Twisted Covariant Noncommutative Self-dual Gravity

Abstract

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the $\theta$-expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in $\theta$ for the Plebański action is explicitly obtained.

23+1 pages, no figures, corrected typos, references and Appendix B is added

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