Let $X$ be a complex manifold, $\pi: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{ g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization algebra $\mathcal{ F}_{ \mathfrak{ g}, \pi}$ on $X$ in the formalism of Costello-Gwilliam. When $X=\mathbb{ C}$, $\mathfrak{ g}$ is simple, and $F$ is a smooth affine variety, we extract from $\mathcal{ F}_{ \mathfrak{ g}, \pi}$ a vertex algebra which is a vacuum module for the universal central extension of the Lie algebra $\mathfrak{ g} \otimes H^{ 0}(F, \mathcal{ O})[z,z^{ -1}]$. As a special case, when $F$ is an algebraic torus $(\mathbb{ C}^{ *})^n$, we obtain a vertex algebra naturally associated to an $(n+1)$--toroidal algebra, generalizing the affine vacuum module.
Categories: math.QA math-ph math.AG math.MP math.RT
