Noncommutative Einstein-AdS Gravity in three Dimensions

TL;DR

This paper develops a noncommutative version of three-dimensional Einstein-AdS gravity using Chern-Simons theory, introducing new fields and symmetries that generalize classical diffeomorphisms.

Contribution

It constructs a Lorentzian noncommutative gravity model in 3D with a novel action involving symmetric and antisymmetric fields, extending the Chern-Simons formulation.

Findings

The deformed action includes a real metric and antisymmetric tensor.

The theory remains invariant under a class of transformations reducing to diffeomorphisms.

The model generalizes classical gravity to a noncommutative setting.

Abstract

We present a Lorentzian version of three-dimensional noncommutative Einstein-AdS gravity by making use of the Chern-Simons formulation of pure gravity in 2+1 dimensions. The deformed action contains a real, symmetric metric and a real, antisymmetric tensor that vanishes in the commutative limit. These fields are coupled to two abelian gauge fields. We find that this theory of gravity is invariant under a class of transformations that reduce to standard diffeomorphisms once the noncommutativity parameter is set to zero.