The charge 2 monopole via the ADHMN construction

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Braden, Harry W.
Enolski, Victor
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This paper describes the exact solution of the gauge and Higgs fields for charge two su(2) Euclidean monopoles. Despite BPS monopoles having been studied for over 35 years, and having uncovered extraordinarily beautiful structures, such analytic reconstruction has (with the exception of some partial results that will later be recalled) proved too hard. We often know more about the moduli space of these solutions than we do the actual fields. This is particularly true in the charge two setting: the Atiyah-Hitchin manifold, the moduli space of the centred charge two monopoles, is a well-studied and rich object and yet the analytic solution of the fields has proved elusive. Recently a general program for reconstructing the gauge theory data for su(2) Euclidean monopoles of general charge has been given, circumventing a number of previously intractable steps. This lowest charge case is a useful testing ground and will produce a number of new results. (The spherically symmetric case for charge one and coincident charge n monopoles is amenable to other approaches.) We will compare our results with some of the numerical studies that have been undertaken. Although constructing exact solutions – be they of gravity or gauge theory – is often viewed as a rather recondite area of research analytic solutions give at the very least some control over numerical results.
Euclidean monopoles, gauge theory, analytic approaches, spectral curve, monopole, ADHMN, article
Braden H. W. The charge 2 monopole via the ADHMN construction / Braden H. W., Enolski V. Z. // Advances in Theoretical and Mathematical Physics. - 2021. - Vol. 25, Number 4. - P. 791-956. -