Transmutations between Singular and Subsingular Vectors of the N=2 Superconformal Algebras

Abstract

We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the Topological algebra become subsingular vectors of the Antiperiodic NS algebra under the topological untwistings. These classes consist of BRST- invariant singular vectors with relative charges $q=-2,-1$ and zero conformal weight, and no-label singular vectors with $q=0,-1$. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the Periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2.

21 pages, Latex. Minor improvements. Very similar to the version published in Nucl. Phys. B

References in corpus (5)

• Chiral Determinant Formulae and Subsingular Vectors for the N=2 Superconformal Algebras
• Determinant Formula for the Topological N=2 Superconformal Algebra
• Construction Formulae for Singular Vectors of the Topological N=2 Superconformal Algebra
• Singular dimensions of the N=2 superconformal algebras. I
• The Even and the Odd Spectral Flows on the N=2 Superconformal Algebras

Cited by in corpus (10)

• The embedding structure of unitary N=2 minimal models
• Determinant Formula for the Topological N=2 Superconformal Algebra
• Embedding Diagrams of the N=2 Superconformal Algebra under Spectral Flow
• Construction Formulae for Singular Vectors of the Topological and of the Ramond N=2 Superconformal Algebras
• Construction Formulae for Singular Vectors of the Topological N=2 Superconformal Algebra
• Singular dimensions of the N=2 superconformal algebras. I
• A Note concerning Subsingular Vectors and Embedding Diagrams of the N=2 Superconformal Algebras
• Recent Results on N=2 Superconformal Algebras
• The Adapted Ordering Method in Representation Theory
• The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations