energy Physics – High Energy Physics - Theory

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26+1 pages, LaTeX. arXiv admin note: substantial text overlap with arXiv:0902.3817

Scientific paper

We use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate transformations and local Lorentz rotations, and has the same degrees of freedom as the commutative gravity action. The expansion is given up to second order in the noncommutativity parameter \theta. A geometric reformulation of the SW map is presented for general abelian twists. Compatibility of the map with hermiticity and charge conjugation conditions is proven. The action at all orders is shown to be real and even in \theta, and hence invariant under charge conjugation.

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