N=4, d=1 Supersymmetric Hyper-Kaehler Sigma Models and Non-Abelian Monopole Background

TL;DR

This paper develops a Lagrangian framework for \\Nf supersymmetric mechanics involving hyper-Kähler sigma models in non-Abelian gauge backgrounds, illustrating with instanton solutions in specific geometries.

Contribution

It introduces a new Lagrangian formulation for supersymmetric mechanics with hyper-Kähler sigma models in non-Abelian backgrounds, including explicit instanton solutions.

Findings

Constructed a Lagrangian for \\Nf supersymmetric mechanics with hyper-Kähler sigma models.

Identified background fields with BPST instantons in flat and Taub-NUT spaces.

Demonstrated the motion of isospin-carrying particles in non-trivial geometries.

Abstract

We construct a Lagrangian formulation of \Nf supersymmetric mechanics with hyper-K\"{a}hler sigma models in a bosonic sector in the non-Abelian background gauge field. The resulting action includes a wide class of \Nf supersymmetric mechanics describing the motion of an isospin-carrying particle over spaces with non-trivial geometry. In two examples we discuss in details, the background fields are identified with the field of BPST instantons in the flat and Taub-NUT spaces.