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

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

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.

Keywords

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

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    G.W. Gibbons and P.K. Townsend, Black holes and Calogero models, Phys. Lett. B 454 (1999) 187 [hep-th/9812034] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  2. [2]
    E. Ivanov, S. Krivonos and O. Lechtenfeld, N = 4, d = 1 supermultiplets from nonlinear realizations of D(2,1: alpha), Class. Quant. Grav. 21 (2004) 1031 [hep-th/0310299] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    A. Galajinsky, \( \mathcal{N} \) = 4 superconformal mechanics from the SU(2) perspective, JHEP 02 (2015) 091 [arXiv:1412.4467] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    A. Galajinsky, Couplings in D(2, 1; α) superconformal mechanics from the SU(2) perspective, JHEP 03 (2017) 054 [arXiv:1702.01955] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    S. Fedoruk and E. Ivanov, New realizations of the supergroup D(2, 1; α) in \( \mathcal{N} \) = 4 superconformal mechanics, JHEP 10 (2015) 087 [arXiv:1507.08584] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    S. Fedoruk, E. Ivanov and O. Lechtenfeld, New D(2, 1, α) mechanics with spin variables, JHEP 04 (2010) 129 [arXiv:0912.3508] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Fedoruk, E. Ivanov and O. Lechtenfeld, OSp(4|2) superconformal mechanics, JHEP 08 (2009) 081 [arXiv:0905.4951] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Krivonos and O. Lechtenfeld, Many-particle mechanics with D(2,1:alpha) superconformal symmetry, JHEP 02 (2011) 042 [arXiv:1012.4639] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    G. d’Ambrosi, S. Satish Kumar and J.W. van Holten, Covariant hamiltonian spin dynamics in curved space-time, Phys. Lett. B 743 (2015) 478 [arXiv:1501.04879] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  10. [10]
    Z.-Y. Fan and X. Wang, Construction of regular black holes in general relativity, Phys. Rev. D 94 (2016) 124027 [arXiv:1610.02636] [INSPIRE].ADSGoogle Scholar
  11. [11]
    G. Antoniou and M. Feigin, Supersymmetric V-systems, JHEP 02 (2019) 115 [arXiv:1812.02643] [INSPIRE].CrossRefGoogle Scholar
  12. [12]
    S. Krivonos, O. Lechtenfeld and A. Sutulin, N-extended supersymmetric Calogero models, Phys. Lett. B 784 (2018) 137 [arXiv:1804.10825] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    T. Hakobyan, S. Krivonos, O. Lechtenfeld and A. Nersessian, Hidden symmetries of integrable conformal mechanical systems, Phys. Lett. A 374 (2010) 801 [arXiv:0908.3290] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    T. Hakobyan, O. Lechtenfeld, A. Nersessian and A. Saghatelian, Invariants of the spherical sector in conformal mechanics, J. Phys. A 44 (2011) 055205 [arXiv:1008.2912] [INSPIRE].ADSzbMATHGoogle Scholar

Copyright information

© 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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