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Domain walls from ∑(36×3), Δ(54) and Δ(27) potentials

Gonçalo Barreto1,*, Ivo de Medeiros Varzielas1,†, and Ye-Ling Zhou2,‡

  • *Contact author: goncalormbarreto@tecnico.ulisboa.pt
  • †Contact author: ivo.de@udo.edu
  • ‡Contact author: zhouyeling@ucas.ac.cn
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Phys. Rev. D 113, 115019 – Published 9 June, 2026

DOI: https://doi.org/10.1103/7qx6-568y

Abstract

We consider the degenerate minima arising from scalar potentials invariant under Σ(36×3), or under its subgroups Δ(54) and Δ(27) (with or without imposed CP symmetries), for a triplet of those symmetries. In this framework, we classify the distinct domain walls between the degenerate minima and calculate the respective tensions.

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References (50)

  1. Z. z. Xing, Phys. Rep. 854, 1 (2020).
  2. F. Feruglio and A. Romanino, Rev. Mod. Phys. 93, 015007 (2021).
  3. G. J. Ding and S. F. King, Rep. Prog. Phys. 87, 084201 (2024).
  4. V. Keus, S. F. King, and S. Moretti, J. High Energy Phys. 01 (2014) 052.
  5. I. P. Ivanov, Prog. Part. Nucl. Phys. 95, 160 (2017).
  6. I. P. Ivanov and E. Vdovin, Eur. Phys. J. C 73, 2309 (2013).
  7. A. Kunčinas, P. Osland, and M. N. Rebelo, arXiv:2512.07657.
  8. N. Darvishi and A. Pilaftsis, Phys. Rev. D 101, 095008 (2020).
  9. N. Darvishi, M. R. Masouminia, and A. Pilaftsis, Phys. Rev. D 104, 115017 (2021).
  10. I. de Medeiros Varzielas and I. P. Ivanov, Phys. Rev. D 100, 015008 (2019).
  11. A. E. Cárcamo Hernández, I. de Medeiros Varzielas, M. L. López-Ibáñez, and A. Melis, J. High Energy Phys. 05 (2021) 215.
  12. I. de Medeiros Varzielas, I. P. Ivanov, and M. Levy, Eur. Phys. J. C 81, 918 (2021).
  13. J. Kalinowski, W. Kotlarski, M. N. Rebelo, and I. de Medeiros Varzielas, J. High Energy Phys. 02 (2023) 231.
  14. I. de Medeiros Varzielas and D. Ivo, Eur. Phys. J. C 82, 415 (2022).
  15. S. Carrolo, J. C. Romao, and J. P. Silva, Eur. Phys. J. C 82, 749 (2022).
  16. A. Kunčinas, O. M. Ogreid, P. Osland, and M. N. Rebelo, J. High Energy Phys. 07 (2023) 013.
  17. G. Barreto and I. de Medeiros Varzielas, Eur. Phys. J. C 85, 1416 (2025).
  18. I. de Medeiros Varzielas, M. S. Liu, A. Sengupta, and J. Talbert, arXiv:2512.19789.
  19. I. de Medeiros Varzielas and J. Talbert, Phys. Lett. B 800, 135091 (2020).
  20. A. E. Cárcamo Hernández, C. Espinoza, J. C. Gómez-Izquierdo, J. Marchant González, and M. Mondragón, Eur. Phys. J. C 84, 1239 (2024).
  21. I. Bree, S. Carrolo, J. C. Romao, and J. P. Silva, Eur. Phys. J. C 83, 292 (2023).
  22. V. V. Vien, Chin. J. Phys. (Taipei) 93, 418 (2025).
  23. T. W. B. Kibble, J. Phys. A 9, 1387 (1976).
  24. A. Afzal et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L11 (2023); 971, L27(E) (2024).
  25. K. Saikawa, Universe 3, 40 (2017).
  26. N. Kitajima, J. Lee, K. Murai, F. Takahashi, and W. Yin, Phys. Lett. B 851, 138586 (2024).
  27. R. Z. Ferreira, S. Gasparotto, T. Hiramatsu, I. Obata, and O. Pujolas, J. Cosmol. Astropart. Phys. 05 (2024) 066.
  28. R. Z. Ferreira, A. Notari, O. Pujolàs, and F. Rompineve, J. Cosmol. Astropart. Phys. 06 (2024) 020.
  29. I. Dankovsky, E. Babichev, D. Gorbunov, S. Ramazanov, and A. Vikman, J. Cosmol. Astropart. Phys. 09 (2024) 047.
  30. Y. J. Li, J. Liu, and Z. K. Guo, Phys. Rev. D 112, 103510 (2025).
  31. S. Blasi, A. Mariotti, A. Rase, and M. Vanvlasselaer, arXiv:2511.16649.
  32. Y. Wu, K. P. Xie, and Y. L. Zhou, Phys. Rev. D 105, 095013 (2022).
  33. Y. Wu, K. P. Xie, and Y. L. Zhou, Phys. Rev. D 106, 075019 (2022).
  34. M. A. Ouahid, M. A. Loualidi, R. A. Laamara, and E. H. Saidi, Phys. Rev. D 102, 115023 (2020).
  35. A. Jueid, M. A. Loualidi, S. Nasri, and M. A. Ouahid, Phys. Rev. D 109, 055048 (2024).
  36. B. Fu, S. F. King, L. Marsili, S. Pascoli, J. Turner, and Y. L. Zhou, J. High Energy Phys. 04 (2025) 142.
  37. B. Fu, S. F. King, L. Marsili, J. Turner, and Y. L. Zhou, arXiv:2512.13784.
  38. G. B. Gelmini, S. Pascoli, E. Vitagliano, and Y. L. Zhou, J. Cosmol. Astropart. Phys. 02 (2021) 032.
  39. M. C. Chen, H. J. Matias, and C. Moffett-Smith, arXiv:2601.14394.
  40. W. M. Fairbairn, T. Fulton, and W. H. Klink, J. Math. Phys. (N.Y.) 5, 1038 (1964).
  41. W. Grimus and P. O. Ludl, J. Phys. A 43, 445209 (2010).
  42. G. C. Branco, J. M. Gerard, and W. Grimus, Phys. Lett. B 136, 383 (1984).
  43. I. de Medeiros Varzielas and D. Emmanuel-Costa, Phys. Rev. D 84, 117901 (2011).
  44. I. de Medeiros Varzielas, D. Emmanuel-Costa, and P. Leser, Phys. Lett. B 716, 193 (2012).
  45. G. Bhattacharyya, I. de Medeiros Varzielas, and P. Leser, Phys. Rev. Lett. 109, 241603 (2012).
  46. C. C. Nishi, Phys. Rev. D 88, 033010 (2013).
  47. I. de Medeiros Varzielas, S. F. King, C. Luhn, and T. Neder, Phys. Lett. B 775, 303 (2017).
  48. I. P. Ivanov and C. C. Nishi, J. High Energy Phys. 01 (2015) 021.
  49. C. L. Wainwright, Comput. Phys. Commun. 183, 2006 (2012).
  50. 10.54499/UID/00777/2025.

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Phys. Rev. D 113, 115019– Published 9 June, 2026
  • Received 18 March 2026
  • Accepted 8 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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