8 papers
Boundary Toda Conformal Field Theory from the path integral
Baptiste Cerclé, Nathan Huguenin
Toda Conformal Field Theories (CFTs hereafter) are generalizations of Liouville CFT where the underlying field is no longer scalar but takes values in a finite-dimensional vector s…
Around the semi-classical limit of boundary Liouville conformal field theory
Baptiste Cerclé
Liouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal cla…
W-algebras, Gaussian Free Fields and -Dotsenko-Fateev integrals
Baptiste Cerclé
Based on the intrinsic connection between Gaussian Free Fields and the Heisenberg vertex algebra, we study some aspects of the correspondence between probability theory and -alg…
Higher equations of motion for boundary Liouville Conformal Field Theory from the Ward identities
Baptiste Cerclé
In this document we prove higher equations of motion at the level 2 for boundary Liouville Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyako…
Three-point correlation functions in the Toda theory I: Reflection coefficients
Baptiste Cerclé
Toda Conformal Field Theories (CFTs) form a family of 2d CFTs indexed by semisimple and complex Lie algebras. They are natural generalizations of the Liouville CFT in that they enj…
Higher-spin symmetry in the boundary Toda conformal field theory II: Singular vectors and BPZ equations
Baptiste Cerclé, Nathan Huguenin
This article is the second chapter of a two-part series dedicated to the mathematical study of the higher-spin symmetry enjoyed by the boundary Toda Conformal Fie…