Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation

Vladimir Belavin ^{1, 2} Xiangyu Cao ³ Benoit Estienne ⁴ Raoul Santachiara ³

Journal of High Energy Physics, Springer, 2017, 3, pp.008

In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. 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.

• 1. P. N. Lebedev Physical Institute of the Russian Academy of Sciences
• 2. IITP – Institute for Information Transmission Problems
• 3. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 4. LPTHE – Laboratoire de Physique Théorique et Hautes Energies