Spinning extensions of D (2 ; 1; α) superconformal mechanics

Abstract

As is known, any realization of SU(2) in the phase space of a dynamical sys- tem can be generalized to accommodate the exceptional supergroup D (2 ; 1;α ), which is the most general N = 4 supersymmetric extension of the conformal group in one spatial dimension. We construct novel spinning extensions of D (2 ; 1;α ) superconformal mechanics by adjusting the SU(2) generators associated with the relativistic spinning particle coupled to a spherically symmetric Einstein-Maxwell background. The angular sector of the full superconformal system corresponds to the orbital motion of a particle coupled to a sym- metric Euler top, which represents the spin degrees of freedom. This particle moves either on the two-sphere, optionally in the external eld of a Dirac monopole, or in the SU(2) group manifold. Each case is proven to be superintegrable, and explicit solutions are given.