Description
Toda conformal field theories are a family of two-dimensional conformal field theories indexed by semi-simple and complex Lie algebras. One of their features is that, in addition to conformal symmetry, they enjoy an extended level of symmetry encoded by W-algebras. Besides, they can be defined via a path integral similar to the one of Liouville theory for which they provide a natural generalization. In this talk we will review recent progress made towards integrabilty of such theories, relying on a probabilistic formulation of the models and additional materials specific to Toda theories.
