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