Periodic monopoles with singularities and N = 2 super-QCD

Sergey A. Cherkis, Anton Kapustin

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We study solutions of the Bogomolny equation on ℝ2 × S1 with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperkähler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N = 2 d = 4 supersymmetric gauge theories on ℝ3 × S1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ2 × S1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.

Original languageEnglish (US)
Pages (from-to)1-35
Number of pages35
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Mar 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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