Calogero models and nonlocal conformal transformations

TL;DR

This paper introduces a universal method to relate Calogero models to free particles, applicable to conformal, nonconformal, and supersymmetric versions, simplifying their analysis despite nonlocal symmetry realizations.

Contribution

It presents a novel, universal approach to connect Calogero models with free particles, including extensions to supersymmetric and nonconformal cases.

Findings

Unified method for Calogero and free particle models

Construction of N=2 superconformal extensions

Nonlocal realization of conformal symmetry

Abstract

We propose a universal method of relating the Calogero model to a set of decoupled particles on the real line, which can be uniformly applied to both the conformal and nonconformal versions as well as to supersymmetric extensions. For conformal models the simplification is achieved at the price of a nonlocal realization of the full conformal symmetry in the Hilbert space of the resulting free theory. As an application, we construct two different N=2 superconformal extensions.