TL;DR
This paper investigates the presence of anti-zeros in SU(2) BPS monopoles with Platonic symmetries, revealing that some monopoles have more Higgs field zeros than their topological charge, indicating complex local winding behavior.
Contribution
It provides the first detailed analysis of anti-zeros in Platonic monopoles, expanding understanding of their Higgs field structure and topological properties.
Findings
Anti-zeros exist in certain Platonic monopoles.
The number of Higgs zeros can exceed the monopole charge.
Anti-zeros have opposite local winding to the total winding.
Abstract
Recently the existence of certain SU(2) BPS monopoles with the symmetries of the Platonic solids has been proved. Numerical results in an earlier paper suggest that one of these new monopoles, the tetrahedral 3-monopole, has a remarkable new property, in that the number of zeros of the Higgs field is greater than the topological charge (number of monopoles). As a consequence, zeros of the Higgs field exist (called anti-zeros) around which the local winding number has opposite sign to that of the total winding. In this letter we investigate the presence of anti-zeros for the other Platonic monopoles. Other aspects of anti-zeros are also discussed.
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