Embedding Diagrams of N=2 Verma Modules and Relaxed ^sl(2) Verma Modules

Abstract

We classify and explicitly construct the embedding diagrams of Verma modules over the N=2 supersymmetric extension of the Virasoro algebra. The essential ingredient of the solution consists in drawing the distinction between two different types of submodules appearing in N=2 Verma modules. The problem is simplified by associating to every N=2 Verma module a relaxed Verma module over the affine algebra ^sl(2) with an isomorphic embedding diagram. We then make use of the mechanism according to which the structure of the N=2/relaxed-sl(2) embedding diagrams can be found knowing the standard embedding diagrams of ^sl(2) Verma modules. The resulting classification of the N=2/relaxed-^sl(2) embedding diagrams follows the I-II-III pattern extended by an additional indication of the number (0, 1, or 2) and the twists of the standard ^sl(2) embedding diagrams contained in a given N=2/relaxed-^sl(2) embedding diagram.

arXiv commentLaTeX 2.09, 52pp

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• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
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• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• sl(2)_{-1/2} and the Triplet Model
• Relaxed highest-weight modules I: rank $1$ cases
• Logarithmic lift of the su(2)_{-1/2} model
• Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models
• The embedding structure of unitary N=2 minimal models
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Rationality of unitary N=2 vertex operator superalgebras
• A Note concerning Subsingular Vectors and Embedding Diagrams of the N=2 Superconformal Algebras