Description
We introduce a CFT factory -- a novel algorithm of methodically generating 2D lattice models that would flow to conformal field theories (CFTs) in the infrared. We realise these models by engineering the boundary conditions of 2+1D topological orders described by string-net models. The critical points are induced by a commensurate condensation of non-commuting anyons. Our structured method generates an infinite family of critical lattice models, including the A-series minimal models, and uncovers previously unknown critical points. Notably, we discover at least three novel CFT candidates (with central charges 1.31, 1.32 and 2.11) that preserve the Haagerup symmetries, in addition to recovering previously reported examples. The critical couplings are precisely encoded in algebraic data (the Frobenius algebras and quantum dimensions of unitary fusion categories), thereby establishing a powerful and systematic route to the discovery and potential classification of new CFTs.
