Representations of $N=1$ Extended Superconformal Algebras with Two Generators

Abstract

In this paper we consider the representation theory of N=1 Super-W-algebras with two generators for conformal dimension of the additional superprimary field between two and six. In the superminimal case our results coincide with the expectation from the ADE-classification. For the parabolic algebras we find a finite number of highest weight representations and an effective central charge $\tilde{c}=3/2$. Furthermore we show that most of the exceptional algebras lead to new rational models with $\tilde{c}>3/2$. The remaining exceptional cases show a new `mixed' structure. Besides a continuous branch of representations discrete values of the highest weight exist, too.

14 pages (Plain TeX), BONN-HE-92-28

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