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Spectral Curves and the Mass of Hyperbolic Monopoles

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Abstract

The moduli spaces of hyperbolic monopoles are naturally fibred by the monopole mass, and this leads to a nontrivial mass dependence of the holomorphic data (spectral curves, rational maps, holomorphic spheres) associated to hyperbolic multi-monopoles. In this paper, we obtain an explicit description of this dependence for general hyperbolic monopoles of magnetic charge two. In addition, we show how to compute the monopole mass of higher charge spectral curves with tetrahedral and octahedral symmetries. Spectral curves of euclidean monopoles are recovered from our results via an infinite-mass limit.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, 3010, Melbourne, Australia

    Paul Norbury

  2. School of Mathematical Sciences, University of Adelaide, 5005, Adelaide, Australia

    Nuno M. Romão

Authors
  1. Paul Norbury
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  2. Nuno M. Romão
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Correspondence to Nuno M. Romão.

Additional information

Communicated by G.W. Gibbons.

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Norbury, P., Romão, N.M. Spectral Curves and the Mass of Hyperbolic Monopoles. Commun. Math. Phys. 270, 295–333 (2007). https://doi.org/10.1007/s00220-006-0148-4

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  • DOI: https://doi.org/10.1007/s00220-006-0148-4

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