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arXiv · hep-th/0108096

NC Branes and Hierarchies in Quantum Hall Fluids

A. El Rhalami·E. M. Sahraoui·E. H. Saidi
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Abstract

We develop the non commutative Chern-Simons gauge model analysis modeling the description of the hierarchical states of fractional quantum Hall fluids. For a generic level $n$ of the hierarchy, we show that the order parameter matrix $K_{ab}$ is given by $ θ^{-2}Tr(τ_a τ_b)$, where $\{τ_a, 1\leq a \leq n \}$ define a specific set of $n\times n$ matrices depending on the parameter $θ$ and the levels $l_a$ of the CS effective field theory. Our analysis predicts the existence of a third order tensor of order parameters $C_{abc}$ induced by the external magnetic field. It is shown that the $C_{abc}$'s are not new order parameters and are given by $θd_{abc}$, where $d_{abc}$ are numbers depending on the $l_a$'s. We also give the generalized quantum Hall soliton extending the one obtained in the case of the Laughlin state.

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A. El Rhalami, E. M. Sahraoui, E. H. Saidi. 2001-10-23. NC Branes and Hierarchies in Quantum Hall Fluids. https://doi.org/10.1088/1126-6708%2F2002%2F05%2F004

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