Global Aspects of Abelian Duality in Dimension Three

TL;DR

This paper explores the extension of abelian duality between gauge fields and scalar fields from Euclidean space to general three-manifolds, emphasizing the role of topological features in the partition function.

Contribution

It analyzes how topological properties of three-manifolds influence abelian duality and the partition function, extending previous Euclidean space results.

Findings

Topological features significantly affect the partition function on three-manifolds.

Duality relations are preserved when considering general three-manifolds.

Connections to operator algebra on surfaces of genus g are discussed in related work.

Abstract

In three dimensions, an abelian gauge field is related by duality to a free, periodic scalar field. Though usually considered on Euclidean space, this duality can be extended to a general three-manifold M, in which case topological features of M become important. Here I comment upon several of these features as related to the partition function on M. In a companion article, arXiv:1405.2483, I discuss similarly the algebra of operators on a surface of genus g.