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

Abstract

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

1+10 pages; v2: extended introduction and conclusions, comments on integrability and two refs. added, matches published version

References in corpus (8)

• $\mathcal{N}$-extended supersymmetric Calogero models
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Supersymmetric many-body Euler-Calogero-Moser model
• Gauged spinning models with deformed supersymmetry
• Extended supersymmetric Calogero model
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• $\mathcal{N}=4$ supersymmetric Calogero-Sutherland models