Noncommutative gravity in two dimensions

We deform a two-dimensional topological gravity making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once the noncommutativity parameter is set to zero. Some solutions of the deformed model, such as fuzzy AdS2, are obtained. Furthermore, the transformation properties of the model under the Seiberg–Witten map are studied.