Chiral Determinant Formulae and Subsingular Vectors for the N=2 Superconformal Algebras

Abstract

We derive conjectures for the N=2 "chiral" determinant formulae of the Topological algebra, the Antiperiodic NS algebra, and the Periodic R algebra, corresponding to incomplete Verma modules built on chiral topological primaries, chiral and antichiral NS primaries, and Ramond ground states, respectively. Our method is based on the analysis of the singular vectors in chiral Verma modules and their spectral flow symmetries, together with some computer exploration and some consistency checks. In addition, and as a consequence, we uncover the existence of subsingular vectors in these algebras, giving examples (subsingular vectors are non-highest-weight null vectors which are not descendants of any highest-weight singular vectors).

Latex, 36 pages. Minor improvements in some paragraphs, typo in eq.(5.10) corrected, ref.[23] corrected and some references added. Very similar to the version published in Nucl. Phys. B503 (97) 447

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• Embedding Diagrams of the N=2 Superconformal Algebra under Spectral Flow
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• Singular dimensions of the N=2 superconformal algebras. I
• The Even and the Odd Spectral Flows on the N=2 Superconformal Algebras
• On resolution of highest weight modules over the $\mathcal{N}=2$ superconformal algebra
• A Note concerning Subsingular Vectors and Embedding Diagrams of the N=2 Superconformal Algebras
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