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

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 $D(2,1 \mid α)$ are given. The $N=1$ and $N=2$ super conformal algebras are discussed in the pertinent cases.