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