A note on vertex algebras and Costello-Gwilliam factorization algebras

TL;DR

This paper demonstrates that vertex algebras can be constructed from Costello-Gwilliam factorization algebras without the discreteness condition, and explores their relation to jet algebras and locally constant factorization algebras.

Contribution

It removes the discreteness condition in the construction of vertex algebras from factorization algebras and links these structures to jet algebras and locally constant factorization algebras.

Findings

Vertex algebras constructed without discreteness condition

Relation established between factorization algebras and jet algebras

Construction of locally constant factorization algebras from commutative vertex algebras

Abstract

We show that the construction of vertex algebras from Costello-Gwilliam factorization algebras on $\mathbb{C}$ can be achieved without the discreteness condition on the weight spaces. Furthermore, we construct locally constant factorization algebras from commutative vertex algebras, and discuss the relationship between this construction and the jet algebras of commutative algebras.