Compute unknown structure constants in boundary Toda conformal field theory

Determine explicit formulas for the boundary structure constants of Toda conformal field theory (including, in particular, the boundary \mathfrak{sl}_3 Toda model) that remain uncomputed in the physics literature. The goal is to identify and compute those boundary three-point and bulk–boundary constants whose values are still unknown, thereby extending the current knowledge beyond the one-point bulk correlator case and enabling a complete characterization of boundary Toda CFT correlation functions.

Background

Liouville theory is the simplest instance of a Toda conformal field theory, and the paper develops methods (Ward identities and higher equations of motion) that could be adapted to more symmetric models such as boundary Toda CFT. While the authors have proved Ward identities and higher equations of motion for the boundary \mathfrak{sl}_3 Toda theory, they note that comparable identities are largely absent in the physics literature beyond very special cases.

Because these identities underpin computations of structure constants, their absence has left several boundary Toda CFT structure constants uncomputed. The authors suggest that establishing such identities should facilitate the determination of these unknown constants, highlighting a specific unresolved aspect of boundary Toda CFT.