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Particle in a self-dual dyon background: Hidden free nature and exotic superconformal symmetry

Mikhail S. Plyushchay1,* and Andreas Wipf2,†

  • 1Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile
  • 2Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany

  • *mikhail.plyushchay@usach.cl
  • †wipf@tpi.uni-jena.de
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Phys. Rev. D 89, 045017 – Published 25 February, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.045017

Abstract

We show that a nonrelativistic particle in a combined field of a magnetic monopole and 1/r2 potential reveals a hidden, partially free dynamics when the strength of the central potential and the charge-monopole coupling constant are mutually fitted to each other. In this case the system admits both a conserved Laplace-Runge-Lenz vector and a dynamical conformal symmetry. The supersymmetrically extended system corresponds then to a background of a self-dual or anti-self-dual dyon. It is described by a quadratically extended Lie superalgebra D(2,1;α) with α=1/2, in which the bosonic set of generators is enlarged by a generalized Laplace-Runge-Lenz vector and its dynamical integral counterpart related to Galilei symmetry, as well as by the chiral Z2-grading operator. The odd part of the nonlinear superalgebra comprises a complete set of 24=2×3×4 fermionic generators. Here a usual duplication comes from the Z2-grading structure; the second factor can be associated with a triad of scalar integrals—the Hamiltonian, the generator of special conformal transformations, and the squared total angular momentum vector, while the quadruplication is generated by a chiral spin vector integral which exits due to the (anti-)self-dual nature of the electromagnetic background.

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Phys. Rev. D 89, 045017– Published 25 February, 2014
  • Received 18 November 2013

© 2014 American Physical Society

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