New ${\cal N}{=}\,2$ superspace Calogero models

TL;DR

This paper develops a superspace framework for ${ m N}=2$ supersymmetric Calogero models, enabling a unified description of various classical series and their hyperbolic/trigonometric variants, and introduces more general supercharges.

Contribution

It provides a superspace formulation for ${ m N}=2$ Calogero models, including a universal nonlinear chirality constraint and generalized supercharges for arbitrary two-body interactions.

Findings

Unified superspace description for all classical Calogero models.

Introduction of a universal nonlinear chirality constraint.

Generalized supercharges for arbitrary two-body potentials.

Abstract

Starting from the Hamiltonian formulation of ${\cal N}{=}\,2$ 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 ${\cal N}{=}\,2$ 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 ${\cal N}{=}\,2$ supersymmetrization for bosonic potentials with arbitrary repulsive two-body interactions.