Nahm transform for periodic monopoles and \(\mathcal N=2\) super Yang-Mills theory
By ``periodic monopoles'' the authors mean solutions of the Bogomolny equation on \(\mathbb R^2\times S^1\) whose Higgs fields grow logarithmically at infinity. A Nahm transform argument establishes a one-to-one correspondence between such objects and solutions of the Hitchin equations on a cylinder growing exponentially at infinity. More precisely, the authors associate spectral data (a complex curve with a line bundle on it) to a periodic monopole, and show that these can be identified with the spectral data coming from a Hitchin pair via the usual Nahm transform. The authors briefly discuss moduli spaces of periodic monopoles, showing that they have a hyper-Kähler structure. The paper also establishes a connection between periodic monopoles and \(\mathcal N=2\), \(SU(k)\) super Yang-Mills theory compactified on a circle, with \(k\) the charge of the periodic monopole.
scientific article; zbMATH DE number 1631791