Full enveloping vertex algebra from factorisation

Vertex operator algebras provide a succinct mathematical description of the chiral sector of two-dimensional conformal field theories. Various extensions of the framework of vertex operator algebras have been proposed in the literature which are capable of describing full two-dimensional conformal field theories, including both chiral and anti-chiral sectors. I will explain how the notion of a full vertex operator algebra can be elegantly described using the modern language of factorisation algebras developed by Costello and Gwilliam. This talk will be mainly based on [arXiv:2501.08412].