New N $$ \mathcal{N} $$ = 2 superspace Calogero models

Abstract

Abstract Starting from the Hamiltonian formulation of N $$ \mathcal{N} $$ = 2 supersymmetric Calogero models associated with the classical A n , B n , C n and D n series and their hyperbolic/trigonometric cousins, we provide their superspace description. The key ingredients include n bosonic and 2n(n−1) fermionic N $$ \mathcal{N} $$ = 2 superfields, the latter being subject to a nonlinear chirality constraint. This constraint has a universal form valid for all Calogero models. With its help we find more general supercharges (and a superspace Lagrangian), which provide the N $$ \mathcal{N} $$ = 2 supersymmetrization for bosonic potentials with arbitrary repulsive two-body interactions.

Keywords

• Extended Supersymmetry
• Superspaces
• Integrable Hierarchies