English

Remarks on the complex geometry of the 3-monopole

Mathematical Physics 2007-05-23 v1 High Energy Physics - Theory Differential Geometry math.MP Exactly Solvable and Integrable Systems

Abstract

We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number theoretic problem and a recently proven identity of Ramanujan provides a solution. The Ercolani-Sinha construction provides a gauge-transform of the Nahm data.

Keywords

Cite

@article{arxiv.math-ph/0601040,
  title  = {Remarks on the complex geometry of the 3-monopole},
  author = {H. W. Braden and V. Z. Enolski},
  journal= {arXiv preprint arXiv:math-ph/0601040},
  year   = {2007}
}

Comments

65 pages, 6 figures

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