Supersymmetrization of the 3-particle elliptic Calogero model

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 $(1,\mathcal{N},\mathcal{N}-1)$, while the sector of relative coordinates is the supermultiplet $(2,\mathcal{N},\mathcal{N}-2)$. The $\mathcal{N}=2$ model described with three supermultiplets $(1,2,1)$ is also presented.

arXiv comment1+8 pages