Supersymmetric Construction of W-Algebras from Super Toda and Wznw Theories

TL;DR

This paper systematically constructs super W-algebras from super Lie algebra-based WZNW models, linking them to super Toda models and classifying them by conformal spin, with explicit examples and discussion of super conformal algebras.

Contribution

It provides a systematic construction and classification of super W-algebras from super Lie algebras, including explicit examples and connections to super Toda models.

Findings

Constructed super W-algebras from super WZNW models.

Established the relation between super W-algebras and super Toda models.

Explicitly derived super W-algebras for specific super Lie algebras.

Abstract

A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy-momentum tensor, is dicussed in general terms for all super Lie algebras whose simple roots are fermionic . A detailed discussion employing the Dirac bracket structure and an explicit construction of W-algebras for the cases of $OSP(1,2)$, $OSP(2,2)$ , $OSP(3,2)$ and $D(2,1 \mid \alpha )$ are given. The $N=1$ and $N=2$ super conformal algebras are discussed in the pertinent cases.