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Gauged compact Q-balls and Q-shells in a multicomponent CPN model

P. Klimas1,*, L. C. Kubaski1,†, N. Sawado2,‡, and S. Yanai3,§

  • *Contact author: pawel.klimas@ufsc.br
  • †Contact author: luizckubaski@gmail.com
  • ‡Contact author: sawadoph@rs.tus.ac.jp
  • §Contact author: yanai@toyota-ct.ac.jp
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Phys. Rev. D 112, 116020 – Published 26 December, 2025

DOI: https://doi.org/10.1103/3xv2-l6w4

Abstract

We study a multicomponent CPN model’s scalar electrodynamics. The model contains Q-balls and Q-shells, which are nontopological compact solitons with time dependency eiωt. Two coupled CPN models can decouple locally if one of their CPN fields takes the vacuum value. Because of the compacton nature of solutions, Q-shells can shelter another compact Q-ball or Q-shell within their hollow region. Even if compactons do not overlap, they can interact through the electromagnetic field. We investigate how the size of multicompacton formations is affected by electric charge, with a focus on structures with nonzero or zero total net charge.

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References (38)

  1. T. D. Lee and Y. Pang, Nontopological solitons, Phys. Rep. 221, 251 (1992).
  2. Sidney R. Coleman, Q-balls, Nucl. Phys. B262, 263 (1985); B269, 744(A) (1986).
  3. R. Friedberg, T. D. Lee, and Y. Pang, Scalar soliton stars and black holes, Phys. Rev. D 35, 3658 (1987).
  4. Philippe Jetzer, Boson stars, Phys. Rep. 220, 163 (1992).
  5. Steven L. Liebling and Carlos Palenzuela, Dynamical boson stars, Living Rev. Relativity 15, 6 (2012).
  6. Burkhard Kleihaus, Jutta Kunz, Claus Lammerzahl, and Meike List, Charged boson stars and black holes, Phys. Lett. B 675, 102 (2009).
  7. Burkhard Kleihaus, Jutta Kunz, Claus Lammerzahl, and Meike List, Boson shells harbouring charged black holes, Phys. Rev. D 82, 104050 (2010).
  8. H. Arodz and J. Lis, Compact Q-balls in the complex signum-Gordon model, Phys. Rev. D 77, 107702 (2008).
  9. Philip Rosenau and James M. Hyman, Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70, 564 (1993).
  10. Philip Rosenau, Nonlinear dispersion and compact structures, Phys. Rev. Lett. 73, 1737 (1994).
  11. C. Adam, J. Sanchez-Guillen, and A. Wereszczynski, BPS submodels of the Skyrme model, Phys. Lett. B 769, 362 (2017).
  12. C. Adam, D. Foster, S. Krusch, and A. Wereszczynski, BPS sectors of the Skyrme model and their non-BPS extensions, Phys. Rev. D 97, 036002 (2018).
  13. C. Adam, J. Sanchez-Guillen, and A. Wereszczynski, A Skyrme-type proposal for baryonic matter, Phys. Lett. B 691, 105 (2010).
  14. C. Adam, J. Sanchez-Guillen, and A. Wereszczynski, A BPS Skyrme model and baryons at large Nc, Phys. Rev. D 82, 085015 (2010).
  15. T. Gisiger and Manu B. Paranjape, Solitons in a baby Skyrme model with invariance under volume/area preserving diffeomorphisms, Phys. Rev. D 55, 7731 (1997).
  16. H. Arodz and J. Lis, Compact Q-balls and Q-shells in a scalar electrodynamics, Phys. Rev. D 79, 045002 (2009).
  17. P. Klimas and L. R. Livramento, Compact Q-balls and Q-shells in CPN type models, Phys. Rev. D 96, 016001 (2017).
  18. Nobuyuki Sawado and Shota Yanai, Compact, charged boson stars and shells in the CPN gravitating nonlinear sigma model, Phys. Rev. D 102, 045007 (2020).
  19. P. Klimas, L. C. Kubaski, N. Sawado, and S. Yanai, Compact Q-balls and Q-shells in a multi-component CPN model, J. High Energy Phys. 09 (2021) 084.
  20. Wojtek J. Zakrzewski, Low-Dimensional Sigma Models (Adam Hilger, Bristol, 1989).
  21. L. A. Ferreira, P. Klimas, and W. J. Zakrzewski, Some (3+1) dimensional vortex solutions of the CPN model, Phys. Rev. D 83, 105018 (2011).
  22. L. A. Ferreira, P. Klimas, and W. J. Zakrzewski, Properties of some (3+1) dimensional vortex solutions of the CPN model, Phys. Rev. D 84, 085022 (2011).
  23. L. A. Ferreira, Exact vortex solutions in an extended Skyrme-Faddeev model, J. High Energy Phys. 05 (2009) 001.
  24. L. A. Ferreira and P. Klimas, Exact vortex solutions in a CPN Skyrme-Faddeev type model, J. High Energy Phys. 10 (2010) 008.
  25. Luiz A. Ferreira and Erica E. Leite, Integrable theories in any dimension and homogeneous spaces, Nucl. Phys. B547, 471 (1999).
  26. B. M. A. G. Piette, B. J. Schroers, and W. J. Zakrzewski, Multi-solitons in a two-dimensional Skyrme model, Z. Phys. C 65, 165 (1995).
  27. B. M. A. G. Piette, B. J. Schroers, and W. J. Zakrzewski, Dynamics of baby skyrmions, Nucl. Phys. B439, 205 (1995).
  28. Itay Hen and Marek Karliner, Rotational symmetry breaking in baby Skyrme models, Nonlinearity 21, 399 (2008).
  29. Marek Karliner and Itay Hen, Rotational symmetry breaking in baby Skyrme models, in The Multifaceted Skyrmion, edited by Gerald E. Brown and Mannque Rho (World Scientific, 2010), pp. 179–213; arXiv:0901.1489.
  30. C. Adam, P. Klimas, J. Sanchez-Guillen, and A. Wereszczynski, Compact baby skyrmions, Phys. Rev. D 80, 105013 (2009).
  31. L. A. Ferreira, J. Jaykka, Nobuyuki Sawado, and Kouichi Toda, Vortices in the extended Skyrme-Faddeev model, Phys. Rev. D 85, 105006 (2012).
  32. Pawel Klimas and Nobuyuki Sawado, Numerical vortex solutions in (3+1) dimensions for the extended CPN Skyrme-Faddeev model, arXiv:1210.7523.
  33. Yuki Amari, Pawel Klimas, Nobuyuki Sawado, and Yuta Tamaki, Potentials and the vortex solutions in the CPN Skyrme-Faddeev model, Phys. Rev. D 92, 045007 (2015).
  34. H. Arodz, P. Klimas, and T. Tyranowski, Field-theoretic models with V-shaped potentials, Acta Phys. Pol. B 36, 3861 (2005).
  35. H. Arodz, P. Klimas, and T. Tyranowski, Signum-Gordon wave equation and its self-similar solutions, Acta Phys. Pol. B 38, 3099 (2007).
  36. Nobuyuki Sawado and Shota Yanai, Phase analyses for compact, charged boson stars and shells harboring black holes in the CPN nonlinear sigma model, Phys. Rev. D 103, 125018 (2021).
  37. A. Yu. Loginov and V. V. Gauzshtein, Radially excited u(1) gauged q-balls, Phys. Rev. D 102, 025010 (2020).
  38. P. Klimas, N. Sawado, and S. Yanai, Nodal compact q-ball and q-shell in the CPN nonlinear sigma model, Phys. Rev. D 105, 085004 (2022).

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Phys. Rev. D 112, 116020– Published 26 December, 2025
  • Received 19 September 2025
  • Accepted 8 December 2025
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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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