- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

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
  • Open Access
  • Access by Xinjiang University

Chiral vortical conductivities and the moment of inertia of a rigidly rotating Fermi gas

M. Abedlou Ahadi* and N. Sadooghi†

  • *Contact author: mohammad_abedlouahadi@physics.sharif.edu
  • †Contact author: sadooghi@physics.sharif.ir
PDF

Phys. Rev. D 111, 116011 – Published 13 June, 2025

DOI: https://doi.org/10.1103/cn47-wdvb

Abstract

We determine the chiral vortical conductivities, as well as the orbital and spin moment of inertia of a charged, chiral, and rigidly rotating free Fermi gas. To this purpose, we begin by calculating the vacuum expectation values of a vector and axial vector current using the free fermion propagator in this medium. This propagator is derived by employing the Fock-Schwinger method based on the solutions of the Dirac equation in the presence of rotation and finite axial chemical potential. We present a complete derivation of these solutions. We demonstrate that in the first approximation, the chiral vortical conductivity associated with the vector current is proportional to the product of the vector and axial chemical potentials. In contrast, the chiral vortical conductivity related to the axial vector current depends on the temperature, the vector, and the axial vector chemical potential squares. We use the relation between the axial vector current and the angular momentum density associated with spin to determine the spin and the orbital moment of inertia of a rigidly rotating Fermi gas in a charged and chirally imbalanced medium separately. In addition, we compute the total moment of inertia by utilizing the methods presented in the first part of the paper and show that the orbital moment of inertia of a free fermion gas vanishes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, The effects of topological charge change in heavy ion collisions: “Event by event P and CP violation,” Nucl. Phys. A803, 227 (2008).
  2. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, The chiral magnetic effect, Phys. Rev. D 78, 074033 (2008).
  3. D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A797, 67 (2007).
  4. D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report, Prog. Part. Nucl. Phys. 88, 1 (2016).
  5. 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).
  6. D. E. Kharzeev, J. Liao, and P. Tribedy, Chiral magnetic effect in heavy ion collisions: The present and future, Int. J. Mod. Phys. E 33, 2430007 (2024).
  7. Y. Feng, S. A. Voloshin, and F. Wang, Experimental search for the chiral magnetic effect in relativistic heavy-ion collisions: A perspective, arXiv:2502.09742.
  8. V. Skokov, A. Y. Illarionov, and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24, 5925 (2009).
  9. F. Becattini, I. Karpenko, M. Lisa, I. Upsal, and S. Voloshin, Global hyperon polarization at local thermodynamic equilibrium with vorticity, magnetic field and feed-down, Phys. Rev. C 95, 054902 (2017).
  10. R. A. Abramchuk, Non-perturbative suppression of the chiral magnetic effect in quark gluon plasma, arXiv:2503.18404.
  11. M. I. Abdulhamid et al. (STAR Collaboration), Observation of the electromagnetic field effect via charge-dependent directed flow in heavy-ion collisions at the relativistic heavy ion collider, Phys. Rev. X 14, 011028 (2024).
  12. Y. Hirono, K. Ikeda, D. E. Kharzeev, Z. Liu, and S. Shi, Optimal observables for the chiral magnetic effect from machine learning, arXiv:2504.03248.
  13. D. E. Kharzeev and H. U. Yee, Chiral magnetic wave, Phys. Rev. D 83, 085007 (2011).
  14. Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosic, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla, Observation of the chiral magnetic effect in ZrTe5, Nat. Phys. 12, 550 (2016).
  15. K. Kamada, N. Yamamoto, and D. L. Yang, Chiral effects in astrophysics and cosmology, Prog. Part. Nucl. Phys. 129, 104016 (2023).
  16. D. T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103, 191601 (2009).
  17. N. Sadooghi and S. M. A. Tabatabaee, The effect of magnetization and electric polarization on the anomalous transport coefficients of a chiral fluid, New J. Phys. 19, 053014 (2017).
  18. K. Landsteiner, E. Megias, L. Melgar, and F. Pena-Benitez, Holographic gravitational anomaly and chiral vortical effect, J. High Energy Phys. 09 (2011) 121.
  19. K. Landsteiner, E. Megias, and F. Pena-Benitez, Frequency dependence of the chiral vortical effect, Phys. Rev. D 90, 065026 (2014).
  20. A. Huang, Y. Jiang, S. Shi, J. Liao, and P. Zhuang, Out-of-equilibrium chiral magnetic effect from chiral kinetic theory, Phys. Lett. B 777, 177 (2018).
  21. V. E. Ambruş and E. Winstanley, Rotating quantum states, Phys. Lett. B 734, 296 (2014).
  22. A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21, 2260 (1980).
  23. N. Sadooghi and F. Taghinavaz, Local electric current correlation function in an exponentially decaying magnetic field, Phys. Rev. D 85, 125035 (2012).
  24. A. Yamamoto and Y. Hirono, Lattice QCD in rotating frames, Phys. Rev. Lett. 111, 081601 (2013).
  25. 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).
  26. K. Mameda and A. Yamamoto, Magnetism and rotation in relativistic field theory, Prog. Theor. Exp. Phys. 2016, 093B05 (2016).
  27. 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.
  28. M. N. Chernodub and S. Gongyo, Effects of rotation and boundaries on chiral symmetry breaking of relativistic fermions, Phys. Rev. D 95, 096006 (2017).
  29. M. N. Chernodub and S. Gongyo, Edge states and thermodynamics of rotating relativistic fermions under magnetic field, Phys. Rev. D 96, 096014 (2017).
  30. V. E. Ambruş and E. Winstanley, Exact solutions in quantum field theory under rotation, Lect. Notes Phys. 987, 95 (2021).
  31. Minghua Wei, Yin Jiang, and M. Huang, Mass splitting of vector mesons and spontaneous spin polarization under rotation, Chin. Phys. C 46, 024102 (2022).
  32. 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).
  33. 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).
  34. H. Mortazavi Ghalati and N. Sadooghi, Magnetic dual chiral density wave phase in rotating cold quark matter, Phys. Rev. D 108, 054032 (2023).
  35. A. Ayala, L. A. Hernández, K. Raya, and R. Zamora, Fermion propagator in a rotating environment, Phys. Rev. D 103, 076021 (2021); 104, 039901(E) (2021).
  36. E. Siri and N. Sadooghi, Thermodynamic properties of a relativistic Bose gas under rigid rotation, Phys. Rev. D 110, 036016 (2024).
  37. E. Siri and N. Sadooghi, Boson propagator under rigid rotation, Trans. Theor. Math. Phys. 1, 105 (2024).
  38. E. Siri and N. Sadooghi, Bose-Einstein condensation in a rigidly rotating relativistic boson gas, Phys. Rev. D 111, 036011 (2025).
  39. V. V. Braguta, M. N. Chernodub, Y. A. Gershtein, and A. A. Roenko, On the origin of mixed inhomogeneous phase in vortical gluon plasma, arXiv:2411.15085.
  40. 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).
  41. Y. Hua and S. Q. Feng, Chiral phase transition and spin alignment of vector mesons with chiral imbalance in a rotating QCD medium, Phys. Rev. D 111, 036012 (2025).
  42. S. N. Iablokov and A. V. Kuznetsov, Exponential operator method for finding exact solutions of the propagator equation in the presence of a magnetic field, J. Phys. Conf. Ser. 1390, 012078 (2019).
  43. S. N. Iablokov and A. V. Kuznetsov, Charged massive vector boson propagator in a constant magnetic field in arbitrary ξ-gauge obtained using the modified Fock-Schwinger method, Phys. Rev. D 102, 096015 (2020).
  44. S. N. Iablokov and A. V. Kuznetsov, Position-space representation of charged particles’ propagators in a constant magnetic field as an expansion over Landau levels, Eur. Phys. J. C 82, 193 (2022).
  45. K. Fukushima, Extreme matter in electromagnetic fields and rotation, Prog. Part. Nucl. Phys. 107, 167 (2019).
  46. V. V. Braguta, M. N. Chernodub, I. E. Kudrov, A. A. Roenko, and D. A. Sychev, Negative Barnett effect, negative moment of inertia of the gluon plasma, and thermal evaporation of the chromomagnetic condensate, Phys. Rev. D 110, 014511 (2024).
  47. E. Speranza and N. Weickgenannt, Spin tensor and pseudo-gauges: From nuclear collisions to gravitational physics, Eur. Phys. J. A 57, 155 (2021).
  48. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Electric-current susceptibility and the chiral magnetic effect, Nucl. Phys. A836, 311 (2010).
  49. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Course of Theoretical Physics Vol. 5 (Elsevier Butterworth-Heinemann, Oxford, 1980).
  50. V. E. Ambruş, Helical massive fermions under rotation, J. High Energy Phys. 08 (2020) 016.
  51. R. C. Tolman, On the weight of heat and thermal equilibrium in general relativity, Phys. Rev. 35, 904 (1930).
  52. R. Tolman and P. Ehrenfest, Temperature equilibrium in a static gravitational field, Phys. Rev. 36, 1791 (1930).
  53. V. E. Ambruş and M. N. Chernodub, Vortical effects in Dirac fluids with vector, chiral and helical charges, Eur. Phys. J. C 83, 111 (2023); 84, 289(E) (2024).
  54. B. R. Iyer, Dirac field theory in rotating coordinates, Phys. Rev. D 26, 1900 (1982).
  55. J. I. Kapusta and C. Gale, Finite Temperature Field Theory, Principles and Applications, 2nd ed. (Cambridge University Press, Cambridge, England, 2006).
  56. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, New York, 1995).

Outline

Information

Phys. Rev. D 111, 116011– Published 13 June, 2025
  • Received 9 March 2025
  • Accepted 14 May 2025
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