Factorization envelopes and enveloping vertex algebras

2025/12/08 by Nishinaka, Yusuke
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2512.07635

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.

Citations

• Full universal enveloping vertex algebras from factorisation
• A note on vertex algebras and Costello-Gwilliam factorization algebras
• Vertex Algebras and Costello-Gwilliam Factorization Algebras
• Geometric Vertex Algebras

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• Supersymmetric extension of universal enveloping vertex algebras