Fractional spin through quatum (super)Virasoro algebras

TL;DR

This paper investigates the properties of quantum (super)Virasoro algebras at roots of unity, revealing their connection to fractional supersymmetry and $k$-fermionic spin, through analysis of $Q$-deformed bosons and fermions.

Contribution

It demonstrates the equivalence between $Q$-fermions and ordinary fermions and explores the algebraic structures at roots of unity, linking them to fractional supersymmetry.

Findings

Quantum (super)Virasoro algebras exhibit fractional supersymmetry at roots of unity.

$Q$-deformed bosons split into fractional spin components in the limit.

$Q$-fermions become equivalent to ordinary fermions at specific limits.

Abstract

The splitting of a $Q$-deformed boson, in the $Q\to q=e^{\frac{\QTR{rm}{2\pi i}}{\QTR{rm}{k}}}$ limit, is discussed. The equivalence between a $Q$-fermion and an ordinary one is established. The properties of the quantum (super)Virasoro algebras when their deformation parameter $Q$ goes to a root of unity, are investigated. These properties are shown to be related to fractional supersymmetry and $k$-fermionic spin.