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Prediction for Maximum Supercooling in SU(N) Confinement Transition

Prateek Agrawal1,2,*, Gaurang Ramakant Kane1,†, Vazha Loladze1,‡, and John March-Russell1,§

  • *Contact author: prateek.agrawal@physics.ox.ac.uk
  • †Contact author: gaurang.kane@physics.ox.ac.uk
  • ‡Contact author: vazha.loladze@physics.ox.ac.uk
  • §Contact author: john.march-russell@physics.ox.ac.uk
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Phys. Rev. Lett. 136, 041902 – Published 29 January, 2026

DOI: https://doi.org/10.1103/3r5x-vhnd

Abstract

The thermal confinement phase transition in SU(N) Yang-Mills theory is first order for N≥3, with bounce action scaling as N2. Remarkably, lattice data for the action include a small coefficient whose presence likely strongly alters the phase transition dynamics. We give evidence, utilizing insights from softly broken supersymmetric Yang-Mills models, that the small coefficient originates from a deconfined phase instability just below the critical temperature. We predict the maximum achievable supercooling in SU(N) theories to be a few percent, which can be tested on the lattice. We briefly discuss the potentially significant suppression of the associated cosmological gravitational wave signals.

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References (40)

  1. A. Kosowsky, M. S. Turner, and R. Watkins, Gravitational waves from first order cosmological phase transitions, Phys. Rev. Lett. 69, 2026 (1992).
  2. S. J. Huber and T. Konstandin, Gravitational wave production by collisions: More bubbles, J. Cosmol. Astropart. Phys. 09 (2008) 022.
  3. C. Caprini, R. Jinno, M. Lewicki, E. Madge, M. Merchand, G. Nardini, M. Pieroni, A. Roper Pol, and V. Vaskonen (LISA Cosmology Working Group), Gravitational waves from first-order phase transitions in LISA: Reconstruction pipeline and physics interpretation, J. Cosmol. Astropart. Phys. 10 (2024) 020.
  4. D. J. Reardon et al., Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array, Astrophys. J. Lett. 951, L6 (2023).
  5. C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: An update, J. Cosmol. Astropart. Phys. 03 (2020) 024.
  6. P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Cosmological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys. 135, 104094 (2024).
  7. D. B. Kaplan and H. Georgi, SU(2)×U(1) breaking by vacuum misalignment, Phys. Lett. 136B, 183 (1984).
  8. H. Georgi and D. B. Kaplan, Composite Higgs and custodial SU(2), Phys. Lett. 145B, 216 (1984).
  9. D. B. Kaplan, Flavor at SSC energies: A new mechanism for dynamically generated fermion masses, Nucl. Phys. B365, 259 (1991).
  10. R. Contino, Y. Nomura, and A. Pomarol, Higgs as a holographic pseudoGoldstone boson, Nucl. Phys. B671, 148 (2003).
  11. K. Agashe, R. Contino, and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B719, 165 (2005).
  12. N. Arkani-Hamed, A. G. Cohen, and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett. B 513, 232 (2001).
  13. Z. Chacko, H.-S. Goh, and R. Harnik, The twin Higgs: Natural electroweak breaking from mirror symmetry, Phys. Rev. Lett. 96, 231802 (2006).
  14. G. D. Kribs and E. T. Neil, Review of strongly-coupled composite dark matter models and lattice simulations, Int. J. Mod. Phys. A 31, 1643004 (2016).
  15. C. Grojean and G. Servant, Gravitational waves from phase transitions at the electroweak scale and beyond, Phys. Rev. D 75, 043507 (2007).
  16. I. Garcia Garcia, R. Lasenby, and J. March-Russell, Twin Higgs WIMP dark matter, Phys. Rev. D 92, 055034 (2015).
  17. P. Asadi, E. D. Kramer, E. Kuflik, G. W. Ridgway, T. R. Slatyer, and J. Smirnov, Thermal squeezeout of dark matter, Phys. Rev. D 104, 095013 (2021).
  18. Y. Gouttenoire, E. Kuflik, and D. Liu, Heavy baryon dark matter from SU(N) confinement: Bubble wall velocity and boundary effects, Phys. Rev. D 109, 035002 (2024).
  19. B. Lucini, M. Teper, and U. Wenger, Properties of the deconfining phase transition in SU(N) gauge theories, J. High Energy Phys. 02 (2005) 033.
  20. A. Salami, T. Rindlisbacher, and K. Rummukainen, The confined-deconfined surface tension in SU(N) gauge theories at large N, Proc. Sci. LATTICE2024 (2025) 406 [arXiv:2502.01396].
  21. M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett. 103, 232001 (2009).
  22. A. Buchel, Hydrodynamics of the cascading plasma, Nucl. Phys. B820, 385 (2009).
  23. E. Morgante, N. Ramberg, and P. Schwaller, Gravitational waves from dark SU(3) Yang-Mills theory, Phys. Rev. D 107, 036010 (2023).
  24. R. K. Mishra and L. Randall, Consequences of a stabilizing field’s self-interactions for RS cosmology, J. High Energy Phys. 12 (2023) 036.
  25. R. K. Mishra and L. Randall, Phase transition to RS: Cool, not supercool, J. High Energy Phys. 06 (2024) 099.
  26. E. Poppitz, T. Schäfer, and M. Unsal, Continuity, deconfinement, and (Super) Yang-Mills theory, J. High Energy Phys. 10 (2012) 115.
  27. E. Poppitz, T. Schäfer, and M. Ünsal, Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups, J. High Energy Phys. 03 (2013) 087.
  28. M. M. Anber, Θ dependence of the deconfining phase transition in pure SU(Nc) Yang-Mills theories, Phys. Rev. D 88, 085003 (2013).
  29. M. M. Anber and V. Pellizzani, Representation dependence of k -strings in pure Yang-Mills theory via supersymmetry, Phys. Rev. D 96, 114015 (2017).
  30. H. Georgi, Lie Algebras in Particle Physics, 2nd ed (Perseus Books, Reading, MA, 1999), Vol. 54.
  31. R. D. Pisarski, Quark gluon plasma as a condensate of Z(3) Wilson lines, Phys. Rev. D 62, 111501 (2000).
  32. R. D. Pisarski, Tests of the Polyakov loops model, Nucl. Phys. A702, 151 (2002).
  33. R. D. Pisarski, Notes on the deconfining phase transition, in Cargese Summer School on QCD Perspectives on Hot and Dense Matter (2002), pp. 353–384.
  34. W.-C. Huang, M. Reichert, F. Sannino, and Z.-W. Wang, Testing the dark SU(N) Yang-Mills theory confined landscape: From the lattice to gravitational waves, Phys. Rev. D 104, 035005 (2021).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/3r5x-vhnd for an example of the bounce profile and trajectories for N=10 highlighting its nontrivial nature in the field space.
  36. P. G. Debenedetti, F. Sciortino, and G. H. Zerze, Second critical point in two realistic models of water, Science 369, 289 (2020).
  37. V. Guada, M. Nemevšek, and M. Pintar, findbounce: Package for multi-field bounce actions, Comput. Phys. Commun. 256, 107480 (2020).
  38. C. Allton, M. Teper, and A. Trivini, On the running of the bare coupling in SU(N) lattice gauge theories, J. High Energy Phys. 07 (2008) 021.
  39. B. Lucini, A. Rago, and E. Rinaldi, SU(Nc) gauge theories at deconfinement, Phys. Lett. B 712, 279 (2012).
  40. R. Seppä, K. Rummukainen, and D. J. Weir, Resolving the critical bubble in SU(8) deconfinement transition, Proc. Sci. LATTICE2024 (2025) 434 [arXiv:2501.17593].

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Phys. Rev. Lett. 136, 041902– Published 29 January, 2026
  • Received 23 August 2025
  • Revised 20 November 2025
  • Accepted 2 January 2026
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