Supersymmetric many-body Euler-Calogero-Moser model

We explicitly construct a supersymmetric $so(n)$ spin-Calogero model with an arbitrary even number $\mathcal{N}$ of supersymmetries. It features $\frac{1}{2}\mathcal{N}n(n+1)$ rather than $\mathcal{N}n$ fermionic coordinates and a very simple structure of the supercharges and the Hamiltonian. The latter, together with additional conserved currents, form an $osp(\mathcal{N}\mathrm{\mid }2)$ superalgebra. We provide a superspace description for the simplest case, namely $\mathcal{N}=2$ supersymmetry. The reduction to an $\mathcal{N}$-extended supersymmetric goldfish model is also discussed.