(Super)conformal many-body quantum mechanics with extended supersymmetry

TL;DR

This paper develops and extends N=4 supersymmetric many-body quantum mechanics models, including conformal and superconformal versions, providing new Hamiltonian and Lagrangian formulations with broader symmetry structures.

Contribution

It constructs conformal N=4 extensions of Calogero models and generalizes them to arbitrary even N, expanding the class of supersymmetric many-body quantum systems.

Findings

Constructed conformal N=4 Calogero models with extended symmetry.

Extended models to arbitrary even N supersymmetry.

Provided Hamiltonian and Lagrangian formulations in component and superfield forms.

Abstract

We study N=4 supersymmetric quantum-mechanical many-body systems with M bosonic and 4M fermionic degrees of freedom. We also investigate the further restrictions of conformal and superconformal invariance. In particular, we construct conformal N=4 extensions of the A_{M-1} Calogero models, which for generic values of the coupling constant are not SU(1,1|2) superconformal. This class of models is also extended to arbitrary (even) N. We give both hamiltonian and (classical) lagrangean formulations. In the latter case we use both component and N=4 superfield formulations.