$\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model

TL;DR

This paper investigates the $ =2$ supersymmetric hyperbolic Calogero-Sutherland model, deriving classical and quantum supercharges, analyzing their differences, and constructing a Lax pair for the supersymmetric extension.

Contribution

It provides the first detailed analysis of quantum supercharges and constructs a Lax pair for the $ =2$ supersymmetric hyperbolic Calogero-Sutherland model.

Findings

Quantum supercharges can be restricted to an invariant sub-sector.

Classical and quantum supercharges have different structures.

A Lax pair for the supersymmetric model is constructed.

Abstract

The $\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model obtained in arXiv:1902.08023 by gauging the $\mathcal{N}{=}\,2$ superfield matrix system is studied. Classical and quantum $\mathcal{N}{=}\,2$ supersymmetry generators are found. The difference in the structure of classical and quantum supercharges is established. It is shown that, unlike classical supercharges, quantum supersymmetry generators can be limited to an invariant sub-sector that does not contain off-diagonal fermion operators. The Lax pair for supersymmetric generalization of the hyperbolic Calogero-Sutherland system is constructed.