On the constraints defining BPS monopoles

Details On the constraints defining BPS monopoles On the constraints defining BPS monopoles

1999-09-23

arxiv.org/abs/hep-th/9909168v1

Commun.Math.Phys. 212 (2000) 219-243

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 7 eps figures

Scientific paper

10.1007/s002200000208

We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an important role in our analysis.

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