- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Particle-Soliton Degeneracy in 2D Quantum Chromodynamics

Clay Córdova*, Diego García-Sepúlveda†, and Nicholas Holfester‡

  • *Contact author: clayc@uchicago.edu
  • †Contact author: dgarciasepulveda@uchicago.edu
  • ‡Contact author: nholfester@uchicago.edu
PDF

Phys. Rev. Lett. 137, 181603 – Published 30 October, 2026

DOI: https://doi.org/10.1103/jckx-z293

Abstract

Quantum chromodynamics in two spacetime dimensions admits a finite noninvertible symmetry described mathematically by a fusion category. This symmetry is spontaneously broken at long distances, leading to distinct vacua. When the theory has a mass gap, the spectrum is therefore characterized by particle excitations above a single vacuum and soliton sectors interpolating between vacua. We use anyon condensation and the representation theory of fusion categories to obtain exact results about this spectrum, exhibiting the allowed multiplets. Often, particles and solitons are in the same representation and therefore must have equal masses. Furthermore, the fusion category symmetry frequently implies the existence of certain stable states in the spectrum. The resulting degeneracies are encoded in quiver diagrams where nodes are vacua and arrows are excited states.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (38)

  1. G. ’t Hooft, Nucl. Phys. B75, 461 (1974).
  2. Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, J. High Energy Phys. 03 (2021) 103.
  3. C. Córdova and D. García-Sepúlveda, J. High Energy Phys. 08 (2026) 141.
  4. D. Delmastro, J. Gomis, and M. Yu, J. High Energy Phys. 02 (2023) 157.
  5. D. Delmastro and J. Gomis, J. High Energy Phys. 09 (2023) 158.
  6. C. Córdova, D. García-Sepúlveda, and N. Holfester, J. High Energy Phys. 07 (2024) 154.
  7. C. Córdova, N. Holfester, and K. Ohmori, J. High Energy Phys. 06 (2025) 001.
  8. J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Nucl. Phys. B763, 354 (2007).
  9. J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, in 16th International Congress on Mathematical Physics (World Scientific, Singapore, 2010), pp. 608–613.
  10. L. Bhardwaj and Y. Tachikawa, J. High Energy Phys. 03 (2018) 189.
  11. C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang, and X. Yin, J. High Energy Phys. 01 (2019) 026.
  12. D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, J. High Energy Phys. 02 (2015) 172.
  13. R. Dempsey, A.-M. E. Glück, S. S. Pufu, and B. T. Søgaard, arXiv:2601.16262.
  14. P. Di Francesco and J. B. Zuber, Nucl. Phys. B338, 602 (1990).
  15. V. B. Petkova and J. B. Zuber, Nucl. Phys. B463, 161 (1996).
  16. R. E. Behrend, P. A. Pearce, V. B. Petkova, and J.-B. Zuber, Nucl. Phys. B570, 525 (2000).
  17. A. Kirillov Jr and V. Ostrik, Adv. Math. 171, 183 (2002).
  18. L.-Y. Hung and Y. Wan, J. High Energy Phys. 07 (2015) 120.
  19. S. Cecotti and C. Vafa, Commun. Math. Phys. 158, 569 (1993).
  20. E. Witten, Commun. Math. Phys. 92, 455 (1984).
  21. W. Ji, S.-H. Shao, and X.-G. Wen, Phys. Rev. Res. 2, 033317 (2020).
  22. R. Thorngren and Y. Wang, J. High Energy Phys. 07 (2024) 051.
  23. C. Córdova and D. García-Sepúlveda, arXiv:2312.16317.
  24. J. A. Damia, G. Galati, and L. Tizzano, J. High Energy Phys. 12 (2024) 230.
  25. L. Kong, Nucl. Phys. B886, 436 (2014).
  26. D. Kutasov and A. Schwimmer, Nucl. Phys. B442, 447 (1995).
  27. A. Kitaev, Ann. Phys. (Amsterdam) 321, 2 (2006).
  28. F. Benini, C. Córdova, and P.-S. Hsin, J. High Energy Phys. 03 (2019) 118.
  29. J. Kaidi, Z. Komargodski, K. Ohmori, S. Seifnashri, and S.-H. Shao, SciPost Phys. 13, 067 (2022).
  30. A. Davydov, M. Müger, D. Nikshych, and V. Ostrik, J. Reine Angew. Math. 2013, 135 (2013).
  31. G. W. Moore and N. Seiberg, Phys. Lett. B 220, 422 (1989).
  32. K. Hori, Commun. Math. Phys. 182, 1 (1996).
  33. N. Carqueville and I. Runkel, Quantum Topol. 7, 203 (2016).
  34. R. Thorngren and Y. Wang, J. High Energy Phys. 04 (2024) 132.
  35. T.-C. Huang, Y.-H. Lin, and S. Seifnashri, J. High Energy Phys. 12 (2021) 028.
  36. O. Diatlyk, C. Luo, Y. Wang, and Q. Weller, J. High Energy Phys. 03 (2024) 127.
  37. P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories: Mathematical Surveys and Monographs (American Mathematical Society, Providence, RI, 2015).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/jckx-z293 for a derivation of the relationship between solitons and one-form symmetry, explicit quiver computations, and the derivation of vacuum condensates.

Outline

Information

Phys. Rev. Lett. 137, 181603– Published 30 October, 2026
  • Received 13 August 2026
  • Accepted 1 October 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation