### Abstract

We study Bogomolny equations on ℝ^{2} × double-struck S sign^{1}1. 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 language | English (US) |
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Pages (from-to) | 333-371 |

Number of pages | 39 |

Journal | Communications in Mathematical Physics |

Volume | 218 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2001 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications in Mathematical Physics*,

*218*(2), 333-371. https://doi.org/10.1007/PL00005558