Factorization envelopes and enveloping vertex algebras

TL;DR

This paper introduces a construction of factorization algebras from Lie conformal algebras, generalizing known examples and extending to superalgebras, with proofs of isomorphisms to enveloping vertex algebras.

Contribution

It provides a new method to construct factorization algebras from Lie conformal algebras, including superalgebras, and proves their isomorphism to enveloping vertex algebras.

Findings

Construction of factorization algebra from Lie conformal algebra

Generalization of Kac--Moody and Virasoro factorization algebras

Extension to superalgebras like Neveu--Schwarz and N=2

Abstract

We construct a factorization algebra, via the factorization envelope, starting from a Lie conformal algebra, and prove that the associated vertex algebra is isomorphic to its enveloping vertex algebra. Our construction generalizes the Kac--Moody factorization algebra of Costello--Gwilliam and the Virasoro factorization algebra of Williams. Moreover, by considering the super analogue of this construction, we obtain new factorization algebras corresponding to vertex superalgebras, such as the Neveu--Schwarz vertex superalgebra and the $N=2$ vertex superalgebra.