Conformal bootstrap for Toda conformal field theory

Develop and establish the conformal bootstrap for Toda conformal field theory, whose symmetry algebra is the W-algebra, including a full characterization of structure constants and conformal blocks consistent with this extended symmetry.

Background

Toda CFT generalizes Liouville theory to fields valued in the Cartan of a semisimple Lie algebra and is expected to be governed by a W-algebra symmetry larger than Virasoro. While probabilistic constructions and partial three-point results exist, a full bootstrap remains elusive.

The authors explicitly identify the bootstrap problem in Toda CFT as an open challenge due to the complexity of the extended symmetry and incomplete knowledge of structure constants.