Neveu-Schwarz and operators algebras II: Unitary series and characters

TL;DR

This paper provides a complete classification of the unitary series of the Neveu-Schwarz algebra, using GKO construction, Kac determinant, and FQS criterion, and derives characters directly without Feigin-Fuchs resolutions.

Contribution

It offers a self-contained proof of the unitary series classification and introduces a direct method for obtaining characters, advancing the understanding of Neveu-Schwarz algebra representations.

Findings

Complete classification of unitary series achieved

Characters derived directly without Feigin-Fuchs resolutions

Connections established to subfactor theory

Abstract

This paper is the second of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we give a unitary complete proof of the classification of the unitary series of the Neveu-Schwarz algebra, by the way of GKO construction, Kac determinant and FQS criterion. We then obtain the characters directly, without Feigin-Fuchs resolutions.