Vertex algebras and factorization algebras are two approaches to chiral conformal field theory. The subject of vertex algebras is well-developed. Some aspects of it have been reformulated in terms of the geometry of C, the plane of complex numbers, or other Riemann surfaces. Factorization algebras as developed by Costello and Gwilliam [3] are a more general approach to quantum field theory which applies to all kinds of geometries, including higher dimensional manifolds. This article compares… Expand