Noncommutative $Ad{S}^3$ with Quantized Cosmological Constant

Abstract

We examine a recent deformation of three-dimensional anti-deSitter gravity based on noncommutative Chern-Simons theory with gauge group $U(1,1)\times U(1,1)$. In addition to a noncommutative analogue of 3D gravity, the theory contains two addition gauge fields which decouple in the commutative limit. It is well known that the level is quantized in noncommutative Chern-Simons theory. Here it implies that the cosmological constant goes like minus one over an integer-squared. We construct the noncommutative $Ad{S}^3$ 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.

16 pp

References in corpus (2)

• A Gravity Theory on Noncommutative Spaces
• (2 + 1) noncommutative gravity and conical spacetimes

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