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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…
Higher-spin symmetry in the boundary Toda conformal field theory I: Ward identities
Baptiste Cerclé, Nathan Huguenin
This article is the first of a two-part series dedicated to studying the symmetries enjoyed by the probabilistic construction of the boundary Toda Conformal Field…
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…
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 II: the Fateev-Litvinov formula
Baptiste Cerclé
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…
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…
Ward identities in the Toda conformal field theory
Baptiste Cerclé, Yichao Huang
Toda conformal field theories are natural generalizations of Liouville conformal field theory that enjoy an enhanced level of symmetry. In Toda conformal field theories this higher…
Unit boundary length quantum disk: a study of two different perspectives and their equivalence
Baptiste Cerclé
The theory of the 2-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces. In a series of art…