Superspace Geometrical Representations of Extended Super Virasoro Algebras

TL;DR

This paper develops geometric representations of extended super Virasoro algebras using super-vector fields, providing explicit formulas and a universal realization that embeds these algebras into superspace structures.

Contribution

It introduces a geometrical realization covering algebra for arbitrary N, extending the understanding of super Virasoro algebra representations in superspace.

Findings

Explicit expressions for superconformal and super Virasoro algebras for N=1,2,4

A universal geometrical realization covering algebra for arbitrary N

Embedding of super Virasoro algebra into superspace structures

Abstract

Utilizing sets of super-vector fields (derivations), explicit expressions are obtained for; (a.) the 1D, N-extended superconformal algebra, (b.) the 1D, N-extended super Virasoro algebra for N = 1, 2 and 4 and (c.) a geometrical realization (GR) covering algebra that contains the super Virasoro algebra for arbitrary values of N. By use of such vector fileds, the super Virasoro algebra is embedded as a geometrical and model-independent structure in 1D and 2D Aleph-null-extended superspace.