Supersymmetrization of the 3-particle elliptic Calogero model

TL;DR

This paper develops supersymmetric extensions of the 3-particle elliptic Calogero model, introducing new supermultiplet structures for different supersymmetry levels, enriching the integrable systems with supersymmetry.

Contribution

It proposes novel $ ext{N}=2$ and $ ext{N}=4$ supersymmetric generalizations of the 3-particle elliptic Calogero system, detailing the supermultiplet structures involved.

Findings

Supersymmetry generators are explicitly constructed.

Center of mass and relative coordinate sectors are described by specific supermultiplets.

The $ ext{N}=2$ model with three supermultiplets is also formulated.

Abstract

$\mathcal{N}{=}\,2$ and $\mathcal{N}{=}\,4$ supersymmetric generalizations of the 3-particle elliptic Calogero system are proposed. Supersymmetry generators of the system are found in which the center of mass sector is described by the supermultiplet ${\bf (1,\mathcal{N},\mathcal{N}-1)}$, while the sector of relative coordinates is the supermultiplet ${\bf (2,\mathcal{N},\mathcal{N}- 2)}$. The $\mathcal{N}{=}\,2$ model described with three supermultiplets ${\bf (1,2,1)}$ is also presented.