129 research outputs found
W-Infinity Algebras from Noncommutative Chern-Simons Theory
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 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.Comment: 9 page
Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz
We study the dimensional aspect of the geometry of quantum spaces.
Introducing a physically motivated notion of the scaling dimension, we study in
detail the model based on a fuzzy torus. We show that for a natural choice of a
deformed Laplace operator, this model demonstrates quite non-trivial behaviour:
the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with
the similar property, the so-called Horava-Lifshitz model, our construction
does not have any preferred direction. The dimension flow is rather achieved by
a rearrangement of the degrees of freedom. In this respect the number of
dimensions is deceptive. Some physical consequences are discussed.Comment: 20 pages + extensive appendix. 3 figure
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