N=4 Supersymmetry and the BPST Instanton

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.Comment: 1+8 pages; v2: two references added, published versio

Extended supersymmetric multiparticle Euler-Calogero-Moser model

We review the construction of supersymmetric extension of the n-particle Euler-Calogero-Moser model within the Hamiltonian approach [1]. The main feature of the proposed supersymmetrization method is that it is automatically adapted for a model with an arbitrary even number of supersymmetries. It is shown that the number of fermions that must be used in this construction is 1/2N n(n+1). We demonstrate that the resulting supersymmetric system is dynamically invariant with respect to the superconformal group and give the explicit realization of its generators in terms of the conserved currents. For the simplest case of the supersymmetric n-particle Euler-Calogero-Moser model we provide its description in superspace by using the corresponding constrained superfields. © 2019 Published under licence by IOP Publishing Ltd

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

We construct a Lagrangian formulation of N = 4 supersymmetric mechanics with hyper-Kähler sigma models in a bosonic sector in a non-Abelian background gauge field. The resulting action includes a wide class of N = 4 supersymmetric mechanics describing the motion of an isospin-carrying particle over spaces with non-trivial geometry. In two examples that we discuss in details, the background fields are identified with the field of BPST instantons in flat and Taub-NUTspaces