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

Understand

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.