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

A M Semikhatov; V A Sirota

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arXiv · hep-th/9712102

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

A M Semikhatov·V A Sirota

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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.

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A M Semikhatov, V A Sirota. 1997-12-09. Embedding Diagrams of N=2 Verma Modules and Relaxed ^sl(2) Verma Modules. https://arxiv.org/abs/hep-th/9712102

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