Spatially periodic instantons: Nahm transform and moduli

Abstract

This paper establishes that the Nahm transform sending spatially periodic instantons (instantons on the product of the real line and a three-torus) to singular monopoles on the dual three-torus is indeed a bijection as suggested by the heuristic. In the process, we show how the Nahm transform intertwines to a Fourier-Mukai transform via Kobayashi-Hitchin correspondences. We also prove existence and non-existence results.

References in corpus (6)

• Instantons on Gravitons
• Moduli Spaces of Instantons on the Taub-NUT Space
• A survey on Nahm transform
• Singular Monopoles via the Nahm Transform
• Domain Walls, Triples and Acceleration
• Some characterizations of Dirac type singularity of monopoles

Cited by in corpus (4)

• Kobayashi-Hitchin correspondence for analytically stable bundles
• A Kobayashi-Hitchin correspondence between Dirac-type singular mini-holomorphic bundles and HE-monopoles
• Construction of Exact Solutions to Nahm's Equations for the Multimonopole
• Instantons and Bows for the Classical Groups