2000/06/30 by Sergey A. Cherkis, Anton Kapustin · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Dyon #Gauge group #Gauge theory #Geometry and complex manifolds #Higgs boson #Infinity #Magnetic monopole #Mathematical analysis #Mathematical physics #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Quantum mechanics #Space (punctuation) #String theory #Yang–Mills existence and mass gap #Yang–Mills theory #hep-th #math.AG #math.DG
paper · pdf · doi:10.1007/pl00005558
published as Commun.Math.Phys. 218 (2001) 333-371 · 48 pages, AMS latex. v2: several minor errors corrected, exposition improved
arxiv created 2000/07/07 · openalex publication_date 2001/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study Bogomolny equations on R2× S1. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperkähler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of \cal N=2 super Yang-Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.