Noncommutative Gravity in two Dimensions

TL;DR

This paper develops a noncommutative deformation of two-dimensional topological gravity, exploring its invariance, solutions like fuzzy AdS_2, and transformation properties under the Seiberg-Witten map.

Contribution

It introduces a novel noncommutative gravity model in two dimensions based on gauge theory deformation, with analysis of its symmetries and solutions.

Findings

Model is invariant under a class of transformations reducing to diffeomorphisms when noncommutativity vanishes.

Fuzzy AdS_2 solution is obtained within the deformed model.

Transformation properties under the Seiberg-Witten map are characterized.

Abstract

We deform two-dimensional topological gravity by 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, like fuzzy AdS_2, are obtained. Furthermore, the transformation properties of the model under the Seiberg-Witten map are studied.