SU(2) reductions in N=4 multidimensional supersymmetric mechanics

Abstract

We perform an su(2) Hamiltonian reduction in the bosonic sector of the su(2)-invariant action for two free (4, 4, 0) supermultiplets. As a result, we get the five dimensional N=4 supersymmetric mechanics describing the motion of an isospin carrying particle interacting with a Yang monopole. We provide the Lagrangian and Hamiltonian descriptions of this system. Some possible generalizations of the action to the cases of systems with a more general bosonic action, a four-dimensional system which still includes eight fermionic components, and a variant of five-dimensional N=4 mechanics constructed with the help of the ordinary and twisted N=4 hypermultiplets were also considered.