Second Hopf map and supersymmetric mechanics with Yang monopole

TL;DR

This paper introduces a reduction method using the second Hopf map to derive five-dimensional supersymmetric systems with SU(2) Yang monopoles from eight-dimensional N=8 supersymmetric mechanics, highlighting symmetry properties.

Contribution

It develops a Lagrangian reduction procedure based on the second Hopf map for supersymmetric mechanics involving Yang monopoles, extending the understanding of symmetry in such systems.

Findings

Reduced systems exhibit N=5 or N=4 supersymmetry

Invariance under supersymmetry generators and BRST charge

Successful reduction from 8D to 5D supersymmetric models

Abstract

We propose to use the second Hopf map for the reduction (via SU(2) group action) of the eight-dimensional N=8 supersymmetric mechanics to five-dimensional supersymmetric systems specified by the presence of an SU(2) Yang monopole. For our purpose we develop the relevant Lagrangian reduction procedure. The reduced system is characterized by its invariance under the N=5 or N=4 supersymmetry generators (with or without an additional conserved BRST charge operator) which commute with the su(2) generators.