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 TMF, 2008, Volume 154, Number 3, Pages 409–423 (Mi tmf6179)

Supersymmetrizing Landau models

E. A. Ivanov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: We review recent progress in constructing and studying superextensions of the Landau problem of a quantum particle on a plane in a uniform magnetic field and also its Haldane $S^2$ generalization. We focus on the planar super Landau models that are invariant under the inhomogeneous supergroup $ISU(1 | 1)$, a contraction of the supergroup $SU(2 | 1)$, and are minimal superextensions of the original Landau model. Their significant common feature is the presence of a hidden dynamical worldline $\mathcal N=2$ supersymmetry, which exists at both the classical and quantum levels and is revealed most naturally in 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 $\mathcal N=2$ supersymmetry becomes explicit.

Keywords: supersymmetry, superfield, supergroup, particle

DOI: https://doi.org/10.4213/tmf6179

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English version:
Theoretical and Mathematical Physics, 2008, 154:3, 349–361

Bibliographic databases:

Citation: E. A. Ivanov, “Supersymmetrizing Landau models”, TMF, 154:3 (2008), 409–423; Theoret. and Math. Phys., 154:3 (2008), 349–361

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf6179
• https://doi.org/10.4213/tmf6179
• http://mi.mathnet.ru/eng/tmf/v154/i3/p409

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Hasebe K., “Hyperbolic supersymmetric quantum Hall effect”, Phys. Rev. D, 78:12 (2008), 125024, 13 pp.
2. Beylin A., Curtright T.L., Ivanov E., Mezincescu L., Townsend P.K., “Unitary spherical super-Landau models”, J. High Energy Phys., 2008, no. 10, 069, 46 pp.
3. Ben Geloun J., Govaerts J., Scholtz F.G., “The $\mathscr N=1$ supersymmetric Landau problem and its supersymmetric Landau level projections: the $\mathscr N=1$ supersymmetric Moyal-Voros superplane”, J. Phys. A, 42:49 (2009), 495203, 18 pp.
4. Ivanov E., Niederle J., “Biharmonic superspace for $N=4$ mechanics”, Phys. Rev. D, 80:6 (2009), 065027, 23 pp.
5. Ivanov E., Konyushikhin M., “N=4, 3D supersymmetric quantum mechanics in a non-Abelian monopole background”, Phys. Rev. D, 82:8 (2010), 085014, 8 pp.
6. Beylin A., Curtright T., Ivanov E., Mezincescu L., “Generalized $\mathscr N=2$ super Landau models”, J. High Energy Phys., 2010, no. 4, 091, 27 pp.
7. Hasebe K., “Supersymmetric quantum hall liquid with a deformed supersymmetry”, Phys. Atomic Nuclei, 73:2 (2010), 345–351
8. Ivanov E.A., “Super-Landau models: unitarity and hidden symmetries”, Phys. Atomic Nuclei, 73:2 (2010), 352–358
9. Ivanov E.A., “Generalized Landau Models with N=2 Worldline Supersymmetry”, Phys. Atom. Nuclei, 75:10 (2012), 1227–1233
10. Bychkov V., Ivanov E., “N=4 Supersymmetric Landau Models”, Nucl. Phys. B, 863:1 (2012), 33–64
11. V. S. Bychkov, E. A. Ivanov, “The $\mathcal N{=}4$ super Landau models”, Theoret. and Math. Phys., 174:1 (2013), 40–51
12. Goykhman M., Ivanov E., Sidorov S., “Super Landau Models on Odd Cosets”, Phys. Rev. D, 87:2 (2013), 025026
13. Ivanov E.A., “Gauge fields, nonlinear realizations, supersymmetry”, Phys. Part. Nuclei, 47:4 (2016), 508–539
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