Abstract
In a recent study we considered \( {\mathcal{W}}_3 \) Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of \( \mathfrak{s}{\mathfrak{l}}_3 \). We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.
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Belavin, V., Cao, X., Estienne, B. et al. Second level semi-degenerate fields in \( {\mathcal{W}}_3 \) Toda theory: matrix element and differential equation. J. High Energ. Phys. 2017, 8 (2017). https://doi.org/10.1007/JHEP03(2017)008
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DOI: https://doi.org/10.1007/JHEP03(2017)008