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.

35 pages, 3 figures

References in corpus (3)

• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Matrix models and growth processes: from viscous flows to the quantum Hall effect
• Hamiltonian Theories of the FQHE

Cited by in corpus (6)

• A note on the topological order of noncommutative Hall fluids
• 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
• Hierarchy Construction of Quantum Hall States and Non-Commutative Chern-Simons Theory