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

TL;DR

This paper introduces a new ${ m N}$-extended supersymmetric $su(n)$ spin-Calogero model, expanding the class of integrable systems with higher supersymmetry and complex fermionic structures.

Contribution

It constructs a novel rational $n$-particle Calogero model with arbitrary even supersymmetries using generalized Hamiltonian reduction, featuring a complex fermionic structure.

Findings

Explicit construction of the supersymmetric Calogero model

Model features ${ m N}n^2$ fermionic coordinates

High fermionic powers in supercharges and Hamiltonian

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.