Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 023, 21 pages      arXiv:0710.0216      http://dx.doi.org/10.3842/SIGMA.2008.023
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry

Kazuki Hasebe
Department of General Education, Takuma National College of Technology, Takuma-cho, Mitoyo-city, Kagawa 769-1192, Japan

Received October 01, 2007, in final form February 07, 2008; Published online February 22, 2008

Abstract
We review the recent developments of the SUSY quantum Hall effect [hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007, arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on supermanifolds. On each of supersphere and superplane, we investigate SUSY Landau problem and explicitly construct SUSY extensions of Laughlin wavefunction and topological excitations. The non-anti-commutative geometry naturally emerges in the lowest Landau level and brings particular physics to the SUSY quantum Hall effect. It is shown that SUSY provides a unified picture of the original Laughlin and Moore-Read states. Based on the charge-flux duality, we also develop a Chern-Simons effective field theory for the SUSY quantum Hall effect.

Key words: quantum hall effect; non-anti-commutative geometry; supersymmetry; Hopf map; Landau problem; Chern-Simons theory; charge-flux duality.

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