# Ruijsenaars-Schneider three-body models with N=2 supersymmetry

## TL;DR

This paper constructs N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models, revealing new links to non-metric connections and expanding the understanding of supersymmetric integrable systems.

## Contribution

It introduces the first N=2 supersymmetric versions of these models and explores their geometric interpretations within Hamiltonian formalism.

## Key findings

- Supersymmetric extensions for rational and hyperbolic models are constructed.
- Hyperbolic models are connected to non-metric geometric structures.
- Rational models relate to geodesic equations with metric connections.

## Abstract

The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.