NC Branes and Hierarchies in Quantum Hall Fluids

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 ${\theta }^{-2}Tr({\tau }_a{\tau }_b)$, where $\{{\tau }_a,1\le a\le n\}$ define a specific set of $n\times n$ matrices depending on the parameter $\theta$ 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 $\theta d_{abc}$, 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.

22pages, 4 figures, Latex

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Cited by in corpus (14)

• Higher-Dimensional Quantum Hall Effect in String Theory
• D-string fluid in conifold: I. Topological gauge model
• D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
• Noncommutative Geometry and Fluid Dynamics
• Noncommutative fluid dynamics in the Snyder space-time
• Algebraic Geometry Realization of Quantum Hall Soliton
• Embedding Fractional Quantum Hall Solitons in M-theory Compactifications
• NC Effective Gauge Model for Multilayer FQH States
• Noncommutative fluid dynamics in the Kähler parametrization
• Brane Realizations of Quantum Hall Solitons and Kac-Moody Lie Algebras
• A Matrix Model for Bilayered Quantum Hall Systems
• Plane waves in noncommutative fluids
• Quantum fluids in the Kaehler parametrization
• Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation