Vertex Algebras and Factorization Algebras

There are several mathematical approaches to chiral two-dimensional conformal field theory. One of them is the notion of a factorization algebra on a Riemann surface, introduced by Costello and Gwilliam and inspired by Beilinson and Drinfeld's algebro-geometric notion of factorization algebra. Costello and Gwilliam construct vertex algebras from holomorphic factorization algebras on C. We construct holomorphic factorizations algebras from vertex algebras using geometric vertex algebras as an intermediate notion. The main theorem is that the constructed precosheaf is a cosheaf for the Weiss topology.