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

TL;DR

This paper develops a five-dimensional N=4 supersymmetric mechanics model describing an isospin particle interacting with a Yang monopole, derived via SU(2) Hamiltonian reduction of supermultiplet actions.

Contribution

It introduces a new supersymmetric mechanics model through SU(2) reduction, extending previous formulations to include interactions with Yang monopoles and generalizations.

Findings

Derived the five-dimensional N=4 supersymmetric mechanics with Yang monopole interaction.

Provided explicit Lagrangian and Hamiltonian formulations of the system.

Explored generalizations to more complex bosonic actions and hypermultiplet variants.

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.