TY - UNPB

T1 - Toroidal prefactorization algebras associated to holomorphic fibrations and a relationship to vertex algebras

AU - Szczesny, Matt

AU - Walters, Jackson

AU - Williams, Brian R

PY - 2019/4/5

Y1 - 2019/4/5

N2 - 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.

AB - 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.

M3 - Working paper

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

PB - ArXiv

ER -