Singular Vectors of the $N=2$ Superconformal Algebra

TL;DR

This paper develops recursion formulas to explicitly construct singular vectors in the N=2 superconformal algebra, enhancing understanding of its structure and representations.

Contribution

It introduces a novel recursive method for deriving explicit singular vectors in the N=2 superconformal algebra, building on previous approaches.

Findings

Explicit formulas for charged singular vectors

Explicit formulas for uncharged singular vectors

Recursion relations for algebraic construction

Abstract

We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged singular vectors and for a class of uncharged singular vectors.