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