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

A M Semikhatov·I Yu Tipunin
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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.

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A M Semikhatov, I Yu Tipunin. 1998-08-29. All Singular Vectors of the N=2 Superconformal Algebra via the Algebraic Continuation Approach. https://arxiv.org/abs/hep-th/9604176

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