All Singular Vectors of the N=2 Superconformal Algebra via the Algebraic Continuation Approach

Abstract

We give general expressions for singular vectors of the N=2 superconformal algebra in the form of {\it monomials} in the continued operators by which the universal enveloping algebra of N=2 is extended. We then show how the algebraic relations satisfied by the continued operators can be used to transform the monomials into the standard Verma-module expressions. Our construction is based on continuing the extremal diagrams of N=2 Verma modules to the states satisfying the twisted \hw{} conditions with complex twists. It allows us to establish recursion relations between singular vectors of different series and at different levels. Thus, the N=2 singular vectors can be generated from a smaller set of the so-called topological singular vectors, which are distinguished by being in a 1:1 correspondence with singular vectors in affine sl(2) Verma modules. The method of `continued products' of fermions is a counterpart of the method of complex powers used in the constructions of singular vectors for affine Lie algebras.

LaTeX 2.09, 33pp

References in corpus (2)

• D-Branes and Topological Field Theories
• Singular Vectors of the Topological Conformal Algebra

Cited by in corpus (9)

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• Past the Highest-Weight, and What You Can Find There
• A Note concerning Subsingular Vectors and Embedding Diagrams of the N=2 Superconformal Algebras
• Staggered modules of $N=2$ superconformal minimal models
• Untwisting Topological Field Theories