N=4 Supersymmetry and the BPST Instanton

TL;DR

This paper develops the Lagrangian and Hamiltonian formulations for N=4 supersymmetric particles moving on conformally flat four-manifolds with SO(4) symmetry, incorporating BPST instanton fields and auxiliary fermionic multiplets.

Contribution

It constructs explicit supersymmetric models with BPST instanton backgrounds, including various conformally flat geometries, and clarifies the role of isospin and auxiliary fermionic degrees of freedom.

Findings

Derived explicit on-shell component actions matching recent proposals

Unified description of supersymmetric particles on different geometries

Clarified the structure of isospin and auxiliary fermions in the models

Abstract

In this paper we construct the Lagrangian and Hamiltonian formulations of N=4 supersymmetric systems describing the motion of an isospin particle on a conformally flat four-manifold with SO(4) isometry carrying the non-Abelian field of a BPST instanton. The conformal factor can be specified to yield various particular systems, such as superconformally invariant mechanics as well as a particle on the four-sphere, the pseudosphere or on R x S^3. The isospin degrees of freedom arise as bosonic components of an additional fermionic N=4 supermultiplet, whose other components are rendered auxiliary by a nonlocal redefinition. Our on-shell component action coincides with the one recently proposed in arXiv:0912.3289.