Twisted Covariant Noncommutative Self-dual Gravity

Understand

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 Pleba\'nski action is explicitly obtained.