2006/10/25 by Andrea Cappelli, Ivan Dario Jimenez Rodriguez, Ivan D. Rodriguez · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum and electron transport phenomena #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/12/056
published as JHEP0612:056,2006 · 35 pages, 3 figures
arxiv created 2006/10/25 · openalex publication_date 2006/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.