Construction Formulae for Singular Vectors of the Topological and of the Ramond N=2 Superconformal Algebras

TL;DR

This paper establishes explicit mappings and construction formulae for singular vectors across different N=2 superconformal algebras, enhancing understanding of their structure and relationships.

Contribution

It provides one-to-one mappings and construction formulae for singular vectors of the Topological and Ramond N=2 algebras based on Neveu-Schwarz algebra results.

Findings

Mapped singular vectors between algebras

Derived construction formulae for topological and Ramond cases

Identified subsingular vectors without existing formulae

Abstract

We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and $16 + 16$ types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains construction formulae for the latter using the construction formulae for the Neveu-Schwarz singular vectors due to D\"orrzapf. The indecomposable singular vectors of the Topological and of the Ramond N=2 algebras (`no-label' and `no-helicity' singular vectors) cannot be mapped to singular vectors of the Neveu-Schwarz N=2 algebra, but to {\it subsingular} vectors, for which no construction formulae exist.