### 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 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.

Original language | English |
---|---|

Article number | 69 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2019*(3), [69]. https://doi.org/10.1007/JHEP03(2019)069

**Spinning extensions of D(2, 1; α) superconformal mechanics.** / Galajinsky, Anton; Lechtenfeld, Olaf.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2019, no. 3, 69. https://doi.org/10.1007/JHEP03(2019)069

}

TY - JOUR

T1 - Spinning extensions of D(2, 1; α) superconformal mechanics

AU - Galajinsky, Anton

AU - Lechtenfeld, Olaf

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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 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.

AB - 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 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.

KW - Classical Theories of Gravity

KW - Conformal and W Symmetry

KW - Extended Supersymmetry

KW - Integrable Field Theories

UR - http://www.scopus.com/inward/record.url?scp=85063051622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063051622&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2019)069

DO - 10.1007/JHEP03(2019)069

M3 - Article

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 69

ER -