Abstract:
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 rôle in our analysis.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 15 October 1999 / Accepted: 19 January 2000
Rights and permissions
About this article
Cite this article
Houghton, C., Manton, N. & Romão, N. On the Constraints Defining BPS Monopoles. Comm Math Phys 212, 219–243 (2000). https://doi.org/10.1007/s002200000208
Issue Date:
DOI: https://doi.org/10.1007/s002200000208