(The) dynamical supersymmetry of the singular point magnetic vortex

Abstract

It is shown that the Pauli-hamiltonian for a spin-$\frac{1}{2}$ charged particle interacting with a magnetic point vortex has a dynamical super $spl^*$(2,1) symmetry, which is the Wick-rotated super spl(2,1) symmetry, on the plane except at the origin where the magnetic vortex is placed. Using this symmetry, the spectrum and the wave functions are constructed. We have considered most general constructions of Calabi-Yau manifolds from complete intersections in products of weighted complex projective spaces. Some of them are closely related to the N = 2 Landau-Ginzburg superconformal descriptions of string compactifications