Abstract
We study various composites of global solitons consisting of domain walls, strings, and monopoles in linear O(N) models with N = 2 and 3. Spontaneous symmetry breaking (SSB) of the O(N) symmetry down to O(N – 1) results in the vacuum manifold SN−1, together with a perturbed scalar potential in the presence of a small explicit symmetry breaking (ESB) interaction. The O(2) model is equivalent to the axion model admitting topological global (axion) strings attached by NDW domain walls. We point out for the NDW = 2 case that the topological stability of the string with two domain walls is ensured by sequential SSBs (ℤ2)2 → ℤ2 → 1, where the first SSB occurs in the vacuum leading to the topological domain wall as a mother soliton, only inside which the second SSB occurs giving rise to a subsequent kink inside the mother wall. From the bulk viewpoint, this kink is identical to a global string as a daughter soliton. This observation can be naturally ex- tended to the O(3) model, where a global monopole as a daughter soliton appears as a kink in a mother string or as a vortex on a mother domain wall, depending on ESB interactions. In the most generic case, the stability of the composite system consisting of the monopole, string, and domain wall is understood by the SSB (ℤ2)3 → (ℤ2)2 → ℤ2 → 1, in which the first SSB at the vacuum gives rise to the domain wall triggering the second one, so that the daughter string appears as a domain wall inside the mother wall triggering the third SSB, which leads to a granddaughter monopole as a kink inside the daughter vortex. We demonstrate numerical simulations for the dynamical evolution of the composite solitons.
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Acknowledgments
This work is supported in part by JSPS Grant-in-Aid for Scientific Research KAKENHI Grant No. JP22H01221 (M. E. and M. N), Grant No. JP19K03839 (M. E.), Grant No. JP21J01117 (Y. H.), and Grant No. JP18H01217 (M. N.). The work of M. E. is also supported by the MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design” No. JP17H06462 from the MEXT of Japan. M.N. is also supported in part by the WPI program “Sustainability with Knotted Chiral Meta Matter (SKCM2)” at Hiroshima University.
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Eto, M., Hamada, Y. & Nitta, M. Composite topological solitons consisting of domain walls, strings, and monopoles in O(N) models. J. High Energ. Phys. 2023, 150 (2023). https://doi.org/10.1007/JHEP08(2023)150
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DOI: https://doi.org/10.1007/JHEP08(2023)150