Generalized N = 2 Super Landau Models

Understand

We generalize previous results for the superplane Landau model to exhibit an explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any two-dimensional manifold.

• Starting from an off-shell N = 2 superfield formalism, we discuss the quantization procedure in the general case characterized by two independent potentials on the manifold and show that the relevant Hamiltonians are factorizable.
• In the restricted case when both the Gauss curvature and the magnetic field are constant over the manifold and, as a consequence, the underlying potentials are related, the Hamiltonians admit infinite series of factorization chains implying the integrability of the associated systems.
• We explicitly determine the spectrum and eigenvectors for the particular model with CP^1 as the bosonic manifold.