In rational conformal field theory, the sewing and factorization properties are probably the most important properties that conformal blocks satisfy. For special examples such as Weiss-Zumino-Witten models and minimal models, these two properties were proved decades ago (assuming the genus is ≤1 for the sewing theorem). But for general (strongly) rational vertex operator algebras (VOAs), their proofs were finished only very recently. In this talk, I will first motivate the definition of conformal blocks and VOAs using Segal's picture of CFT. I will then explain the importance of Sewing and Factorization Theorem in the construction of full rational conformal field theory.
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- Topology Seminar