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

Five-dimensional N = 4 Supersymmetric Mechanics

We perform an su(2) Hamiltonian reduction in the bosonic sector of the su(2)-invariant action for two free (4, 4, 0) supermultiplets. As a result, we get the five dimensional N = 4 supersymmetric mechanics describing the motion of an isospin carrying particle interacting with a Yang monopole. Some possible generalizations of the action to the cases of systems with a more general bosonic action constructed with the help of ordinary and twisted N = 4 hypermultiplets are considered

N=8 supersymmetric mechanics on the sphere S^3

Starting from quaternionic N=8 supersymmetric mechanics we perform a reduction over a bosonic radial variable, ending up with a nonlinear off-shell supermultiplet with three bosonic end eight fermionic physical degrees of freedom. The geometry of the bosonic sector of the most general sigma-model type action is described by an arbitrary function obeying the three dimensional Laplace equation on the sphere S^3. Among the bosonic components of this new supermultiplet there is a constant which gives rise to potential terms. After dualization of this constant one may come back to the supermultiplet with four physical bosons. However, this new supermultiplet is highly nonlinear. The geometry of the corresponding sigma-model action is briefly discussed.Comment: 9 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-

Symmetries of N=4 supersymmetric CP(n) mechanics

We explicitly constructed the generators of $SU(n+1)$ group which commute with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the background U(n) gauge fields. The corresponding Hamiltonian can be represented as a direct sum of two Casimir operators: one Casimir operator on $SU(n+1)$ group contains our bosonic and fermionic coordinates and momenta, while the second one, on the SU(1,n) group, is constructed from isospin degrees of freedom only.Comment: 10 pages, PACS numbers: 11.30.Pb, 03.65.-w; minor changes in Introduction, references adde