# Supersymmetric V-systems

## TL;DR

This paper develops supersymmetric quantum mechanical systems based on V-systems, extending Calogero-Moser models with superconformal symmetry, and constructs related Hamiltonians for various root systems.

## Contribution

It introduces a general construction of ${
m N}=4$ superconformal systems for any V-system configuration, including new supersymmetric Calogero-Moser and Sutherland Hamiltonians.

## Key findings

- Constructed ${
m N}=4$ superconformal systems for V-systems.
- Extended Calogero-Moser potentials to supersymmetric cases.
- Developed supersymmetric Hamiltonians for root systems like $BC_N$.

## Abstract

We construct ${\mathcal N}=4 \,$ $\, D(2,1;\alpha)$ superconformal quantum mechanical system for any configuration of vectors forming a V-system. In the case of a Coxeter root system the bosonic potential of the supersymmetric Hamiltonian is the corresponding generalised Calogero-Moser potential. We also construct supersymmetric generalised trigonometric Calogero-Moser-Sutherland Hamiltonians for some root systems including $BC_N$.