Noncommutative AdS3 with quantized cosmological constant

We examine a recent deformation of three-dimensional anti-de Sitter gravity based on noncommutative Chern-Simons theory with gauge group U(1, 1) x U(1, 1). In addition to a noncommutative analogue of 3D gravity, the theory contains two gauge fields which decouple in the commutative limit. It is well known that the level is quantized in noncommutative Chern-Simons theory. Here we show that it implies that the cosmological constant goes like -1 over an integer squared. We also construct the noncommutative AdS3 vacuum by applying a Seiberg-Witten map from the commutative case. The procedure is repeated for the case of a conical space resulting from a massive spinning particle