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arXiv · 2512.07635

Factorization envelopes and enveloping vertex algebras

Yusuke Nishinaka
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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.

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Yusuke Nishinaka. 2025-12-08. Factorization envelopes and enveloping vertex algebras. https://arxiv.org/abs/2512.07635

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