Abelian Duality and Abelian Wilson Loops

TL;DR

This paper investigates the duality properties of Abelian gauge theories on compact four-manifolds, focusing on Wilson loop insertions, topological sectors, and the conditions for manifest duality.

Contribution

It introduces the necessity of twisted topological sectors for manifest duality in Abelian gauge theories on four-manifolds.

Findings

Partition function with Wilson loops exhibits duality covariance.

Topological selection rules constrain Wilson loop configurations.

Existence of twisted sectors is essential for manifest duality.

Abstract

We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.