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

Carlos Leiva; Mikhail S. Plyushchay

doi:10.1016/j.physletb.2003.12.041

paper

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

arXiv:hep-th/0311150 · doi:10.1016/j.physletb.2003.12.041

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 $os p (2∣2) \oplus s u (2)$ . 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.

13 pages; comments and ref added; V.3: misprints corrected, journal version