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All Singular Vectors of the N=2 Superconformal Algebra via the Algebraic Continuation Approach | | A M Semikhatov
; I Yu Tipunin
; | | Date: |
29 May 1996 | | 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. | | Source: | arXiv, hep-th/9604176 | | Services: | Forum | Review | PDF | Favorites | |
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