Global Aspects of Abelian and Center Projections in SU(2) Gauge Theory

TL;DR

This paper introduces a new differential topological framework using Deligne cohomology and Cho structures to analyze global aspects of Abelian and center projections in SU(2) gauge theory, revealing natural emergence of monopole charges.

Contribution

It presents a novel approach employing Deligne cohomology and Cho structures to understand the global properties of gauge projections in SU(2) theory, including monopole charges.

Findings

Global aspects described by smooth Deligne cohomology.

Introduction of Cho structures as a new differential topological tool.

Natural appearance of half-integer monopole charges.

Abstract

We show that the global aspects of Abelian and center projection of a SU(2) gauge theory on an arbitrary manifold are naturally described in terms of smooth Deligne cohomology. This is achieved through the introduction of a novel type of differential topological structure, called Cho structure. Half integral monopole charges appear naturally in this framework.