The Nahm transform of spatially periodic instantons

TL;DR

This paper develops a mathematical transformation linking finite energy instantons on a line times a 3-torus to monopoles on the dual torus, revealing a correspondence between their asymptotic behaviors.

Contribution

It introduces the Nahm transform for spatially periodic instantons and establishes a correspondence with monopoles at singular points.

Findings

Constructed the Nahm transform for instantons on R x T^3.

Established the relationship between instanton asymptotics and monopole singularities.

Demonstrated the correspondence between instanton data and monopole data.

Abstract

We construct the Nahm transform from finite energy instantons on the product of a real line and a three dimensional torus to Dirac-type singular monopoles on the dual torus. Moreover, we show the correspondence between the data which handle the asymptotic behavior of instantons at infinity and one of monopoles at singular points.