Singular Vectors of the Topological Conformal Algebra

Abstract

A general construction is found for `topological' singular vectors of the twisted N=2 superconformal algebra. It demonstrates many parallels with the known construction for sl(2) singular vectors due to Malikov--Feigin--Fuchs, but is formulated independently of the latter. The two constructions taken together provide an isomorphism between topological and sl(2)- singular vectors. The general formula for topological singular vectors can be reformulated as a chain of direct recursion relations that allow one to derive a given singular vector |S(r,s)> from the lower ones |S(r,s'<s)>. We also introduce generalized Verma modules over the twisted N=2 algebra and show that they provide a natural setup for the new construction for topological singular vectors.

LaTeX 2.09, 19 pages. Minor changes, making the paper identical to the one to be published in IJMPA

References in corpus (1)

• Integral Intertwining Operators and Complex Powers of Differential ($q-$Difference) Operators

Cited by in corpus (10)

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• Families of Singular and Subsingular Vectors of the Topological N=2 Superconformal Algebra
• The Even and the Odd Spectral Flows on the N=2 Superconformal Algebras
• Interpretation of the Determinant Formulae for the Chiral Representations of the N=2 Superconformal Algebra
• $sl(2{)}_{-4}$ WZW Model as an N=4 Supersymmetric Bosonic String with $c=-2$ matter
• A Note concerning Subsingular Vectors and Embedding Diagrams of the N=2 Superconformal Algebras
• On the Equivalence of Affine sl(2) and N=2 Superconformal Representation Theories
• No isomorphism between the affine $\hat{s}l(2)$ algebra and the N=2 superconformal algebras