A Super-flag Landau Model

We consider the quantum mechanics of a particle on the coset superspace SU(2|1)/[U(1)×U(1)], which is a super-flag manifold with SU(2)/U(1) ∼= S2 ‘body’. By incorporating the Wess-Zumino terms associated with the U(1) × 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).