Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole

TL;DR

This paper uncovers a nonlinear superconformal symmetry in a fermion-monopole system, revealing a complex algebraic structure that generalizes known superalgebras and introduces new insights into the system's integrals of motion.

Contribution

It identifies a nonlinear superalgebra structure in the fermion-monopole system, extending the understanding of its symmetries beyond traditional linear superalgebras.

Findings

The integrals of motion generate a nonlinear superalgebra.

The algebra includes a central charge related to angular momentum.

The system exhibits a nonlinear supersymmetry with a grading operator.

Abstract

We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z_2-graded Poisson, or quantum super- algebra, which may be treated as a nonlinear generalization of the $osp(2|2)\oplus su(2)$. In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2|2) spin operator. As an odd integral, the osp(2|2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra.