1996/04/28 by A M Semikhatov, Semikhatov, A M, I Yu Tipunin +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9604176
LaTeX 2.09, 33pp
arxiv created 1998/08/29 · arxiv updated 2009/11/30
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.