Abelian duality in three dimensions

TL;DR

This paper explores Abelian duality in three-dimensional manifolds by explicitly calculating and comparing partition functions of U(1) gauge theory and circle-valued scalar field theory, demonstrating their mutual duality.

Contribution

It provides explicit calculations of partition functions for dual theories on three-dimensional manifolds, confirming their duality.

Findings

Partition functions for U(1) gauge theory and scalar field theory are explicitly computed.

The two theories are shown to be mutually dual on closed three-dimensional manifolds.

Abstract

Abelian duality on the closed three-dimensional Riemannian manifold M is discussed. Partition functions for the ordinary U(1) gauge theory and a circle-valued scalar field theory on M are explicitly calculated and compared. It is shown that the both theories are mutually dual.