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arXiv · 2303.18189

Towards a Classification of Charge-3 Monopoles with Symmetry

H. W. Braden·Linden Disney-Hogg
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Abstract

We classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole spectral curve become ones regarding periods of elliptic functions. We construct the Nahm data and new monopole spectral curves with $D_6$ and $V_4$ symmetry, the latter based on an integrable complexification of Euler's equations, and for which energy density isosurfaces are plotted. Extensions of our approach to higher charge and hyperbolic monopoles are discussed.

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H. W. Braden, Linden Disney-Hogg. 2023-03-31. Towards a Classification of Charge-3 Monopoles with Symmetry. https://doi.org/10.1007/s11005-023-01708-5

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