Fusion and the Neveu-Schwarz Singular Vectors

TL;DR

This paper extends an existing algorithm for constructing singular vectors from the Virasoro algebra to the Neveu-Schwarz superalgebra, broadening the tools available for superconformal algebra analysis.

Contribution

The authors adapt and extend the fusion-based algorithm to compute singular vectors in the Neveu-Schwarz superalgebra, a significant step in superconformal representation theory.

Findings

Extended the fusion algorithm to Neveu-Schwarz superalgebra

Provided a systematic method for singular vector construction in superalgebras

Enhanced understanding of superconformal algebra representations

Abstract

Bauer, Di Francesco, Itzykson and Zuber proposed recently an algorithm to construct all singular vectors of the Virasoro algebra. It is based on the decoupling of (already known) singular fields in the fusion process. We show how to extend their algorithm to the Neveu-Schwarz superalgebra.