Nahm transform for periodic monopoles and \(\mathcal N=2\) super Yang-Mills theory
type: Item
instance of: scholarly article
title: Nahm transform for periodic monopoles and \(\mathcal N=2\) super Yang-Mills theory
zbMATH Open document ID: 1003.53025
DOI: 10.1007/PL00005558
author: Sergey A. Cherkis
author: Anton Kapustin
published in: Communications in Mathematical Physics
publication date: 2001-08-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0006050
review text: 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.
reviewed by: Ugo Bruzzo
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 58D27
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 70S15
zbMATH DE Number: 1631791
zbMATH Keywords: periodic monopoles
zbMATH Keywords: Nahm transform
zbMATH Keywords: super Yang-Mills theory
zbMATH Keywords: Bogomolny equation
zbMATH Keywords: hyper-Kähler structure
MaRDI profile type: Publication
arXiv ID: hep-th/0006050
description: scientific article; zbMATH DE number 1631791