Abstract
My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.
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References
A.Y. Alekseev, V.V. Cheianov, J. Frohlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly. Phys. Rev. Lett. 81, 3503–3506 (1998). doi:10.1103/PhysRevLett.81.3503
P.W. Anderson, J.M. Rowell, Probable observation of the Josephson superconducting tunneling effect. Phys. Rev. Lett. 10, 230 (1963). doi:10.1103/PhysRevLett.10.230
A. Ballon-Bayona, K. Peeters, M. Zamaklar, A chiral magnetic spiral in the holographic Sakai-Sugimoto model. J. High Energy Phys. 11, 164 (2012). doi:10.1007/JHEP11(2012)164
J. Bardeen, Tunneling into superconductors. Phys. Rev. Lett. 9, 147 (1962). doi:10.1103/PhysRevLett.9.147
G. Basar, G.V. Dunne, D.E. Kharzeev, Chiral magnetic spiral. Phys. Rev. Lett. 104, 232301 (2010). doi:10.1103/PhysRevLett.104.232301
P. Buividovich, M. Chernodub, E. Luschevskaya, M. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory. Phys. Rev. D 80, 054503 (2009). doi:10.1103/PhysRevD.80.054503
D. Deryagin, D.Y. Grigoriev, V. Rubakov, Standing wave ground state in high density, zero temperature QCD at large N c . Int. J. Mod. Phys. A 7, 659–681 (1992). doi:10.1142/S0217751X92000302
E.J. Ferrer, V. de la Incera, C. Manuel, Magnetic color flavor locking phase in high density QCD. Phys. Rev. Lett. 95, 152002 (2005). doi:10.1103/PhysRevLett.95.152002
K. Fukushima, QCD matter in extreme environments. J. Phys. G 39, 013101 (2012). doi:10.1088/0954-3899/39/1/013101
K. Fukushima, F. Gelis, The evolving Glasma. Nucl. Phys. A 874, 108–129 (2012). doi:10.1016/j.nuclphysa.2011.11.003
K. Fukushima, D.E. Kharzeev, H.J. Warringa, The chiral magnetic effect. Phys. Rev. D 78, 074033 (2008). doi:10.1103/PhysRevD.78.074033
K. Fukushima, D.E. Kharzeev, H.J. Warringa, Electric-current susceptibility and the chiral magnetic effect. Nucl. Phys. A 836, 311–336 (2010). doi:10.1016/j.nuclphysa.2010.02.003
K. Fukushima, D.E. Kharzeev, H.J. Warringa, Real-time dynamics of the chiral magnetic effect. Phys. Rev. Lett. 104, 212001 (2010). doi:10.1103/PhysRevLett.104.212001
K. Fukushima, K. Mameda, Wess-Zumino-Witten action and photons from the chiral magnetic effect. Phys. Rev. D 86, 071501 (2012). doi:10.1103/PhysRevD.86.071501
K. Fukushima, M. Ruggieri, Dielectric correction to the chiral magnetic effect. Phys. Rev. D 82, 054001 (2010). doi:10.1103/PhysRevD.82.054001
K. Fukushima, H.J. Warringa, Color superconducting matter in a magnetic field. Phys. Rev. Lett. 100, 032007 (2008). doi:10.1103/PhysRevLett.100.032007
C. Gale, S. Jeon, B. Schenke, P. Tribedy, R. Venugopalan, Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics. Phys. Rev. Lett. 100, 012302 (2013). doi:10.1103/PhysRevLett.110.012302
J.H. Gao, Z.T. Liang, S. Pu, Q. Wang, X.N. Wang, Chiral anomaly and local polarization effect from quantum kinetic approach. Phys. Rev. Lett. 109, 232301 (2012). doi:10.1103/PhysRevLett.109.232301
M. Giovannini, M. Shaposhnikov, Primordial hypermagnetic fields and triangle anomaly. Phys. Rev. D 57, 2186–2206 (1998). doi:10.1103/PhysRevD.57.2186
M. Giovannini, M. Shaposhnikov, Primordial magnetic fields, anomalous isocurvature fluctuations and big bang nucleosynthesis. Phys. Rev. Lett. 80, 22–25 (1998). doi:10.1103/PhysRevLett.80.22
E. Gorbar, V. Miransky, I. Shovkovy, Chiral asymmetry of the Fermi surface in dense relativistic matter in a magnetic field. Phys. Rev. C 80, 032801 (2009). doi:10.1103/PhysRevC.80.032801
V. Gusynin, V. Miransky, I. Shovkovy, Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in (3+1)-dimensions. Phys. Lett. B 349, 477–483 (1995). doi:10.1016/0370-2693(95)00232-A
R. Kaiser, Anomalies and WZW term of two flavor QCD. Phys. Rev. D 63, 076010 (2001). doi:10.1103/PhysRevD.63.076010
T. Kalaydzhyan, Chiral superfluidity of the quark-gluon plasma (2012)
T. Kalaydzhyan, I. Kirsch, Fluid/gravity model for the chiral magnetic effect. Phys. Rev. Lett. 106, 211601 (2011). doi:10.1103/PhysRevLett.106.211601
D. Kharzeev, Parity violation in hot QCD: why it can happen, and how to look for it. Phys. Lett. B 633, 260–264 (2006). doi:10.1016/j.physletb.2005.11.075
D.E. Kharzeev, Topologically induced local P and CP violation in QCD × QED. Ann. Phys. 325, 205–218 (2010). doi:10.1016/j.aop.2009.11.002
D.E. Kharzeev, L.D. McLerran, H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘Event by event P and CP violation’. Nucl. Phys. A 803, 227–253 (2008). doi:10.1016/j.nuclphysa.2008.02.298
D.E. Kharzeev, H.J. Warringa, Chiral magnetic conductivity. Phys. Rev. D 80, 034028 (2009). doi:10.1103/PhysRevD.80.034028
D.E. Kharzeev, H.U. Yee, Chiral magnetic wave. Phys. Rev. D 83, 085007 (2011). doi:10.1103/PhysRevD.83.085007
M. Luscher, SO(4) symmetric solutions of Minkowskian Yang-Mills field equations. Phys. Lett. B 70, 321 (1977). doi:10.1016/0370-2693(77)90668-2
M.A. Metlitski, A.R. Zhitnitsky, Anomalous axion interactions and topological currents in dense matter. Phys. Rev. D 72, 045011 (2005). doi:10.1103/PhysRevD.72.045011
E. Nakano, T. Tatsumi, Chiral symmetry and density wave in quark matter. Phys. Rev. D 71, 114006 (2005). doi:10.1103/PhysRevD.71.114006
J.L. Noronha, I.A. Shovkovy, Color-flavor locked superconductor in a magnetic field. Phys. Rev. D 76, 105030 (2007). doi:10.1103/PhysRevD.76.105030. Erratum: doi:10.1103/PhysRevD.86.049901
H. Ooguri, M. Oshikawa, Instability in magnetic materials with dynamical axion field. Phys. Rev. Lett. 108, 161803 (2012). doi:10.1103/PhysRevLett.108.161803
H. Primakoff, Photoproduction of neutral mesons in nuclear electric fields and the mean life of the neutral meson. Phys. Rev. 81, 899 (1951). doi:10.1103/PhysRev.81.899
G. Raffelt, L. Stodolsky, Mixing of the photon with low mass particles. Phys. Rev. D 37, 1237 (1988). doi:10.1103/PhysRevD.37.1237
A. Rebhan, A. Schmitt, S.A. Stricker, Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model. J. High Energy Phys. 1001, 026 (2010). doi:10.1007/JHEP01(2010)026
V. Rubakov, On chiral magnetic effect and holography (2010)
B.M. Schechter, Yang-Mills theory on the hypertorus. Phys. Rev. D 16, 3015 (1977). doi:10.1103/PhysRevD.16.3015
V. Schon, M. Thies, 2-D model field theories at finite temperature and density (2000)
J.S. Schwinger, On gauge invariance and vacuum polarization. Phys. Rev. 82, 664–679 (1951). doi:10.1103/PhysRev.82.664
P. Sikivie, Experimental tests of the invisible axion. Phys. Rev. Lett. 51, 1415 (1983). doi:10.1103/PhysRevLett.51.1415
D. Son, M. Stephanov, Axial anomaly and magnetism of nuclear and quark matter. Phys. Rev. D 77, 014021 (2008). doi:10.1103/PhysRevD.77.014021
D.T. Son, N. Yamamoto, Berry curvature, triangle anomalies, and chiral magnetic effect in Fermi liquids. Phys. Rev. Lett. 109, 181602 (2012). doi:10.1103/PhysRevLett.109.181602
M. Stephanov, Y. Yin, Chiral kinetic theory. Phys. Rev. Lett. 109, 162001 (2012). doi:10.1103/PhysRevLett.109.162001
A. Vilenkin, Equilibrium parity violating current in a magnetic field. Phys. Rev. D 22, 3080–3084 (1980). doi:10.1103/PhysRevD.22.3080
A. Yamamoto, Chiral magnetic effect in lattice QCD with a chiral chemical potential. Phys. Rev. Lett. 107, 031601 (2011). doi:10.1103/PhysRevLett.107.031601
H.U. Yee, Holographic chiral magnetic conductivity. J. High Energy Phys. 0911, 085 (2009). doi:10.1088/1126-6708/2009/11/085
I. Zahed, Anomalous chiral Fermi surface. Phys. Rev. Lett. 109, 091603 (2012). doi:10.1103/PhysRevLett.109.091603
Acknowledgements
The author would like to express his sincere thanks to his collaborators, Dima Kharzeev, Kazuya Mameda, and Harmen Warringa. The contents of this article are based on the fruitful collaboration with them. Especially, this article is dedicated to Harmen Warringa, who inspired me enough to initiate my working on the Chiral Magnetic Effect. Harmen’s contribution to physics of the Chiral Magnetic Effect should be memorable as long as the CME-related physics is of our interest. The author is also grateful to Tigran Kalaydzhyan, Dima Kharzeev, Toni Rebhan, Mikhail Shaposhnikov, Igor Shovkovy for useful comments on this article.
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Fukushima, K. (2013). Views of the Chiral Magnetic Effect. In: Kharzeev, D., Landsteiner, K., Schmitt, A., Yee, HU. (eds) Strongly Interacting Matter in Magnetic Fields. Lecture Notes in Physics, vol 871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37305-3_9
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