Symmetries of deformed supersymmetric mechanics on Kahler manifolds

Based on the systematic Hamiltonian and superfield approaches, we construct the deformed N = 4, 8 supersymmetric mechanics on Kahler manifolds interacting with a constant magnetic field and study their symmetries. First, we construct the deformed N = 4, 8 supersymmetric Landau problem via the minimal coupling of standard (undeformed) N = 4, 8 supersymmetric free particle systems on a Kahler manifold with a constant magnetic field. We show that the initial "flat" supersymmetries are necessarily deformed to SU(2 vertical bar 1) and SU(4 vertical bar 1) supersymmetries, with the magnetic field playing the role of a deformation parameter, and that the resulting systems inherit all the kinematical symmetries of the initial ones. Then we construct SU(2 vertical bar 1) supersymmetric Kahler oscillators and find that they include, in particular cases, the harmonic oscillator models on complex Euclidian and complex projective spaces, as well as super-integrable deformations thereof, viz. C-N-Smorodinsky-Wintemitz and CPN-Rosochatius systems. We show that the supersymmetric extensions proposed inherit all the kinematical symmetries of the initial bosonic models. They also inherit, at least in the case of the C-N systems, hidden (nonkinematical) symmetries. The superfield formulation of these supersymmetric systems is presented, based on the worldline SU(2 vertical bar 1) and SU(4 vertical bar 1) superspace formalisms.