N=4 Supersymmetry and the BPST Instanton

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.

1+8 pages; v2: two references added, published version

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• N=4 chiral supermultiplet interacting with a magnetic field
• Supercharges in the HKT Supersymmetric Sigma Models
• Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics
• Symmetries of N=4 supersymmetric CP(n) mechanics
• N=2 supersymmetric S^2 -> CP^3 -> S^4 fibration viewed as superparticle mechanics
• N=4, d=1 Supersymmetric Hyper-Kaehler Sigma Models with Isospin Variables
• SU(2) reductions in N=4 multidimensional supersymmetric mechanics
• Superintegrable deformations of oscillator and Coulomb systems