Three-point correlation functions in the $\mathfrak{sl}_3$ Toda theory II: the Fateev-Litvinov formula

Understand

Toda Conformal Field Theories (CFTs) form a family of two-dimensional CFTs indexed by semisimple and complex Lie algebras.

• One of their remarkable features is that they are natural generalizations of Liouville CFT that enjoy an enhanced level of symmetry, prescribed by $W$-algebras.
• They likewise admit a probabilistic formulation in terms of Gaussian Multiplicative Chaos.
• Based on this probabilistic framework, this second article in a two-part series is dedicated to providing a first step towards integrability of these theories.