In previous papers we solved the Landau problems, indexed by 2M, for a particle on the "superflag" SU(2|1)/[U(1) × U(1)], the M ≤ 0 case being equivalent to the Landau problem for a particle on the "supersphere" SU(2|1)/[U(1|1)]. Here we solve these models in the planar limit. For M ≤ 0 we have a particle on the complex superplane ℂ(1|1); its Hilbert space is the tensor product of that of the Landau model with the 4-state space of a ''fermionic'' Landau model. Only the lowest level is ghost-free, but for M > 0 there are no ghosts in the first [2M]+1 levels. When 2M is an integer, the (2M+1)th level states form short supermultiplets as a consequence of a fermionic gauge invariance analogous to the ''kappa-symmetry'' of the superparticle.
- Integrable Equations in Physics
ASJC Scopus subject areas
- Nuclear and High Energy Physics