Nahm transform for periodic monopoles and N = 2 super Yang-Mills theory

Sergey Cherkis, Anton Kapustin

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


We study Bogomolny equations on ℝ2 × double-struck S sign11. 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 the 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 N = 2 super Yang-Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.

Original languageEnglish (US)
Pages (from-to)333-371
Number of pages39
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Apr 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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