Fractional Superspace Formulation of Generalized Super-Virasoro Algebras

TL;DR

This paper introduces a fractional superspace approach to generalized super-Virasoro algebras, unifying parasuper and fractional super-Virasoro structures, and explores their relation to $q$-oscillator algebras.

Contribution

It develops a fractional superspace framework for generalized super-Virasoro algebras, encompassing parasuper and fractional variants, and clarifies their algebraic connections.

Findings

Unified fractional superspace formulation of super-Virasoro algebras

Identification of parameters $M$ and $F$ for different algebra types

Connection established between these algebras and $q$-oscillator algebras

Abstract

We present a fractional superspace formulation of the centerless parasuper-Viraso-ro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by $t$ and $\theta$, with $t$ a real coordinate and $\theta$ a paragrassmann variable of order $M$ and canonical dimension $1/F$. We further describe a more general structure labelled by $M$ and $F$ with $M\geq F$. The case $F=2$ corresponds to the parasuper-Virasoro algebra of order $M$, while the case $F=M$ leads to the fractional super-Virasoro algebra of order $F$. The ordinary super-Virasoro algebra is recovered at $F=M=2$. The connection with $q$-oscillator algebras is discussed.