W-Infinity Algebras from Noncommutative Chern-Simons Theory

Details W-Infinity Algebras from Noncommutative Chern-Simons Theory W-Infinity Algebras from Noncommutative Chern-Simons Theory

2002-06-11

arxiv.org/abs/hep-th/0206095v3

Mod.Phys.Lett. A18 (2003) 1215-1224

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

10.1142/S021773230301106X

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.

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