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

TL;DR

This paper explores the representation theory of N=1 Super-W-algebras with two generators, revealing finite and infinite representations, connections to ADE-classification, and new rational models with effective central charge.

Contribution

It provides a detailed classification of representations for N=1 Super-W-algebras, including new rational models and the analysis of exceptional cases with mixed structures.

Findings

Finite highest weight representations for parabolic algebras

New rational models with effective central charge $ ilde c = 3/2$

Existence of discrete highest weight values and mixed structures

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.