On some 3-point functions in the $W_4$ CFT and related braiding matrix

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. 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 $3\times 3$ submatrix of the generic $6\times 6$ 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.

27 pages, TeX with harvmac; v2: Content substantially extended, new references added

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• Correlation functions in conformal Toda field theory I
• Correlation functions in conformal Toda field theory II
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• Wilson Loop Invariants from $W_N$ Conformal Blocks
• On some Coulomb gas integrals in higher dimensions
• The imaginary Toda field theory
• $W_4$ Toda example as hidden Liouville CFT