Super-Calogero-Moser-Sutherland systems and free super-oscillators : a mapping

TL;DR

This paper demonstrates that certain supersymmetric Calogero-Moser-Sutherland models can be transformed into free super-oscillators, enabling straightforward construction of their spectra and eigenfunctions, and extends this to a broader class of super-Hamiltonians with OSp(2|2) symmetry.

Contribution

It introduces a method to map supersymmetric CMS models and related super-Hamiltonians to free super-oscillators, simplifying spectral analysis and eigenfunction construction.

Findings

Supersymmetric CMS models are equivalent to free super-oscillators via similarity transformation.

Complete eigen-spectrum and eigen-functions can be constructed from free super-oscillator basis.

The method applies to a broad class of super-Hamiltonians with OSp(2|2) supersymmetry.

Abstract

We show that the supersymmetric rational Calogero-Moser-Sutherland (CMS) model of A_{N+1}-type is equivalent to a set of free super-oscillators, through a similarity transformation. We prescribe methods to construct the complete eigen-spectrum and the associated eigen-functions, both in supersymmetry preserving as well as supersymmetry breaking phases, from the free super-oscillator basis. Further we show that a wide class of super-Hamiltonians realizing dynamical OSp(2|2) supersymmetry, which also includes all types of rational super-CMS as a small subset, are equivalent to free super-oscillators. We study BC_{N+1}-type super-CMS model in some detail to understand the subtleties involved in this method.