Communications in Analysis and Geometry

Volume 29 (2021)

Number 7

The Nahm transform of spatially periodic instantons

Pages: 1691 – 1747



Masaki Yoshino (Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku , Kyoto, Japan)


We construct the Nahm transform from finite energy instantons on the product of a real line $\mathbb{R}$ and a three-dimensional torus $T^3$ to Dirac-type singular monopoles on the dual torus $\hat{T}^3$. Moreover, we show the correspondence between the data which handle the asymptotic behavior of instantons at infinity and one of monopoles at singular points.

Received 29 April 2018

Accepted 29 March 2019

Published 17 May 2022