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

  • Anton Galajinsky
  • Olaf LechtenfeldEmail author
Open Access
Regular Article - Theoretical Physics


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.


Extended Supersymmetry Integrable Field Theories Classical Theories of Gravity Conformal and W Symmetry 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.School of PhysicsTomsk Polytechnic UniversityTomskRussia
  2. 2.Institut für Theoretische Physik and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany

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