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arXiv · hep-th/0404108

A Super-Flag Landau Model

Evgeny Ivanov·Luca Mezincescu·Paul K. Townsend
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Abstract

We consider the quantum mechanics of a particle on the coset superspace $SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated with the $U(1)\times U(1)$ stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of $SU(2|1)$.

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Evgeny Ivanov, Luca Mezincescu, Paul K. Townsend. 2004-04-18. A Super-Flag Landau Model. https://doi.org/10.1142/9789812775344_0054

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