The Nahm transform of spatially periodic instantons

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.

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Received 29 April 2018

Accepted 29 March 2019

Published 17 May 2022