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

Matt Szczesny, Jackson Walters, Brian R Williams

Research output: Working paper

Abstract

Let X be a complex manifold, π:E→X a locally trivial holomorphic fibration with fiber F, and g a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization algebra Fg,π on X in the formalism of Costello-Gwilliam. When X=C, g is simple, and F is a smooth affine variety, we extract from Fg,π a vertex algebra which is a vacuum module for the universal central extension of the Lie algebra g⊗H0(F,O)[z,z−1]. As a special case, when F is an algebraic torus (C∗)n, we obtain a vertex algebra naturally associated to an (n+1)--toroidal algebra, generalizing the affine vacuum module.
Original languageEnglish
PublisherArXiv
Number of pages40
Publication statusPublished - 5 Apr 2019

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