Decomposition of \widehat\mathfraksl_2,k ⊕ \widehat\mathfraksl_2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models

2023/12/22 by Hadasz, Leszek, Ruba, Błażej
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2312.14695

Abstract

We construct highest weight vectors of \widehat\mathfraksl_2,k+1 ⊕ Vir in tensor products of highest weight modules of \widehat\mathfraksl_2,k and \widehat\mathfraksl_2,1, and thus for generic weights we find the decomposition of the tensor product into irreducibles of \widehat\mathfraksl_2,k+1 ⊕ Vir. The construction uses Wakimoto representations of \widehat\mathfraksl_2,k, but the obtained vectors can be mapped back to Verma modules. Singularities of this mapping are cancelled by a renormalization. A detailed study of ``degenerations'' of Wakimoto modules allowed to find the renormalization factor explicitly. The obtained result is a significant step forward in a proof of equivalence of certain two-dimesnional CFT models.

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