Factorization envelopes and enveloping vertex algebras

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.