N=4, d=1 Supersymmetric Hyper-Kaehler Sigma Models with Isospin Variables

TL;DR

This paper develops a supersymmetric mechanics model for particles with isospin on hyper-Kähler spaces, incorporating non-Abelian gauge fields, with explicit examples involving BPST instantons in flat and Taub-NUT geometries.

Contribution

It introduces a new Lagrangian formulation for N=4 supersymmetric isospin particles on hyper-Kähler manifolds with non-Abelian gauge backgrounds, including explicit instanton solutions.

Findings

Constructed explicit supersymmetric models with isospin variables.

Identified non-Abelian gauge backgrounds as BPST instantons.

Analyzed particle dynamics on hyper-Kähler spaces with instanton fields.

Abstract

We provide a Lagrangian formulation of \Nf supersymmetric mechanics describing the motion of an isospin carrying particle on conformal to hyper-K\"{a}hler spaces in a non-Abelian background gauge field. In two examples we discuss in details, this background field is identified with the field of BPST instantons in the flat and Taub-NUT spaces.