Daniel Bruegmann

Vertex Algebras and Factorization Algebras

Vertex algebras and factorization algebras are two approaches to chiral conformal field theory, a part of quantum field theory related to holomorphic functions of a single variable. Many examples of chiral CFT's have been constructed as vertex algebras. Factorization algebras as studied by Costello and Gwilliam are a relatively new approach to quantum field theory which applies to all kinds of geometries, including higher-dimensional ones. We focus on ℂ, the plane of complex numbers.

Some examples of chiral CFT's have already been constructed as factorization algebras but not all of them. Furthermore, Costello and Gwilliam show how every suitable factorization algebra on ℂ gives rise to a vertex algebra. In my thesis, I show that every vertex algebra arises from a factorization algebra.