Higher-Dimensional Quantum Hall Effect in String Theory

Abstract

We construct a string theory realization of the 4+1d quantum Hall effect recently discovered by Zhang and Hu. The string theory picture contains coincident D4-branes forming an S^4 and having D0-branes (i.e. instantons) in their world-volume. The charged particles are modelled as string ends. Their configuration space approaches in the large n limit a CP^3, which is an S^2 fibration over S^4, the extra S^2 being made out of the Chan-Paton degrees of freedom. An alternative matrix theory description involves the fuzzy four-sphere. We also find that there is a hierarchy of quantum Hall effects in odd-dimensional spacetimes, generalizing the known cases in 2+1d and 4+1d.

13 pages, 2 figures, references added

References in corpus (17)

• Quantum Hall states as matrix Chern-Simons theory
• Fluxbranes in String Theory
• On spherical harmonics for fuzzy spheres in diverse dimensions
• Non-abelian Brane Intersections
• Quantum Hall Physics = Noncommutative Field Theory
• Flux-branes and the Dielectric Effect in String Theory
• Higher Dimensional Geometries from Matrix Brane constructions
• Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
• Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions
• Gravitating Fluxbranes
• Finite Noncommutative Chern-Simons with a Wilson Line and the Quantum Hall Effect
• D-brane Dynamics and the Quantum Hall Effect
• NC Branes and Hierarchies in Quantum Hall Fluids
• Supergravity Fluxbranes in Various Dimensions
• Fluxbranes from p-branes
• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
• On the stability of the Quantum Hall soliton

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• Quantum Hall Effect on Odd Spheres
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• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Theory of Four-dimensional Fractional Quantum Hall States
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