N = 2 Calogero models within superfields

Abstract

We provide a superspace description of $\cal N{=}\,2$ supersymmetric Calogero models associated with the classical $A_n, B_n, C_n$ and $D_n$ Lie algebras and their hyperbolic/trigonometric versions. These models are described by $n$ 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 and guarantees an existence of more general supercharges (and a superspace Lagrangian), which provide the $\cal N{=}\,2$ supersymmetrization for bosonic potentials with arbitrary repulsive pairwise interactions.