Abstract
We show that the Higgs and gauge fields for a BPS monopole may be constructed directly from the spectral curve without having to solve the gauge constraint needed to obtain the Nahm data. The result is the analogue of the instanton result: given ADHM data one can reconstruct the gauge fields algebraically together with differentiation. Here, given the spectral curve, one can similarly reconstruct the Higgs and gauge fields. This answers a problem that has remained open since the discovery of monopoles.
Highlights
Despite the study of BPS monopoles being a mature subject, over 35 years old, and having uncovered many remarkable results, a number of the original questions that sparked its development remain unanswered
Numerical results based on these constructions and utilising the increase in computing power over the period have meant that we can understand a number of qualitative aspects of monopole behaviour; at the very least analytic solutions would give some control over these
In this paper we shall describe how to explicitly construct the Higgs and gauge fields for a monopole and circumvent those usually intractable steps; a number of new results will appear in the process
Summary
Despite the study of BPS monopoles being a mature subject, over 35 years old, and having uncovered many remarkable results, a number of the original questions that sparked its development remain unanswered. Enolski is implicit in the Bäcklund transformation construction of Forgács et al [8] This curve gives a point in the moduli space of SU (2) charge-n monopoles and we note that the relationship between this description of the moduli space and both Donaldson’s rational map and Jarvis’s rational map descriptions remains still poorly understood. We conclude with a limited example showing how our construction yields a known result in the charge 2 setting; in a sequel paper we shall present the general results for the fields of the charge 2 monopole
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