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  • Open Access

Chiral symmetry breaking in accelerating and rotating frames

Zhi-Bin Zhu1, Hao-Lei Chen2,3,4,*, and Xu-Guang Huang1,3,4,†

  • 1Physics Department and Center for Particle Physics and Field Theory, Fudan University, Shanghai 200438, China
  • 2Department of Physics, Shanghai University, Shanghai 200444, China
  • 3Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai 200433, China
  • 4Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China

  • *Contact author: hlchen@shu.edu.cn
  • †Contact author: huangxuguang@fudan.edu.cn

Phys. Rev. D 113, 034005 – Published 4 February, 2026

DOI: https://doi.org/10.1103/yxj9-33z6

Abstract

We study chiral symmetry breaking and restoration in accelerating and rotating frames using low-energy effective models. By analyzing the chiral condensate in Rindler coordinates, we show that different renormalization schemes lead to distinct conclusions in the accelerating frame: the scheme with subtracting divergences in the Rindler vacuum supports an acceleration-independent critical temperature, while the other scheme with subtracting divergences in Minkowski vacuum suggests an enhanced critical temperature. We further investigate a system with both rotation and acceleration. We find that the critical acceleration for chiral symmetry restoration decreases with angular velocity, indicating cooperative effects from acceleration-induced thermalization and rotation-induced effective chemical potential.

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References (106)

  1. K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rept. Prog. Phys. 74, 014001 (2011).
  2. J. N. Guenther, Overview of the QCD phase diagram: Recent progress from the lattice, Eur. Phys. J. A 57, 136 (2021).
  3. A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, Mapping the phases of quantum chromodynamics with beam energy scan, Phys. Rep. 853, 1 (2020).
  4. M. Buballa, NJL model analysis of quark matter at large density, Phys. Rep. 407, 205 (2005).
  5. K. Fukushima, Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop, Phys. Rev. D 77, 114028 (2008); 78, 039902(E) (2008).
  6. M. Buballa and S. Carignano, Inhomogeneous chiral condensates, Prog. Part. Nucl. Phys. 81, 39 (2015).
  7. M. Mannarelli, Meson condensation, Particles 2, 411 (2019).
  8. C. Ratti, Lattice QCD and heavy ion collisions: A review of recent progress, Rep. Prog. Phys. 81, 084301 (2018).
  9. H.-T. Ding, F. Karsch, and S. Mukherjee, Thermodynamics of strong-interaction matter from Lattice QCD, Int. J. Mod. Phys. E 24, 1530007 (2015).
  10. G. Aarts et al., Phase transitions in particle physics: Results and perspectives from lattice quantum chromo-dynamics, Prog. Part. Nucl. Phys. 133, 104070 (2023).
  11. J. M. Pawlowski, Aspects of the functional renormalisation group, Ann. Phys. (Amsterdam) 322, 2831 (2007).
  12. M. Drews and W. Weise, Functional renormalization group studies of nuclear and neutron matter, Prog. Part. Nucl. Phys. 93, 69 (2017).
  13. N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J. M. Pawlowski, M. Tissier, and N. Wschebor, The nonperturbative functional renormalization group and its applications, Phys. Rep. 910, 1 (2021).
  14. W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101, 054032 (2020).
  15. W.-j. Fu, QCD at finite temperature and density within the fRG approach: An overview, Commun. Theor. Phys. 74, 097304 (2022).
  16. C. S. Fischer, QCD at finite temperature and chemical potential from Dyson–Schwinger equations, Prog. Part. Nucl. Phys. 105, 1 (2019).
  17. F. Gao and Y.-x. Liu, QCD phase transitions via a refined truncation of Dyson-Schwinger equations, Phys. Rev. D 94, 076009 (2016).
  18. E. Gutiérrez, A. Ahmad, A. Ayala, A. Bashir, and A. Raya, The QCD phase diagram from Schwinger–Dyson equations, J. Phys. G 41, 075002 (2014).
  19. R. Rougemont, J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, and C. Ratti, Hot QCD phase diagram from holographic Einstein–Maxwell–Dilaton models, Prog. Part. Nucl. Phys. 135, 104093 (2024).
  20. Y.-Q. Zhao, S. He, D. Hou, L. Li, and Z. Li, Phase structure and critical phenomena in two-flavor QCD by holography, Phys. Rev. D 109, 086015 (2024).
  21. X.-Y. Liu, X.-C. Peng, Y.-L. Wu, and Z. Fang, Holographic study on QCD phase transition and phase diagram with two flavors, Phys. Rev. D 109, 054032 (2024).
  22. J. O. Andersen, W. R. Naylor, and A. Tranberg, Phase diagram of QCD in a magnetic field: A review, Rev. Mod. Phys. 88, 025001 (2016).
  23. V. A. Miransky and I. A. Shovkovy, Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals, Phys. Rep. 576, 1 (2015).
  24. G. Cao and X.-G. Huang, Electromagnetic triangle anomaly and neutral pion condensation in QCD vacuum, Phys. Lett. B 757, 1 (2016).
  25. H.-L. Chen, X.-G. Huang, and J. Liao, QCD phase structure under rotation, Lect. Notes Phys. 987, 349 (2021).
  26. X.-G. Huang, Vorticity and spin polarization—a theoretical perspective, Nucl. Phys. A1005, 121752 (2021).
  27. X.-G. Huang, J. Liao, Q. Wang, and X.-L. Xia, Vorticity and spin polarization in heavy ion collisions: Transport models, Lect. Notes Phys. 987, 281 (2021).
  28. J. M. Lattimer and M. Prakash, Neutron star observations: Prognosis for equation of state constraints, Phys. Rep. 442, 109 (2007).
  29. V. Paschalidis and N. Stergioulas, Rotating stars in relativity, Living Rev. Relativity 20, 7 (2017).
  30. H.-L. Chen, K. Fukushima, X.-G. Huang, and K. Mameda, Analogy between rotation and density for Dirac fermions in a magnetic field, Phys. Rev. D 93, 104052 (2016).
  31. Y. Jiang and J. Liao, Pairing phase transitions of matter under rotation, Phys. Rev. Lett. 117, 192302 (2016).
  32. M. N. Chernodub and S. Gongyo, Interacting fermions in rotation: Chiral symmetry restoration, moment of inertia and thermodynamics, J. High Energy Phys. 01 (2017) 136.
  33. M. N. Chernodub and S. Gongyo, Effects of rotation and boundaries on chiral symmetry breaking of relativistic fermions, Phys. Rev. D 95, 096006 (2017).
  34. Y. Liu and I. Zahed, Pion condensation by rotation in a magnetic field, Phys. Rev. Lett. 120, 032001 (2018).
  35. X.-G. Huang, K. Nishimura, and N. Yamamoto, Anomalous effects of dense matter under rotation, J. High Energy Phys. 02 (2018) 069.
  36. H. Zhang, D. Hou, and J. Liao, Mesonic condensation in isospin matter under rotation, Chin. Phys. C 44, 111001 (2020).
  37. X. Wang, M. Wei, Z. Li, and M. Huang, Quark matter under rotation in the NJL model with vector interaction, Phys. Rev. D 99, 016018 (2019).
  38. L. Wang, Y. Jiang, L. He, and P. Zhuang, Local suppression and enhancement of the pairing condensate under rotation, Phys. Rev. C 100, 034902 (2019).
  39. H.-L. Chen, X.-G. Huang, and K. Mameda, Do charged-pions condense in a magnetic field with rotation?, J. High Energy Phys. 02 (2024) 216.
  40. X. Chen, L. Zhang, D. Li, D. Hou, and M. Huang, Gluodynamics and deconfinement phase transition under rotation from holography, J. High Energy Phys. 07 (2021) 132.
  41. M. N. Chernodub, Inhomogeneous confining-deconfining phases in rotating plasmas, Phys. Rev. D 103, 054027 (2021).
  42. Y. Fujimoto, K. Fukushima, and Y. Hidaka, Deconfining phase boundary of rapidly rotating hot and dense matter and analysis of moment of inertia, Phys. Lett. B 816, 136184 (2021).
  43. Y. Jiang, Chiral vortical catalysis, Eur. Phys. J. C 82, 949 (2022).
  44. N. Sadooghi, S. M. A. Tabatabaee Mehr, and F. Taghinavaz, Inverse magnetorotational catalysis and the phase diagram of a rotating hot and magnetized quark matter, Phys. Rev. D 104, 116022 (2021).
  45. M. Eto, K. Nishimura, and M. Nitta, Phases of rotating baryonic matter: Non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization, J. High Energy Phys. 08 (2022) 305.
  46. Y. Chen, D. Li, and M. Huang, Inhomogeneous chiral condensation under rotation in the holographic QCD, Phys. Rev. D 106, 106002 (2022).
  47. Y.-Q. Zhao, S. He, D. Hou, L. Li, and Z. Li, Phase diagram of holographic thermal dense QCD matter with rotation, J. High Energy Phys. 04 (2023) 115.
  48. S. Chen, K. Fukushima, and Y. Shimada, Perturbative confinement in thermal Yang-Mills theories induced by imaginary angular velocity, Phys. Rev. Lett. 129, 242002 (2022).
  49. H.-L. Chen, Z.-B. Zhu, and X.-G. Huang, Quark-meson model under rotation: A functional renormalization group study, Phys. Rev. D 108, 054006 (2023).
  50. F. Sun, K. Xu, and M. Huang, Splitting of chiral and deconfinement phase transitions induced by rotation, Phys. Rev. D 108, 096007 (2023).
  51. K. Mameda and K. Takizawa, Deconfinement transition in the revolving bag model, Phys. Lett. B 847, 138317 (2023).
  52. G. Cao, Effects of imaginary and real rotations on QCD matters, Phys. Rev. D 109, 014001 (2024).
  53. M. Eto, K. Nishimura, and M. Nitta, Domain-wall Skyrmion phase in a rapidly rotating QCD matter, J. High Energy Phys. 03 (2024) 019.
  54. M. Eto, K. Nishimura, and M. Nitta, Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes, J. High Energy Phys. 03 (2024) 035.
  55. F. Sun, J. Shao, R. Wen, K. Xu, and M. Huang, Chiral phase transition and spin alignment of vector mesons in the polarized-Polyakov-loop Nambu–Jona-Lasinio model under rotation, Phys. Rev. D 109, 116017 (2024).
  56. S. Chen, K. Fukushima, and Y. Shimada, Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity, Phys. Lett. B 859, 139107 (2024).
  57. Y. Chen, X. Chen, D. Li, and M. Huang, Deconfinement and chiral restoration phase transition under rotation from holography in an anisotropic gravitational background, Phys. Rev. D 111, 046006 (2025).
  58. J.-H. Wang and S.-Q. Feng, Rotation effect on the deconfinement phase transition in holographic QCD, Phys. Rev. D 109, 066019 (2024).
  59. P. Singha, V. E. Ambrus, and M. N. Chernodub, Inhibition of the splitting of the chiral and deconfinement transition due to rotation in QCD: The phase diagram of the linear sigma model coupled to Polyakov loops, Phys. Rev. D 110, 094053 (2024).
  60. S. Morales-Tejera, V. E. Ambrus, and M. N. Chernodub, Firewall boundaries and mixed phases of rotating quark matter in linear sigma model, Phys. Rev. D 112, 054031 (2025).
  61. L. Kiefer, A. Dash, and D. H. Rischke, Magnetization by rotation: Spin and chiral condensates in the NJL model, arXiv:2509.18881.
  62. R. M. Nunes, R. L. S. Farias, W. R. Tavares, and V. S. Timóteo, Chiral vortical catalysis constrained by LQCD simulations, Phys. Rev. D 111, 056026 (2025).
  63. V. E. Ambrus, Helical massive fermions under rotation, J. High Energy Phys. 08 (2020) 016.
  64. R. L. S. Farias and W. R. Tavares, Chiral and deconfinement transitions in spin-polarized quark matter, Phys. Rev. D 112, L051902 (2025).
  65. V. V. Braguta, A. Y. Kotov, D. D. Kuznedelev, and A. A. Roenko, Influence of relativistic rotation on the confinement-deconfinement transition in gluodynamics, Phys. Rev. D 103, 094515 (2021).
  66. M. N. Chernodub, V. A. Goy, and A. V. Molochkov, Inhomogeneity of a rotating gluon plasma and the Tolman-Ehrenfest law in imaginary time: Lattice results for fast imaginary rotation, Phys. Rev. D 107, 114502 (2023).
  67. V. V. Braguta, M. N. Chernodub, A. A. Roenko, and D. A. Sychev, Negative moment of inertia and rotational instability of gluon plasma, Phys. Lett. B 852, 138604 (2024).
  68. J.-C. Yang and X.-G. Huang, QCD on rotating lattice with staggered fermions, arXiv:2307.05755.
  69. V. V. Braguta, M. N. Chernodub, and A. A. Roenko, New mixed inhomogeneous phase in vortical gluon plasma: First-principle results from rotating SU(3) lattice gauge theory, Phys. Lett. B 855, 138783 (2024).
  70. Y. Jiang, Inhomogeneous SU(2) gluon matter under rotation, Phys. Rev. D 110, 054047 (2024).
  71. S. Wang, J.-X. Chen, D. Hou, and H.-C. Ren, Strong coupling expansion of gluodynamics on a lattice under rotation, arXiv:2505.15487.
  72. K. Fukushima and Y. Shimada, Imaginary rotating gluonic matter at strong coupling, Phys. Lett. B 868, 139716 (2025).
  73. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
  74. W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976).
  75. L. C. B. Crispino, A. Higuchi, and G. E. A. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80, 787 (2008).
  76. D. Kharzeev and K. Tuchin, From color glass condensate to quark gluon plasma through the event horizon, Nucl. Phys. A753, 316 (2005).
  77. G. Y. Prokhorov, D. A. Shohonov, O. V. Teryaev, N. S. Tsegelnik, and V. I. Zakharov, Modeling of acceleration in heavy-ion collisions: Occurrence of temperature below the Unruh temperature, Phys. Rev. C 112, 064907 (2025).
  78. P. Candelas and D. J. Raine, Quantum field theory on incomplete manifolds, J. Math. Phys. (N.Y.) 17, 2101 (1976).
  79. P. Candelas and D. Deutsch, On the vacuum stress induced by uniform acceleration or supporting the ether, Proc. R. Soc. A 354, 79 (1977).
  80. P. Candelas and D. Deutsch, Fermion fields in accelerated states, Proc. R. Soc. A 362, 251 (1978).
  81. T. D. Lee, Are black holes black bodies?, Nucl. Phys. B264, 437 (1986).
  82. T. Ohsaku, Dynamical chiral symmetry breaking and its restoration for an accelerated observer, Phys. Lett. B 599, 102 (2004).
  83. D. Ebert and V. C. Zhukovsky, Restoration of dynamically broken chiral and color symmetries for an accelerated observer, Phys. Lett. B 645, 267 (2007).
  84. P. Castorina and M. Finocchiaro, Symmetry restoration by acceleration, J. Mod. Phys. 3, 1703 (2012).
  85. S. Benic and K. Fukushima, Unruh effect and condensate in and out of an accelerated vacuum, arXiv:1503.05790.
  86. A. Casado-Turrión and A. Dobado, Triggering the QCD phase transition through the Unruh effect: Chiral symmetry restoration for uniformly accelerated observers, Phys. Rev. D 99, 125018 (2019).
  87. P. Basu, H. S. R, and P. Samantray, Aspects of spontaneous symmetry breaking in Rindler and anti–de Sitter spacetimes for the O(N) linear sigma model, Phys. Rev. D 107, 105004 (2023).
  88. W. Kou and X. Chen, Locating quark-antiquark string breaking in QCD through chiral symmetry restoration and Hawking-Unruh effect, Phys. Lett. B 856, 138942 (2024).
  89. M. N. Chernodub, Acceleration as refrigeration: Acceleration-induced spontaneous symmetry breaking in thermal medium, arXiv:2501.16129.
  90. F. Becattini, M. Buzzegoli, and A. Palermo, Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Scalar field, J. High Energy Phys. 02 (2021) 101.
  91. A. Palermo, M. Buzzegoli, and F. Becattini, Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field, J. High Energy Phys. 10 (2021) 077.
  92. G. Y. Prokhorov, O. V. Teryaev, and V. I. Zakharov, Effects of rotation and acceleration in the axial current: Density operator vs Wigner function, J. High Energy Phys. 02 (2019) 146.
  93. G. Y. Prokhorov, O. V. Teryaev, and V. I. Zakharov, Thermodynamics of accelerated fermion gases and their instability at the Unruh temperature, Phys. Rev. D 100, 125009 (2019).
  94. G. Y. Prokhorov, O. V. Teryaev, and V. I. Zakharov, Unruh effect for fermions from the Zubarev density operator, Phys. Rev. D 99, 071901 (2019).
  95. V. E. Ambrus and M. N. Chernodub, Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism, Phys. Lett. B 855, 138757 (2024); 863, 139344(E) (2025).
  96. M. N. Chernodub, V. A. Goy, A. V. Molochkov, D. V. Stepanov, and A. S. Pochinok, Extreme softening of QCD phase transition under weak acceleration: First-principles Monte Carlo results for gluon plasma, Phys. Rev. Lett. 134, 111904 (2025).
  97. W. G. Unruh and N. Weiss, Acceleration radiation in interacting field theories, Phys. Rev. D 29, 1656 (1984).
  98. D. G. Salluce, M. Pasini, A. Flachi, A. Pittelli, and S. Ansoldi, Symmetry restoration and uniformly accelerated observers in Minkowski spacetime, J. High Energy Phys. 05 (2024) 218.
  99. F. Becattini, Covariant statistical mechanics and the stress-energy tensor, Phys. Rev. Lett. 108, 244502 (2012).
  100. F. Becattini, Thermodynamic equilibrium with acceleration and the Unruh effect, Phys. Rev. D 97, 085013 (2018).
  101. M. Buzzegoli, Thermodynamic equilibrium of massless fermions with vorticity, chirality and electromagnetic field, Lect. Notes Phys. 987, 59 (2021).
  102. F. Becattini, W. Florkowski, and E. Speranza, Spin tensor and its role in non-equilibrium thermodynamics, Phys. Lett. B 789, 419 (2019).
  103. X.-G. Huang, An introduction to relativistic spin hydrodynamics, Nucl. Sci. Tech. 36, 208 (2025).
  104. G. Y. Prokhorov, O. V. Teryaev, and V. I. Zakharov, Novel phase transition at the Unruh temperature, arXiv:2304.13151.
  105. S. Ebihara, K. Fukushima, and K. Mameda, Boundary effects and gapped dispersion in rotating fermionic matter, Phys. Lett. B 764, 94 (2017).
  106. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1982).

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