Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry

TL;DR

This paper establishes the existence of a line bundle with the factorization property on Beilinson-Drinfeld Grassmannians associated with certain gerbes, leading to a factorization algebra, advancing the understanding of geometric structures in differential geometry.

Contribution

It constructs a line bundle with the factorization property on Beilinson-Drinfeld Grassmannians for multiplicative gerbes, linking geometric and algebraic structures.

Findings

Existence of line bundle with factorization property

Construction of a factorization algebra from global sections

Extension of geometric structures to higher dimensions

Abstract

We prove that for any k greater or equal to 2, given a smooth compact k-dimensional manifold and a multiplicative k-1-gerbe on a Lie group, together with an integrable connection, there is a line bundle on the corresponding Beilinson-Drinfeld Grassmannian having the factorization property. We show that taking global sections of this line bundle we obtain a factorization algebra.