A Note on Representations of N=2 SW-Algebras

TL;DR

This paper studies the representation theory of certain N=2 super W-algebras with two generators, classifying known models and analyzing their properties, especially focusing on rationality and spectral flow effects.

Contribution

It classifies all known N=2 super W-algebras with two generators into four classes and analyzes their representation properties, especially for c >= 3.

Findings

No new rational models outside the unitary minimal series.

All known algebras with c >= 3 relate to spectral flow of N=2 super Virasoro algebra.

Representations for c >= 3 have quantized U(1) charge.

Abstract

We investigate the representation theory of some recently constructed N=2 super W-algebras with two generators. Except for the central charges in the unitary minimal series of the N=2 super Virasoro algebra we find no new rational models. However, from our results it is possible to arrange all known N=2 super W-algebras with two generators and vanishing self-coupling constant into four classes. For the algebras existing for c >= 3 which can be understood by the spectral flow of the N=2 super Virasoro algebra we find that the representations have quantized U(1) charge.