Given a chiral vertex operator algebra satisfying a suitable finiteness condition with semisimplicity of the zero-mode algebra as well as a regularity condition for induced modules, we construct conformal field theories over the projective line and prove the factorization theorem. We appropriately generalize the arguments in [TUY] so that we are able to define sheaves of conformal blocks and study them in detail.
Kiyokazu Nagatomo. Akihiro Tsuchiya. "Conformal field theories associated to regular chiral vertex operator algebras, I: Theories over the projective line." Duke Math. J. 128 (3) 393 - 471, 15 June 2005. https://doi.org/10.1215/S0012-7094-04-12831-3