A probabilistic approach to Toda Conformal Field Theories

par Baptiste Cerclé (EPFL)

jeudi 20 mars 2025, 11:00 → 12:00 Europe/Paris

Auditorium Vivargent (LAPTh)

Conformal invariance is a feature that arises for a large class of models of statistical physics at criticality. To address the issue of understanding the conformal field theory (CFT) thus defined, Belavin-Polyakov-Zamolodchikov designed in 1984 a general method for solving such a theory, dubbed conformal bootstrap. However there is a large class of models, such as the critical three-states Potts model, that enjoy in addition to conformal invariance an enhanced level of symmetry called higher-spin symmetry. Capturing this feature led to the introduction by Zamolodchikov of the notion of W-algebras, which are Vertex Algebras containing the Virasoro algebra.

 

In this talk we will explain how this higher-spin symmetry manifests itself for Toda CFTs, generalizations of Liouville CFT that enjoy this higher level of symmetry. Namely in a first part we will explain how probability theory allows to define rigorously such models. We will then explain how this symmetry manifests itself within this probabilistic framework and describe some of its implications, such as the computation of a family of correlation functions of the theory.