Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 4

The charge $2$ monopole via the ADHMN construction

Pages: 791 – 956



H. W. Braden (School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, Scotland, United Kingdom)

V. Z. Enolski (National University of Kyiv-Mohyla Academy, Kyiv, Ukraine)


Recently we have shown how one may use use integrable systems techniques to implement the ADHMN construction and obtain general analytic formulae for the charge $n \: su(2)$ Euclidean monopole. Here we do this for the case of charge $2$ giving the first analytic expressions (for general $x \in \mathbb{R}^3$) for the gauge invariant $\mathrm{Tr} \Phi^2$, where $\Phi$ is the Higgs field, and the energy density. A comparison with known results and other approaches is made and new results presented.

V. Z. Enolski died in 2019.

Appendix by David E. Braden, Peter Braden, and H. W. Braden

Published 12 April 2022