Particle in a Self-Dual Dyon Background: Hidden Free Nature and Exotic Superconformal Symmetry

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;?) with ?=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. © 2014 American Physical Society.