W-Infinity Algebras from Noncommutative Chern-Simons Theory

Abstract

We examine Chern-Simons theory written on a noncommutative plane with a `hole', and show that the algebra of observables is a nonlinear deformation of the $w_{\infty }$ algebra. The deformation depends on the level (the coefficient in the Chern-Simons action), and the noncommutativity parameter, which were identified, respectively, with the inverse filling fraction and the inverse density in a recent description of the fractional quantum Hall effect. We remark on the quantization of our algebra. The results are sensitive to the choice of ordering in the Gauss law.

9 pages

References in corpus (3)

• On Level Quantization for the Noncommutative Chern-Simons Theory
• Chern-Simons Theories on Noncommutative Plane
• A note on the non-commutative Chern-Simons model on manifolds with boundary

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