# Supersymmetric many-body Euler-Calogero-Moser model

## TL;DR

This paper constructs a new supersymmetric many-body model with $so(n)$ symmetry, featuring a simplified structure of supercharges and Hamiltonian, and explores its algebraic properties and special cases.

## Contribution

It introduces a novel supersymmetric $so(n)$ spin-Calogero model with an arbitrary even number of supersymmetries and a simplified algebraic structure.

## Key findings

- The model has $rac{1}{2}{
m N}n(n+1)$ fermionic coordinates.
- The supercharges and Hamiltonian form an $osp({
m N}|2)$ superalgebra.
- A superspace description is provided for the ${
m N}=2$ case.

## Abstract

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