Supersymmetrizing Landau Models
Abstract
This is an overview of recent progress in constructing and studying superextensions of the Landau problem of a quantum particle on a plane in the uniform magnetic field, as well as of its Haldane's S2 generalization ( hep-th/0311159, hep-th/0404108, hep-th/0510019, hep-th/0612300). The main attention is paid to the planar super Landau models which are invariant under the inhomogeneous supergroup ISU(1|1), a contraction of the supergroup SU(2|1), and provide minimal superextensions of the original Landau model. Their common notable feature is the presence of a hidden dynamical worldline N=2 supersymmetry. It exists at the classical and quantum levels and is revealed most naturally while passing to the new invariant inner products in the space of quantum states in order to make the norms of all states positive. For one of the planar models, the superplane Landau model, we present an off-shell worldline superfield formulation in which the N=2 supersymmetry gets manifest.