SUSY QuantumHall Effect on Non-Anti-Commutative Geometry
نویسنده
چکیده
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 effects on supermanifolds. On each of supersphere and superplane, we investigate SUSY Landau problem and explicitly construct SUSY extensions of the Laughlin wavefunction and topological excitations. The non-anticommutative geometry naturally emerges in the lowest Landau level and brings particular physics to the SUSY quantum Hall effect. We show 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.
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