Related papers: $\mathcal{N}{=}\,4$ supersymmetric $\mathrm{U}(2)$…
Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and…
We consider the spherical reduction of the rational Calogero model (of type $A_{n-1}$, without the center of mass) as a maximally superintegrable quantum system. It describes a particle on the $(n{-}2)$-sphere in a very special potential. A…
We present the first example of super Landau model with both N=4 worldline supersymmetry and non-trivial target space supersymmetry ISU(2|2). The model also reveals a hidden second N=4 supersymmetry which, together with the manifest one,…
We comment on the relationships between several supersymmetric lattice models; the ``orbifold lattice theory'' by Cohen-Kaplan-Katz-Unsal (CKKU), lattice regularization of the topological field theory by Sugino and the ``geometrical…
We provide a Lagrangian formulation of \Nf supersymmetric mechanics describing the motion of an isospin carrying particle on conformal to hyper-K\"{a}hler spaces in a non-Abelian background gauge field. In two examples we discuss in…
We construct two different Calogero-Sutherland type models with only two-body interactions in arbitrary dimensions. We obtain some exact wave functions, including the ground states, of these two models for arbitrary number of spinless…
In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…
We study N=4 supersymmetric quantum-mechanical many-body systems with M bosonic and 4M fermionic degrees of freedom. We also investigate the further restrictions of conformal and superconformal invariance. In particular, we construct…
We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-dimensional Minkowski spacetime, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description [1],…
We numerically study the SU(2)$\otimes$SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially…
It is shown that the previously known $N=3$ and $N=4$ superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the later case, by a contraction which depends on the central term, we obtain a…
We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable $S$-matrix theory with…
We address the construction of four-dimensional N=2 supersymmetric nonlinear sigma models on tangent bundles of arbitrary Hermitian symmetric spaces starting from projective superspace. Using a systematic way of solving the (infinite number…
We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the…
The existence of intimate relation between generalized statistics and supersymmetry is established by observation of hidden supersymmetric structure in pure parabosonic systems. This structure is characterized generally by a nonlinear…
The main result of this paper is the evidence of an explicit linearization of dynamical systems of Ruijsenaars-Schneider type and of the perturbations introduced by F. Calogero of these systems with all orbits periodic of same period.…
The degeneracy structure of the eigenspace of the N-particle Calogero-Sutherland model is studied from an algebraic point of view. Suitable operators satisfying SU(2) algebras and acting on the degenerate eigenspace are explicitly…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
Matrix models and related Spin-Calogero-Sutherland models are of major relevance in a variety of subjects, ranging from condensed matter physics to QCD and low dimensional string theory. They are characterized by integrability and exact…
Recently it was conjectured by Gibbons and Townsend that the large n limit of an N=4 superconformal extension of the n-particle Calogero model might provide a microscopic description of the extreme Reissner-Nordstrom black hole near the…