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PreprintarXiv licencearXiv

The stability of non-Abelian A4 vortices in SO(3) gauge theory

  • Yoshihiko Abe
  • Tetsutaro Higaki
  • Kazuya Murakami
  • Muneto Nitta
  • Ryo Yokokura
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Abstract

We study the linear energetic stability of non-Abelian vortices in an SO(3) gauge-Higgs theory with residual gauge group A4. In our previous work, we identified two families of such vortices associated with order-two and order-three elements of A4, and found Bogomol'nyi--Prasad--Sommerfield-like behavior at special ratios of the Higgs and gauge-boson mass scales. Here, we investigate their stability against SO(3) gauge and Higgs perturbations by analyzing the second order variation of the vortex tension using analytical and numerical methods. In particular, when all relevant mass scales are equal, we prove linear stability for all vortices in the order-three family. By contrast, at the same mass point, we prove that a vortex in the order-two family is unstable. Thus, although both vortex families exhibit Bogomol'nyi--Prasad--Sommerfield-like behavior in their reduced equations at this mass point, their stability properties in the full SO(3) theory are qualitatively different.

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Cite

BibTeXRIS
BibTeX
@misc{abe2026stability,
  title = {{The stability of non-Abelian $A_4$ vortices in $SO(3)$ gauge theory}},
  author = {Yoshihiko Abe and Tetsutaro Higaki and Kazuya Murakami and Muneto Nitta and Ryo Yokokura},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19963},
  eprint = {2610.19963},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19963},
}
RIS
TY  - UNPB
TI  - The stability of non-Abelian A_4 vortices in SO(3) gauge theory
AU  - Yoshihiko Abe
AU  - Tetsutaro Higaki
AU  - Kazuya Murakami
AU  - Muneto Nitta
AU  - Ryo Yokokura
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19963
UR  - https://arxiv.org/abs/2610.19963
AB  - We study the linear energetic stability of non-Abelian vortices in an SO(3) gauge-Higgs theory with residual gauge group A_4. In our previous work, we identified two families of such vortices associated with order-two and order-three elements of A_4, and found Bogomol'nyi--Prasad--Sommerfield-like behavior at special ratios of the Higgs and gauge-boson mass scales. Here, we investigate their stability against SO(3) gauge and Higgs perturbations by analyzing the second order variation of the vortex tension using analytical and numerical methods. In particular, when all relevant mass scales are equal, we prove linear stability for all vortices in the order-three family. By contrast, at the same mass point, we prove that a vortex in the order-two family is unstable. Thus, although both vortex families exhibit Bogomol'nyi--Prasad--Sommerfield-like behavior in their reduced equations at this mass point, their stability properties in the full SO(3) theory are qualitatively different.
ER  -