Spinning extensions of $D(2,1;\alpha )$ superconformal mechanics

Abstract

As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup $D(2,1;\alpha )$, which is the most general $\mathcal{N}=4$ supersymmetric extension of the conformal group in one spatial dimension. We construct novel spinning extensions of $D(2,1;\alpha )$ 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 symmetric Euler top, which represents the spin degrees of freedom. This particle moves either on the two-sphere, optionally in the external field of a Dirac monopole, or in the SU(2) group manifold. Each case is proven to be superintegrable, and explicit solutions are given.

arXiv comment1+14 pages

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Cited by in corpus (5)

• Hidden symmetry and (super)conformal mechanics in a monopole background
• Superfield approach to higher derivative N=1 superconformal mechanics
• Bianchi type-V spinning particle on 2-sphere
• Spinning particles on 2-sphere in accord with the Bianchi classification
• SU$(2|1)$ supersymmetric spinning models of chiral superfields