REPRESENTATIONS OF N=1 EXTENDED SUPERCONFORMAL ALGEBRAS WITH TWO GENERATORS

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 $\tilde c = \frac{3}{2}$. Furthermore we show that most of the exceptional algebras lead to new rational models with $\tilde c > \frac{3}{2}$. The remaining exceptional cases show a new ‘mixed’ structure. Besides a continuous branch of representations discrete values of the highest weight also exist.