Abstract
In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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. A 803 (2008) 227 [arXiv:0711.0950] [SPIRES].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [SPIRES].
D.E. Kharzeev and H.J. Warringa, Chiral magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [SPIRES].
STAR collaboration, S.A. Voloshin, Probe for the strong parity violation effects at RHIC with three particle correlations, arXiv:0806.0029 [SPIRES].
STAR collaboration and others, Azimuthal charged-particle correlations and possible local strong parity violation, arXiv:0909.1739 [SPIRES].
F. Wang, Effects of cluster particle correlations on local parity violation observables, arXiv:0911.1482 [SPIRES].
H.-U. Yee, Holographic chiral magnetic conductivity, JHEP 11 (2009) 085 [arXiv:0908.4189] [SPIRES].
D.T. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [SPIRES].
M.A. Metlitski and A.R. Zhitnitsky, Anomalous axion interactions and topological currents in dense matter, Phys. Rev. D 72 (2005) 045011 [hep-ph/0505072] [SPIRES].
E.V. Gorbar, V.A. Miransky and I.A. Shovkovy, Chiral asymmetry of theFermi surface in dense relativistic matter in a magnetic field, Phys. Rev. C 80 (2009) 032801 [arXiv:0904.2164] [SPIRES].
J. Charbonneau and A. Zhitnitsky, Topological currents in neutron stars: kicks, precession, toroidal fields and magnetic helicity, arXiv:0903.4450 [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
M.G. Alford, K. Rajagopal and F. Wilczek, Color-flavor locking and chiral symmetry breaking in high density QCD, Nucl. Phys. B 537 (1999) 443 [hep-ph/9804403] [SPIRES].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [SPIRES].
T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [SPIRES].
O. Bergman, G. Lifschytz and M. Lippert, Magnetic properties of dense holographic QCD, Phys. Rev. D 79 (2009) 105024 [arXiv:0806.0366] [SPIRES].
E.G. Thompson and D.T. Son, Magnetized baryonic matter in holographic QCD, Phys. Rev. D 78 (2008) 066007 [arXiv:0806.0367] [SPIRES].
A. Rebhan, A. Schmitt and S.A. Stricker, Meson supercurrents and the Meissner effect in the Sakai-Sugimoto model, JHEP 05 (2009) 084 [arXiv:0811.3533] [SPIRES].
G. Lifschytz and M. Lippert, Anomalous conductivity in holographic QCD, Phys. Rev. D 80 (2009) 066005 [arXiv:0904.4772] [SPIRES].
P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev. D 80 (2009) 054503 [arXiv:0907.0494] [SPIRES].
H. Hata, M. Murata and S. Yamato, Chiral currents and static properties of nucleons in holographic QCD, Phys. Rev. D 78 (2008) 086006 [arXiv:0803.0180] [SPIRES].
L. McLerran and R.D. Pisarski, Phases of cold, dense quarks at large-N c , Nucl. Phys. A 796 (2007) 83 [arXiv:0706.2191] [SPIRES].
H. Hata, T. Sakai, S. Sugimoto and S. Yamato, Baryons from instantons in holographic QCD, Prog. Theor. Phys. 117 (2007) 1157 [hep-th/0701280] [SPIRES].
K. Hashimoto, T. Sakai and S. Sugimoto, Holographic baryons: static properties and form factors from gauge/string duality, Prog. Theor. Phys. 120 (2008) 1093 [arXiv:0806.3122] [SPIRES].
K.-Y. Kim and I. Zahed, Electromagnetic baryon form factors from holographic QCD, JHEP 09 (2008) 007 [arXiv:0807.0033] [SPIRES].
K.-Y. Kim and I. Zahed, Nucleon-nucleon potential from holography, JHEP 03 (2009) 131 [arXiv:0901.0012] [SPIRES].
W.A. Bardeen, Anomalous Ward identities in spinor field theories, Phys. Rev. 184 (1969) 1848 [SPIRES].
C.T. Hill, Anomalies, Chern-Simons terms and chiral delocalization in extra dimensions, Phys. Rev. D 73 (2006) 085001 [hep-th/0601154] [SPIRES].
J.S. Bell and R. Jackiw, A PCAC puzzle: π 0 → γγ in the σ-model, Nuovo Cim. A 60 (1969) 47 [SPIRES].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [SPIRES].
O. Kaymakcalan, S. Rajeev and J. Schechter, Nonabelian anomaly and vector meson decays, Phys. Rev. D 30 (1984) 594 [SPIRES].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [SPIRES].
N. Banerjee et al., Hydrodynamics from charged black branes, arXiv:0809.2596 [SPIRES].
M. Torabian and H.-U. Yee, Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries, JHEP 08 (2009) 020 [arXiv:0903.4894] [SPIRES].
D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [SPIRES].
O. Bergman, G. Lifschytz and M. Lippert, Response of holographic QCD to electric and magnetic fields, JHEP 05 (2008) 007 [arXiv:0802.3720] [SPIRES].
C.V. Johnson and A. Kundu, External fields and chiral symmetry breaking in the Sakai-Sugimoto model, JHEP 12 (2008) 053 [arXiv:0803.0038] [SPIRES].
K.-Y. Kim, S.-J. Sin and I. Zahed, Dense holographic QCD in the Wigner-Seitz approximation, JHEP 09 (2008) 001 [arXiv:0712.1582] [SPIRES].
J. Ambjørn, J. Greensite and C. Peterson, The axial anomaly and the lattice Dirac sea, Nucl. Phys. B 221 (1983) 381 [SPIRES].
G. Lifschytz and M. Lippert, Holographic magnetic phase transition, Phys. Rev. D 80 (2009) 066007 [arXiv:0906.3892] [SPIRES].
S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the canonical quantization of the Chern-Simons-Witten theory, Nucl. Phys. B 326 (1989) 108 [SPIRES].
G.M. Newman and D.T. Son, Response of strongly-interacting matter to magnetic field: some exact results, Phys. Rev. D 73 (2006) 045006 [hep-ph/0510049] [SPIRES].
H.B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. B 130 (1983) 389 [SPIRES].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Holographic non-Fermi liquid in a background magnetic field, arXiv:0908.1436 [SPIRES].
F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, arXiv:0908.1788 [SPIRES].
H.-U. Yee, private communication, (2009).
N. Horigome and Y. Tanii, Holographic chiral phase transition with chemical potential, JHEP 01 (2007) 072 [hep-th/0608198] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 0909.4782
Rights and permissions
About this article
Cite this article
Rebhan, A., Schmitt, A. & Stricker, S.A. Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model. J. High Energ. Phys. 2010, 26 (2010). https://doi.org/10.1007/JHEP01(2010)026
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2010)026