${\cal N}$-extended supersymmetric Calogero models

Abstract

We propose a new ${\cal N}$-extended supersymmetric $su(n)$ spin-Calogero model. Employing a generalized Hamiltonian reduction adopted to the supersymmetric case, we explicitly construct a novel rational $n$-particle Calogero model with an arbitrary even number of supersymmetries. It features ${\cal N}n^2$ rather than ${\cal N}n$ fermionic coordinates and increasingly high fermionic powers in the supercharges and the Hamiltonian.