SUSY Quantum Hall Effect on NonAntiCommutative Geometry
Abstract
We review the recent developments of the SUSY quantum Hall effect [hepth/0409230, hepth/0411137, hepth/0503162, hepth/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 nonanticommutative 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 MooreRead states. Based on the chargeflux duality, we also develop a ChernSimons effective field theory for the SUSY quant!
um Hall effect.
 Publication:

SIGMA
 Pub Date:
 February 2008
 DOI:
 10.3842/SIGMA.2008.023
 arXiv:
 arXiv:0710.0216
 Bibcode:
 2008SIGMA...4..023H
 Keywords:

 quantum hall effect;
 nonanticommutative geometry;
 supersymmetry;
 Hopf map;
 Landau problem;
 ChernSimons theory;
 chargeflux duality;
 High Energy Physics  Theory;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect
 EPrint:
 This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 2430, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/