A Super-Flag Landau Model

We consider the quantum mechanics of a particle on the coset superspace $SU(2\mathrm{\mid }1)\mathrm{/}[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)\mathrm{/}U(1)\cong S^2$ `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 $SU(2\mathrm{\mid }1)$.