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.