Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids

Abstract

We study the spectrum of density fluctuations of Fractional Hall Fluids in the context of the noncommutative hidrodynamical model of Susskind. We show that, within the weak-field expansion, the leading correction to the noncommutative Chern--Simons Lagrangian (a Maxwell term in the effective action,) destroys the incompressibility of the Hall fluid due to strong UV/IR effects at one loop. We speculate on possible relations of this instability with the transition to the Wigner crystal, and conclude that calculations within the weak-field expansion must be carried out with an explicit ultraviolet cutoff at the noncommutativity scale. We point out that the noncommutative dipoles exactly match the spatial structure of the Halperin--Kallin quasiexcitons. Therefore, we propose that the noncommutative formalism must describe accurately the spectrum at very large momenta, provided no weak-field approximations are made. We further conjecture that the noncommutative open Wilson lines are `vertex operators' for the quasiexcitons.

20 pages, harvmac

References in corpus (4)

• Quantum Hall states as matrix Chern-Simons theory
• Quantum Hall Physics = Noncommutative Field Theory
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Absence of the Holographic Principle in Noncommutative Chern-Simons Theory

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• General Properties of Noncommutative Field Theories
• Matrix Model Description of Laughlin Hall States
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• Noncommutative Geometry and Fluid Dynamics
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• NC Effective Gauge Model for Multilayer FQH States
• Noncommutative fluid dynamics in the Kähler parametrization
• Exciton in Matrix Formulation of Quantum Hall Effect
• Higher derivative Chern-Simons extension in the noncommutative QED${}_3$
• Non-commutative massive unquenched ABJM
• Noncommutative geometry induced by spin effects
• Induced Chern-Simons action on noncommutative torus
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Plane waves in noncommutative fluids
• On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory
• Matrix oscillator and Laughlin Hall states
• Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation
• Renormalization Group Flow for Noncommutative Fermi Liquids