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W-Infinity Algebras from Noncommutative Chern-Simons Theory

A. Pinzul·A. Stern
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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.

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BibTeXRIS

A. Pinzul, A. Stern. 2003-05-16. W-Infinity Algebras from Noncommutative Chern-Simons Theory. https://doi.org/10.1142/s021773230301106x

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