## Abstract

An Abelian gauge field theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the first Chern class ci(L) and by a certain intersection number obtained from the multivortices. We show that E = 2ir(N + P). To realize such topological invariants as minimum energies, an existence and uniqueness theorem is established under the necessary and sufficient condition that |ci(L)| = \N -P\ < (total volume of M)/27r.

Original language | English (US) |
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Pages (from-to) | 593-613 |

Number of pages | 21 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 456 |

Issue number | 1995 |

DOIs | |

State | Published - 2000 |

## Keywords

- Characteristic classes
- Complex line bundles
- Leray-schauder theorem
- Self-duality
- Trudinger-moser inequality
- Vortices

## ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)