Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature

TL;DR

This paper investigates the long-term behavior of doubly periodic instantons with finite energy and demonstrates their equivalence to wild harmonic bundles on the dual torus via the Nahm transform.

Contribution

It establishes the asymptotic analysis of doubly periodic instantons and proves their equivalence to wild harmonic bundles through the Nahm transform.

Findings

Asymptotic behavior characterized for instantons with square-integrable curvature.

Established the Nahm transform as an equivalence between instantons and harmonic bundles.

Demonstrated the correspondence on the dual torus.

Abstract

We study the asymptotic behaviour of doubly periodic instantons with square-integrable curvature. Then, we establish the equivalence given by the Nahm transform between the doubly periodic instantons with square integrable curvature and the wild harmonic bundles on the dual torus.