arXiv subjects
Publications and source records attributed to C. J. Houghton.
In the generalized Legendre transform construction the Kaehler potential is related to a particular function. Here, the form of this function appropriate to the monopole metric is calculated from the known twistor theory of monopoles.
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.