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; α), 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; 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 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.
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ArXiv ePrint: 1902.06851
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Galajinsky, A., Lechtenfeld, O. Spinning extensions of D(2, 1; α) superconformal mechanics. J. High Energ. Phys. 2019, 69 (2019). https://doi.org/10.1007/JHEP03(2019)069
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DOI: https://doi.org/10.1007/JHEP03(2019)069