Correlation functions with fusion-channel multiplicity in W 3 $$ {\mathcal{W}}_3 $$ Toda field theory

Vladimir Belavin (1, 2) , Benoit Estienne (3) , Omar Foda (4) , Raoul Santachiara (5)

1 IITP - Institute for Information Transmission Problems
2 LPI RAS - P. N. Lebedev Physical Institute of the Russian Academy of Sciences [Moscow]
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
4 University of Melbourne
5 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

Current studies of W N WN Toda field theory focus on correlation functions such that the W N WN highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W 3 W3 Toda 4-point functions with multiplicity in the fusion channel. The conformal blocks of these 4-point functions involve matrix elements of a fully-degenerate primary field with a highest-weight in the adjoint representation of s l 3 sl3 , and a fully-degenerate primary field with a highest-weight in the fundamental representation of s l 3 sl3 . We show that, when the fusion rules do not involve multiplicities, the matrix elements of the fully-degenerate adjoint field, between two arbitrary descendant…

Domaines: Physique [physics]

Vladimir Belavin, Benoit Estienne, Omar Foda, Raoul Santachiara. Correlation functions with fusion-channel multiplicity in W 3 $$ {\mathcal{W}}_3 $$ Toda field theory. Journal of High Energy Physics, 2016, 2016 (6), pp.1-39. ⟨10.1007/JHEP06(2016)137⟩. ⟨hal-01380067⟩