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

Abstract

We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r^2 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;alpha) with alpha=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 Z_2-grading operator. The odd part of the nonlinear superalgebra comprises a complete set of 24=2 x 3 x 4 fermionic generators. Here a usual duplication comes from the Z_2-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.

23 pages; refs and comments added, version to appear in Phys. Rev. D

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• OSp(4|2) Superconformal Mechanics
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Multi-center MICZ-Kepler system, supersymmetry and integrability
• Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• Mechanics and Quantum Supermechanics of a Monopole Probe Including a Coulomb Potential
• Applications of chiral supersymmetry for spin fields in self-dual backgrounds

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