Complete classification of rational conformal field theories (RCFTs)

Develop a complete classification of two‑dimensional rational conformal field theories, including all possible chiral algebras, modular invariants, and consistent spectra consistent with unitarity and modular invariance.

Background

RCFTs play a central role in exactly solvable models and in the paper of 2D critical phenomena. While many families (e.g., WZW models, cosets, orbifolds, rational points of marginal deformations) are known, a comprehensive classification is lacking.

A full classification would systematize the landscape of solvable 2D CFTs and clarify relations among known constructions (cosets, orbifolds, tensor products) and modular invariants (ADE‑type and beyond).