Abstract
The topological structure of vacuum is the cornerstone of non-Abelian gauge theories describing strong and electroweak interactions within the standard model of particle physics. However, transitions between different topological sectors of the vacuum (believed to be at the origin of the baryon asymmetry of the Universe) have never been observed directly. An experimental observation of such transitions in quantum chromodynamics (QCD) has become possible in heavy-ion collisions, where the chiral magnetic effect converts the chiral asymmetry (generated by topological transitions in hot QCD matter) into an electric current, under the presence of the magnetic field produced by the colliding ions. The Relativistic Heavy Ion Collider programme on heavy-ion collisions such as the zirconium–zirconium and ruthenium–ruthenium isobars thus has the potential to uncover the topological structure of vacuum in a laboratory experiment. This discovery would have far-reaching implications for the understanding of QCD, the origin of the baryon asymmetry in the present-day Universe, and other areas, including condensed matter physics.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$99.00 per year
only $8.25 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Sakharov, A. D. Violation of CP invariance, C asymmetry, and baryon asymmetry of the Universe. Sov. Phys. Usp. 34, 392–393 (1991).
Belavin, A. A., Polyakov, A. M., Schwartz, A. S. & Tyupkin, Y. S. Pseudoparticle solutions of the Yang–Mills equations. Phys. Lett. B 59, 85–87 (1975).
‘t Hooft, G. Computation of the quantum effects due to a four-dimensional pseudoparticle. Phys. Rev. D 14, 3432–3450 (1976).
Jackiw, R. & Rebbi, C. Vacuum periodicity in a Yang–Mills quantum theory. Phys. Rev. Lett. 37, 172–175 (1976).
Callan, C. G. Jr., Dashen, R. F. & Gross, D. J. The structure of the gauge theory vacuum. Phys. Lett. B 63, 334–340 (1976).
Chern, S. S. & Simons, J. Characteristic forms and geometric invariants. Ann. Math. 99, 48–69 (1974).
Klinkhamer, F. R. & Manton, N. S. A saddle point solution in the Weinberg–Salam theory. Phys. Rev. D. 30, 2212 (1984).
Rubakov, V. A. & Shaposhnikov, M. E. Electroweak baryon number nonconservation in the early Universe and in high-energy collisions. Usp. Fiz. Nauk. 166, 493–537 (1996).
Ringwald, A. High-energy breakdown of perturbation theory in the electroweak instanton sector. Nucl. Phys. B 330, 1–18 (1990).
Tye, S. H. H. & Wong, S. S. C. Baryon number violating scatterings in laboratories. Phys. Rev. D 96, 093004 (2017).
Adler, S. L. Axial vector vertex in spinor electrodynamics. Phys. Rev. 177, 2426–2438 (1969).
Bell, J. S. & Jackiw, R. A PCAC puzzle: π0 → γγ in the σ model. Nuovo Cim. A 60, 47–61 (1969).
Kharzeev, D. Parity violation in hot QCD: why it can happen, and how to look for it. Phys. Lett. B 633, 260–264 (2006).
Kharzeev, D. & Zhitnitsky, A. Charge separation induced by P-odd bubbles in QCD matter. Nucl. Phys. A 797, 67–79 (2007).
Kharzeev, D. E., McLerran, L. D. & Warringa, H. J. The effects of topological charge change in heavy ion collisions: ‘Event by event P and CP violation’. Nucl. Phys. A 803, 227–253 (2008).
Fukushima, K., Kharzeev, D. E. & Warringa, H. J. The chiral magnetic effect. Phys. Rev. D 78, 074033 (2008).
Kharzeev, D. E., Liao, J., Voloshin, S. A. & Wang, G. Chiral magnetic and vortical effects in high-energy nuclear collisions — a status report. Prog. Part. Nucl. Phys. 88, 1–28 (2016).
Gross, D. J. & Wilczek, F. Ultraviolet behavior of nonabelian gauge theories. Phys. Rev. Lett. 30, 1343–1346 (1973).
Politzer, H. D. Reliable perturbative results for strong interactions? Phys. Rev. Lett. 30, 1346–1349 (1973).
Ellis, J. R. Aspects of conformal symmetry and chirality. Nucl. Phys. B 22, 478–492 (1970).
Collins, J. C., Duncan, A. & Joglekar, S. D. Trace and dilatation anomalies in gauge theories. Phys. Rev. D 16, 438–449 (1977).
Schäfer, T. & Shuryak, E. V. Instantons in QCD. Rev. Mod. Phys. 70, 323–426 (1998).
Vilenkin, A. Cancellation of equilibrium parity violating currents. Phys. Rev. D 22, 3067–3079 (1980).
Moffatt, H. K. The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117–129 (1969).
Berger, M. A. & Field, G. B. The topological properties of magnetic helicity. J. Fluid Mech. 147, 61 (1984).
Hirono, Y., Kharzeev, D. E. & Yin, Y. Quantized chiral magnetic current from reconnections of magnetic flux. Phys. Rev. Lett. 117, 172301 (2016).
Volovik, G. E. The Universe in a Helium Droplet (Oxford Univ. Press, 2009).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Burkov, A. A. Weyl metals. Annu. Rev. Condens. Matter Phys. 9, 359–378 (2018).
Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550–554 (2016).
Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).
Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. 5, 031023 (2015).
Kaushik, S. & Kharzeev, D. E. Quantum oscillations in the chiral magnetic conductivity. Phys. Rev. B 95, 235136 (2017).
Parameswaran, S. A., Grover, T., Abanin, D. A., Pesin, D. A. & Vishwanath, A. Probing the chiral anomaly with nonlocal transport in three-dimensional topological semimetals. Phys. Rev. 4, 031035 (2014).
Zhang, C. et al. Room-temperature chiral charge pumping in Dirac semimetals. Nat. Commun. 8, 13741 (2017).
Kaushik, S., Kharzeev, D. E. & Philip, E. J. Chiral magnetic photocurrent in Dirac and Weyl materials. Phys. Rev. B 99, 075150 (2019).
Borsanyi, S. et al. Full result for the QCD equation of state with 2+1 flavors. Phys. Lett. B 730, 99–104 (2014).
Bazavov, A. et al. [HotQCD]. Equation of state in (2+1)-flavor QCD. Phys. Rev. D 90, 094503 (2014).
Bzdak, A. et al. Mapping the phases of quantum chromodynamics with beam energy scan. Phys. Rep. 853, 1–87 (2020).
Bloczynski, J., Huang, X. G., Zhang, X. & Liao, J. Azimuthally fluctuating magnetic field and its impacts on observables in heavy-ion collisions. Phys. Lett. B 718, 1529–1535 (2013).
McLerran, L. & Skokov, V. Comments about the electromagnetic field in heavy-ion collisions. Nucl. Phys. A 929, 184–190 (2014).
Inghirami, G. et al. Numerical magneto-hydrodynamics for relativistic nuclear collisions. Eur. Phys. J. C 76, 659 (2016).
Adamczyk, L. et al. [STAR collaboration]. Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid. Nature 548, 62–65 (2017).
Erdmenger, J., Haack, M., Kaminski, M. & Yarom, A. Fluid dynamics of R-charged black holes. J. High Energy Phys. 01, 055 (2009).
Banerjee, N. et al. Hydrodynamics from charged black branes. J. High Energy Phys. 01, 094 (2011).
Son, D. T. & Surowka, P. Hydrodynamics with triangle anomalies. Phys. Rev. Lett. 103, 191601 (2009).
Kharzeev, D. E. & Son, D. T. Testing the chiral magnetic and chiral vortical effects in heavy ion collisions. Phys. Rev. Lett. 106, 062301 (2011).
Landsteiner, K., Megias, E. & Pena-Benitez, F. Gravitational anomaly and transport. Phys. Rev. Lett. 107, 021601 (2011).
Gooth, J. et al. Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP. Nature 547, 324–327 (2017).
Takahashi, R. et al. Spin hydrodynamic generation. Nat. Phys. 12, 52–56 (2016).
Voloshin, S. A. Parity violation in hot QCD: how to detect it. Phys. Rev. C 70, 057901 (2004).
Bzdak, A., Koch, V. & Liao, J. Charge-dependent correlations in relativistic heavy ion collisions and the chiral magnetic effect. Lect. Notes Phys. 871, 503–536 (2013).
Xu, H. J. et al. Varying the chiral magnetic effect relative to flow in a single nucleus–nucleus collision. Chin. Phys. C 42, 084103 (2018).
Zhao, J., Li, H. & Wang, F. Isolating the chiral magnetic effect from backgrounds by pair invariant mass. Eur. Phys. J. C 79, 168 (2019).
Voloshin, S. A. Estimate of the signal from the chiral magnetic effect in heavy-ion collisions from measurements relative to the participant and spectator flow planes. Phys. Rev. C 98, 054911 (2018).
Choudhury, S., Wang, G., He, W., Hu, Y. & Huang, H. Z. Background evaluations for the chiral magnetic effect with normalized correlators using a multiphase transport model. Eur. Phys. J. C 80, 383 (2020).
Wen, F., Bryon, J., Wen, L. & Wang, G. Event-shape-engineering study of charge separation in heavy-ion collisions. Chin. Phys. C 42, 014001 (2018).
Adamczyk, L. et al. [STAR]. Measurement of charge multiplicity asymmetry correlations in high-energy nucleus–nucleus collisions at √sNN = 200 GeV. Phys. Rev. C 89, 044908 (2014).
Acharya, S. et al. [ALICE Collaboration]. Constraining the magnitude of the chiral magnetic effect with event shape engineering in Pb–Pb collisions at √sNN = 2.76 TeV. Phys. Lett. B 777, 151 (2018).
Sirunyan, A. M. et al. [CMS Collaboration]. Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pPb and PbPb collisions at the CERN Large Hadron Collider. Phys. Rev. C 97, 044912 (2018).
Magdy, N., Shi, S., Liao, J., Ajitanand, N. & Lacey, R. A. New correlator to detect and characterize the chiral magnetic effect. Phys. Rev. C 97, 061901 (2018).
Tang, A. Probe chiral magnetic effect with signed balance function. Chin. Phys. C 44, 054101 (2020).
Abelev, B. et al. [STAR]. Azimuthal charged-particle correlations and possible local strong parity violation. Phys. Rev. Lett. 103, 251601 (2009).
Abelev, B. et al. [STAR]. Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions. Phys. Rev. C 81, 054908 (2010).
Adamczyk, L. et al. [STAR]. Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC. Phys. Rev. Lett. 113, 052302 (2014).
Tribedy, P. [STAR]. Disentangling flow and signals of chiral magnetic effect in U+U, Au+Au and p+Au collisions. Nucl. Phys. A 967, 740–743 (2017).
Adam, J. et al. [STAR]. Charge-dependent pair correlations relative to a third particle in p+Au and d+Au collisions at RHIC. Phys. Lett. B 798, 134975 (2019).
Adam, J. et al. [STAR]. Charge separation measurements in p(d)+Au and Au+Au collisions; implications for the chiral magnetic effect. Preprint at https://arXiv.org/2006.04251 (2020).
Adam, J. et al. [STAR]. Pair invariant mass to isolate background in the search for the chiral magnetic effect in Au+Au collisions at √sNN = 200 GeV. Preprint at https://arXiv.org/2006.05035 (2020).
Abelev, B. et al. [ALICE]. Charge separation relative to the reaction plane in Pb–Pb collisions at √sNN = 2.76 TeV. Phys. Rev. Lett. 110, 012301 (2013).
Khachatryan, V. et al. [CMS Collaboration]. Observation of charge-dependent azimuthal correlations in p–Pb collisions and its implication for the search for the chiral magnetic effect. Phys. Rev. Lett. 118, 122301 (2017).
Zhao, J. & Wang, F. Experimental searches for the chiral magnetic effect in heavy-ion collisions. Prog. Part. Nucl. Phys. 107, 200–236 (2019).
Zhao, J. [STAR]. Measurements of the chiral magnetic effect with background isolation in 200 GeV Au+Au collisions at STAR. Nucl. Phys. A 982, 535–538 (2019).
Li, W. & Wang, G. Chiral magnetic effects in nuclear collisions. Annu. Rev. Nucl. Part. Sci. 70, 293–321 (2020).
Kharzeev, D. E. & Yee, H. U. Chiral magnetic wave. Phys. Rev. D 83, 085007 (2011).
Burnier, Y., Kharzeev, D. E., Liao, J. & Yee, H. U. Chiral magnetic wave at finite baryon density and the electric quadrupole moment of quark–gluon plasma in heavy ion collisions. Phys. Rev. Lett. 107, 052303 (2011).
Gorbar, E. V., Miransky, V. A. & Shovkovy, I. A. Normal ground state of dense relativistic matter in a magnetic field. Phys. Rev. D 83, 085003 (2011).
Adamczyk, L. et al. [STAR]. Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions. Phys. Rev. Lett. 114, 252302 (2015).
Adam, J. et al. [ALICE]. Charge-dependent flow and the search for the chiral magnetic wave in Pb–Pb collisions at √sNN = 2.76 TeV. Phys. Rev. C 93, 044903 (2016).
Voloshin, S. A. Testing the chiral magnetic effect with central U+U collisions. Phys. Rev. Lett. 105, 172301 (2010).
Koch, V. et al. Status of the chiral magnetic effect and collisions of isobars. Chin. Phys. C 41, 072001 (2017).
Kharzeev, D. E. & Liao, J. Isobar collisions at RHIC to test local parity violation in strong interactions. Nucl. Phys. N 29, 26–31 (2019).
Kharzeev, D. E., Stephanov, M. A. & Yee, H. U. Anatomy of chiral magnetic effect in and out of equilibrium. Phys. Rev. D 95, 051901 (2017).
Gorbar, E. V., Miransky, V. A., Shovkovy, I. A. & Sukhachov, P. O. Consistent chiral kinetic theory in Weyl materials: chiral magnetic plasmons. Phys. Rev. Lett. 118, 127601 (2017).
Chen, J. Y. & Son, D. T. Berry Fermi liquid theory. Ann. Phys. 377, 345 (2017).
Mueller, N. & Venugopalan, R. The chiral anomaly, Berry’s phase and chiral kinetic theory, from world-lines in quantum field theory. Phys. Rev. D 97, 051901 (2018).
Hidaka, Y., Pu, S. & Yang, D. L. Nonlinear responses of chiral fluids from kinetic theory. Phys. Rev. D 97, 016004 (2018).
Huang, A., Shi, S., Jiang, Y., Liao, J. & Zhuang, P. Complete and consistent chiral transport from Wigner function formalism. Phys. Rev. D 98, 036010 (2018).
Müller, N., Schlichting, S. & Sharma, S. Chiral magnetic effect and anomalous transport from real-time lattice simulations. Phys. Rev. Lett. 117, 142301 (2016).
Horvath, M., Hou, D., Liao, J. & Ren, H. C. Chiral magnetic response to arbitrary axial imbalance. Phys. Rev. D 101, 076026 (2020).
Shi, S., Jiang, Y., Lilleskov, E. & Liao, J. Anomalous chiral transport in heavy ion collisions from anomalous-viscous fluid dynamics. Ann. Phys. 394, 50 (2018).
Jiang, Y., Shi, S., Yin, Y. & Liao, J. Quantifying the chiral magnetic effect from anomalous-viscous fluid dynamics. Chin. Phys. C 42, 011001 (2018).
Shi, S., Zhang H., Hou, D. & Liao, J. Signatures of chiral magnetic effect in the collisions of isobars. Phys. Rev. Lett. In Press (2020).
Xu, H. J. et al. Importance of isobar density distributions on the chiral magnetic effect search. Phys. Rev. Lett. 121, 022301 (2018).
Hammelmann, J., Soto-Ontoso, A., Alvioli, M., Elfner, H. & Strikman, M. Influence of the neutron-skin effect on nuclear isobar collisions at RHIC. Phys. Rev. C 101, 061901 (2020).
Zhao, X. L., Ma, G. L. & Ma, Y. G. Impact of magnetic-field fluctuations on measurements of the chiral magnetic effect in collisions of isobaric nuclei. Phys. Rev. C 99, 034903 (2019).
Magdy, N., Shi, S., Liao, J., Liu, P. & Lacey, R. A. Examination of the observability of a chiral magnetically driven charge-separation difference in collisions of the \({}_{44}{}^{96}{\rm{Ru}}+{}_{44}{}^{96}{\rm{Ru}}\) and \({}_{40}{}^{96}{\rm{Zr}}+{}_{40}{}^{96}{\rm{Zr}}\) isobars at energies available at the BNL relativistic heavy ion collider. Phys. Rev. C 98, 061902 (2018).
Deng, W. T., Huang, X. G., Ma, G. L. & Wang, G. Predictions for isobaric collisions at √sNN = 200 GeV from a multiphase transport model. Phys. Rev. C 97, 044901 (2018).
Sun, Y. & Ko, C. M. Chiral kinetic approach to the chiral magnetic effect in isobaric collisions. Phys. Rev. C 98, 014911 (2018).
Adam J. et al. [STAR]. Methods for a blind analysis of isobar data collected by the STAR collaboration. Preprint at https://arXiv.org/1911.00596 (2019).
Adam, J. et al. [STAR Collaboration]. Low-pT e+e− pair production in Au+Au collisions at √sNN = 200 GeV and U+U collisions at √sNN = 193 GeV at STAR. Phys. Rev. Lett. 121, 132301 (2018).
Acharya, S. et al. [ALICE Collaboration]. Probing the effects of strong electromagnetic fields with charge-dependent directed flow in Pb–Pb collisions at the LHC. Phys. Rev. Lett. 125, 022301 (2020).
Gürsoy, U., Kharzeev, D., Marcus, E., Rajagopal, K. & Shen, C. Charge-dependent flow induced by magnetic and electric fields in heavy ion collisions. Phys. Rev. C 98, 055201 (2018).
Müller, B. & Schäfer, A. Chiral magnetic effect and an experimental bound on the late time magnetic field strength. Phys. Rev. D 98, 071902 (2018).
Guo, Y., Shi, S., Feng, S. & Liao, J. Magnetic field induced polarization difference between hyperons and anti-hyperons. Phys. Lett. B 798, 134929 (2019).
Guo, X., Liao, J. & Wang, E. Spin hydrodynamic generation in the charged subatomic swirl. Sci. Rep. 10, 2196 (2020).
Müller, B. Looking for parity violation in heavy-ion collisions. Physics 2, 104 (2009).
Acknowledgements
This work is partly supported by the US Department of Energy, Office of Nuclear Physics, within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration. The authors also acknowledge support by the US Department of Energy, Office of Nuclear Physics contracts no. DE-FG-88ER40388 and no. DE-SC0012704 (DK), and by NSF grant no. PHY-1913729 (JL). We thank B. Liao, S. Mukherjee, S. Shi, P. Tribedy, G. Wang and H. Zhang for help.
Author information
Authors and Affiliations
Contributions
The authors contributed equally to all aspects of the article.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information
Nature Reviews Physics thanks the anonymous reviewers for their contribution to the peer review of this work.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kharzeev, D.E., Liao, J. Chiral magnetic effect reveals the topology of gauge fields in heavy-ion collisions. Nat Rev Phys 3, 55–63 (2021). https://doi.org/10.1038/s42254-020-00254-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s42254-020-00254-6
This article is cited by
-
Intrinsic chiral field as vector potential of the magnetic current in the zig-zag lattice of magnetic dipoles
Scientific Reports (2023)
-
Probing the chiral magnetic wave with charge-dependent flow measurements in Pb-Pb collisions at the LHC
Journal of High Energy Physics (2023)
-
Experimental signatures of the chiral anomaly in Dirac–Weyl semimetals
Nature Reviews Physics (2021)
-
Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation
Journal of High Energy Physics (2021)