### 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) |
---|---|

Pages (from-to) | 333-371 |

Number of pages | 39 |

Journal | Communications in Mathematical Physics |

Volume | 218 |

Issue number | 2 |

State | Published - Apr 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*218*(2), 333-371.

**Nahm transform for periodic monopoles and N = 2 super Yang-Mills theory.** / Cherkis, Sergey; Kapustin, Anton.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 218, no. 2, pp. 333-371.

}

TY - JOUR

T1 - Nahm transform for periodic monopoles and N = 2 super Yang-Mills theory

AU - Cherkis, Sergey

AU - Kapustin, Anton

PY - 2001/4

Y1 - 2001/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035531907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035531907&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035531907

VL - 218

SP - 333

EP - 371

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -