Null vectors of the superconformal algebra: the Ramond sector

TL;DR

This paper investigates the Ramond sector of the N=1 superconformal algebra, deriving explicit singular vector expressions in reducible modules using the fusion principle, advancing understanding of superconformal representation theory.

Contribution

It provides new explicit formulas for singular vectors in the Ramond sector, applying the fusion principle to superconformal algebra representations.

Findings

Explicit singular vector expressions derived for the Ramond sector.

Application of the fusion principle to superconformal algebra.

Enhanced understanding of the structure of reducible modules.

Abstract

We consider the Ramond sector of the $N=1$ superconformal algebra and find expressions for the singular vectors in reducible highest weight Verma module representations by the fusion principle of Bauer et al.