Supersymmetry of parafermions

TL;DR

This paper demonstrates that single-mode parafermionic systems exhibit supersymmetry, with the superalgebra structure depending on the parafermion order, applicable in both unbroken and broken phases.

Contribution

It introduces the supersymmetry of parafermionic systems based on characteristic functions and classifies various supersymmetric parafermionic models.

Findings

Supersymmetry exists in both unbroken and broken phases.

Superalgebra can be linear or nonlinear depending on parafermion order.

Includes models like q-deformed and internal $Z_2$ parafermionic oscillators.

Abstract

We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The supersymmetry is realized in both unbroken and spontaneously broken phases. As in the case of parabosonic supersymmetry observed recently by one of the authors, the form of the associated superalgebra depends on the order of the parafermion and can be linear or nonlinear in the Hamiltonian. The list of supersymmetric parafermionic systems includes usual parafermions, finite-dimensional q-deformed oscillator, q-deformed parafermionic oscillator and parafermionic oscillator with internal $Z_2$ structure.