Chiral Algebras, Factorization Algebras, and Borcherds’s “Singular Commutative Rings” Approach to Vertex Algebras

Abstract

We recall Borcherds’s approach to vertex algebras via “singular commutative rings”, and introduce new examples of his constructions which we compare to vertex algebras, chiral algebras, and factorization algebras. We show that all vertex algebras (resp. chiral algebras or equivalently factorization algebras) can be realized in these new categories $$\text {VA}(A,H,S)$$ .