# Supersymmetric hyperbolic Calogero-Sutherland models by gauging

## TL;DR

This paper develops new supersymmetric extensions of the hyperbolic Calogero-Sutherland models using gauging techniques, introducing models with enhanced symmetry and additional spin variables.

## Contribution

It presents novel $ ext{N}=2$ and $ ext{N}=4$ supersymmetric hyperbolic Calogero-Sutherland models derived from gauging matrix superfield models, including spin extensions.

## Key findings

- $ ext{N}=2$ model reduces to standard hyperbolic Calogero-Sutherland system.
- $ ext{N}=4$ model incorporates semi-dynamical spin variables.
- Two versions of the $ ext{N}=4$ model are constructed, with and without center-of-mass interaction.

## Abstract

Novel $\mathcal{N}{=}\,2$ and $\mathcal{N}{=}\,4$ supersymmetric extensions of the Calogero-Sutherland hyperbolic systems are obtained by gauging the ${\rm U}(n)$ isometry of matrix superfield models. The bosonic core of the $\mathcal{N}{=}\,2$ models is the standard $A_{n-1}$ Calogero-Sutherland hyperbolic system, whereas the ${\mathcal N}{=}\,4$ model contains additional semi-dynamical spin variables and is an extension of the U(2) spin Calogero-Sutherland hyperbolic system. We construct two different versions of the ${\mathcal N}{=}\,4$ model, with and without the interacting center-of-mass coordinate in the bosonic sector.