Notes on Curtright-Zachos Deformations of osp(1,2) and Super Virasoro Algebras

TL;DR

This paper explores supersymmetric extensions of q-deformed Virasoro and super-Virasoro algebras using quantum superspace, revealing new algebraic structures relevant to string theory and conformal field theory.

Contribution

It introduces a supersymmetric extension of the q-deformed Virasoro algebra within the quantum superspace framework, connecting it to super Virasoro and affine sl(2) algebras.

Findings

Identified supersymmetric deformations of Virasoro algebra

Connected deformations to super Virasoro and affine sl(2) algebras

Applied quantum superspace to conformal field theory

Abstract

Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of two-dimensional string theory. We analyze two types of deformed super-Virasoro algebra as well as their $osp(1,2)$ subalgebras. Applying our quantum superspace structure to conformal field theory, we find the same type of deformation of affine $sl(2)$ algebra.