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Arithmetic Constraints on Charges of Symmetric Monopoles

  • Paul Cusson
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Abstract

For Euclidean BPS monopoles with gauge group SU(N), maximal symmetry breaking, and sufficiently generic spectral data, we produce necessary congruence relations that their magnetic charges must satisfy when N ≥ 3. As such, a monopole as above with given charges can have certain subgroups of SO(3) ruled out as possible groups of symmetries. In particular, the axially symmetric case may only admit non-trivial magnetic charges in the non-generic setting.

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Cite

BibTeXRIS
BibTeX
@misc{cusson2026arithmetic,
  title = {{Arithmetic Constraints on Charges of Symmetric Monopoles}},
  author = {Paul Cusson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24139},
  eprint = {2610.24139},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24139},
}
RIS
TY  - UNPB
TI  - Arithmetic Constraints on Charges of Symmetric Monopoles
AU  - Paul Cusson
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.24139
UR  - https://arxiv.org/abs/2610.24139
AB  - For Euclidean BPS monopoles with gauge group SU(N), maximal symmetry breaking, and sufficiently generic spectral data, we produce necessary congruence relations that their magnetic charges must satisfy when N ≥ 3. As such, a monopole as above with given charges can have certain subgroups of SO(3) ruled out as possible groups of symmetries. In particular, the axially symmetric case may only admit non-trivial magnetic charges in the non-generic setting.
ER  -