Related papers: K\"ahler geometry for $su(1,N|M)$-superconformal m…
We propose the description of superintegrable models with dynamical $so(1.2)$ symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the non-compact analog of…
We construct the $\mathcal{N}=8$ supersymmetric mechanics with potential term whose configuration space is the special K\"ahler manifold of rigid type and show that it can be viewed as the K\"ahler counterpart of $\mathcal{N}=4$ mechanics…
The geometric models of N=4 supersymmetric mechanics with $(2d.2d)_{\DC}$-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models by Alvarez-Gaum\'e and…
We present two examples of SUSY mechanics related with K\"ahler geometry. The first system is the N=4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N=2 SUSY mechanics whose phase space is the…
We consider supersymmetric quantum mechanics on a K\"{a}hler cone, regulated via a suitable resolution of the conical singularity. The unresolved space has a $\mathfrak{u}(1,1|2)$ superconformal symmetry and we propose the existence of an…
We take a fresh look at the relation between generalised K\"ahler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield…
We construct a new version of the worldline SU(2|1) superspace as a deformation of the standard N =4, d=1 superspace and show that it naturally provides off- and on-shell description of general supersymmetric K\"ahler oscillator model…
Based on the systematic Hamiltonian and superfield approaches we construct the deformed $\mathcal{N}=4,8$ supersymmetric mechanics on K\"ahler manifolds interacting with constant magnetic field, and study their symmetries. At first we…
We use the manifestly N=2 supersymmetric, off-shell, harmonic (or twistor) superspace approach to solve the constraints implied by four-dimensional N=2 superconformal symmetry on the N=2 non-linear sigma-model target space, known as the…
We introduce a new superintegrable Kepler-Coulomb system with non-central terms in $N$-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates.…
Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some…
Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1,1|2) in mechanics. Remarking that SU(1,1|2) is a particular member of a chain of supergroups SU(1,1|n) parametrized by an integer n,…
We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…
We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various…
By imposing global supersymmetry and scale invariance we construct an N=8 superconformal mechanical system based on the inhomogeneous (2,8,6) linear multiplet. The unique action describes a special K"ahler sigma model with a Calogero-type…
In this work we extend Onofri and Perelomov's coherent states methods to the recently introduced $OSp(1/2)$ coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely the homogeneous…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle…
The issue of constructing an N=4 superconformal mechanics in one dimension is reconsidered with a special emphasis put on the realizations of the su(2)-subalgebra in the full su(1,1|2)-superalgebra. New dynamical realizations of su(1,1|2)…
Using the worldline SU(2|1) superfield approach, we construct N=4 superconformally invariant actions for the d=1 multiplets (1, 4, 3) and (2, 4, 2). The SU(2|1) superfield framework automatically implies the trigonometric realization of the…