Abstract
We construct a class of 3-point constants in the sl(4) Toda conformal theory W 4, extending the examples in Fateev and Litvinov [1]. Their knowledge allows to determine the braiding/fusing matrix transforming 4-point conformal blocks of one fundamental, labelled by the 6-dimensional sl(4) representation, and three partially degenerate vertex operators. It is a 3 × 3 submatrix of the generic 6 × 6 fusing matrix consistent with the fusion rules for the particular class of representations. We check a braiding relation which has wider applications to conformal models with sl(4) symmetry. The 3-point constants in dual regions of central charge are compared in preparation for a BPS like relation in the \( \widehat{sl}(4) \) WZW model.
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Furlan, P., Petkova, V. On some 3-point functions in the W 4 CFT and related braiding matrix. J. High Energ. Phys. 2015, 1–23 (2015). https://doi.org/10.1007/JHEP12(2015)079
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DOI: https://doi.org/10.1007/JHEP12(2015)079