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Nahm equations in supersymmetric mechanics

  • Sergey Fedoruk
  • Evgeny Ivanov
  • Olaf LechtenfeldEmail author
Article

Abstract

We elaborate on a novel model of \( \mathcal{N} = {4} \) supersymmetric mechanics with extra spin variables. A dynamical linear (1,4,3) multiplet is coupled to a “semi-dynamical” linear (3,4,1) multiplet representing spin degrees of freedom in a Wess-Zumino action. The unique coupling of these two multiplets relates the dynamical bosonic variable to an arbitrary harmonic function of the SU(2) triplet of spin variables. As we prove at the classical and quantum level, \( \mathcal{N} = {4} \) supersymmetry is equivalent to the Nahm equations for the spin variables, with the dynamical boson as evolution parameter. We treat in detail the one- and two-monopole as well as some special multi-monopole configurations. While one monopole exhibits superconformal OSp(4|2) symmetry and was worked out previously, only \( \mathcal{N} = {4} \) , d = 1 Poincaré supersymmetry survives for multi-monopole configurations.

Keywords

Extended Supersymmetry Solitons Monopoles and Instantons Field Theories in Lower Dimensions Superspaces 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Sergey Fedoruk
    • 1
  • Evgeny Ivanov
    • 1
  • Olaf Lechtenfeld
    • 2
    Email author
  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJINRDubnaRussia
  2. 2.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany

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