Non-commutative Chern-Simons for the Quantum Hall System and Duality

Details Non-commutative Chern-Simons for the Quantum Hall System and Duality Non-commutative Chern-Simons for the Quantum Hall System and Duality

2002-05-30

arxiv.org/abs/cond-mat/0205653v1

Nucl.Phys. B642 (2002) 483-500

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

21 pages (preprint), 3 figures

Scientific paper

The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of Chern-Simons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.

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