Global Aspects of Abelian Duality in Dimension Three

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.