Homotopy colimits and global observables in Abelian gauge theory

TL;DR

This paper develops a homotopy-theoretic framework to extend local Abelian gauge theory data from contractible to non-contractible manifolds, capturing global observables and configurations.

Contribution

It introduces a method using homotopy theory to extend chain complexes of gauge fields and observables to general manifolds, preserving their local-to-global structure.

Findings

Successfully extends local gauge data to global settings

Provides functorial descriptions of gauge theories on various manifolds

Ensures the original local data is recovered up to weak equivalence

Abstract

We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds by using techniques from homotopy theory. The extension prescription yields functors from a category of manifolds to suitable categories of chain complexes. The extended functors properly describe the global field and observable content of Abelian gauge theory, while the original gauge field configurations and observables on contractible manifolds are recovered up to a natural weak equivalence.