Analytic Expressions for Singular Vectors of the $N=2$ Superconformal Algebra

Details Analytic Expressions for Singular Vectors of the $N=2$ Superconformal Algebra Analytic Expressions for Singular Vectors of the $N=2$ Superconformal Algebra

1996-01-11

arxiv.org/abs/hep-th/9601056v1

Commun.Math.Phys. 180 (1996) 195-232

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, LATEX

Scientific paper

10.1007/BF02101186

Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent neutral singular vectors at the same grade. We construct this two dimensional space and we identify the singular vectors of the original Verma modules. We show that in some Verma modules these expressions lead to two linearly independent singular vectors which are at the same grade and have the same charge.

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