N-fold Parasupersymmetry

TL;DR

This paper introduces N-fold parasupersymmetry, a novel non-linear supersymmetry generalization, providing a framework and specific models, including a reduction to known models and conjectures for further generalizations.

Contribution

It formulates N-fold parasupersymmetry, constructs a second-order example, and explores its algebraic structure, extending supersymmetry concepts.

Findings

Reduction to Rubakov-Spiridonov model at N=1

Existence of a generalized type C 2N-fold superalgebra

Conjecture of other N-fold supersymmetry generalizations

Abstract

We find a new type of non-linear supersymmetries, called N-fold parasupersymmetry, which is a generalization of both N-fold supersymmetry and parasupersymmetry. We provide a general formulation of this new symmetry and then construct a second-order N-fold parasupersymmetric quantum system where all the components of N-fold parasupercharges are given by type A N-fold supercharges. We show that this system exactly reduces to the Rubakov-Spiridonov model when N=1 and admits a generalized type C 2N-fold superalgebra. We conjecture the existence of other `N-fold generalizations' such as N-fold fractional supersymmetry, N-fold orthosupersymmetry, and so on.