Toroidal prefactorization algebras associated to holomorphic fibrations and a relationship to vertex algebras

Let X be a complex manifold, π:E→X locally trivial holomorphic fibration with fiber F, and (g,〈•,•〉) Lie algebra an invariant symmetric form. We associate to this data prefactorization Fg,π on in the formalism of Costello-Gwilliam. When X=C, g is simple, F smooth affine variety, we extract from vertex which vacuum module for universal central extension g⊗H0(F,O)[z,z−1]. As special case, when algebraic torus (C⁎)n, obtain naturally associated (n+1)–toroidal algebra, generalizing module.