Three dimensionalN=4supersymmetric mechanics with Wu-Yang monopole

Abstract

We propose Lagrangian and Hamiltonian formulations of a $N=4$ supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific scalar potential. This additional potential is completely fixed by $N=4$ supersymmetry, and in the simplest case of flat metrics it coincides with that which provides the existence of the Runge-Lenz vector for the bosonic subsector. The isospin degrees of freedom are described on the Lagrangian level by bosonic auxiliary variables forming $N=4$ supermultiplet with additional, also auxiliary, fermions. Being quite general, the constructed systems include such interesting cases as $N=4$ superconformally invariant systems with Wu-Yang monopole, the particles living in the flat ${\mathbb{R}}^{3}$ and in the $\mathbb{R}\ifmmode\times\else\texttimes\fi{}{\mathbb{S}}^{2}$ spaces and interacting with the monopole, and also the particles moving on three-dimensional sphere and pseudosphere with the Wu-Yang monopole sitting in the center. The superfield Lagrangian description of these systems is so simple that one could wonder to see how all couplings and the proper coefficients arise while passing to the component action.