Jain States in a Matrix Theory of the Quantum Hall Effect

Abstract

The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension of Susskind's noncommutative approach. The theory describes D0-branes, nonrelativistic particles with matrix coordinates and gauge symmetry, that realize a matrix generalization of the quantum Hall effect. Matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the expected Laughlin and Jain hierarchical states. The Jain composite-fermion construction follows by gauge invariance via the Gauss law constraint. In the limit of commuting, ``normal'' matrices the theory reduces to eigenvalue coordinates that describe realistic electrons with Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier noncommutative approaches and could provide another effective theory of the fractional Hall effect.

arXiv comment35 pages, 3 figures

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• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
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• Lowest Landau level theory of the bosonic Jain states
• ADHM and the 4d Quantum Hall Effect
• Edge excitations of the Chern Simons matrix theory for the FQHE
• A note on the topological order of noncommutative Hall fluids
• Non-commutative massive unquenched ABJM
• Vortex description of quantum Hall ferromagnets
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Semiclassical Droplet States in Matrix Quantum Hall Effect
• Twisted Conformal Field Theories and Morita equivalence
• Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons theory
• Paired quantum Hall states on noncommutative two-tori
• Hierarchy Construction of Quantum Hall States and Non-Commutative Chern-Simons Theory