Abstract
Hydrodynamics with both vector and axial currents is under study within a holographic model, consisting of canonical U(1)V × U(1)A gauge fields in an asymptotically AdS5 black brane. When gravitational back-reaction is taken into account, the chiral electric separation effect (CESE), namely the generation of an axial current as the response to an external electric field, is realized naturally. Via fluid/gravity correspondence, all the first order transport coefficients in the hydrodynamic constitutive relations are evaluated analytically: they are functions of vector chemical potential μ, axial chemical potential μ5 and the fluid’s temperature T . Apart from the proportionality factor μμ5, the CESE conductivity is found to be dependent on the dimensionless quantities μ/T and μ5/T nontrivially. As a complementary study, frequency-dependent transport phenomena are revealed through linear response analysis, demonstrating perfect agreement with the results obtained from fluid/gravity correspondence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Kharzeev, Parity violation in hot QCD: Why it can happen and how to look for it, Phys. Lett. B 633 (2006) 260 [hep-ph/0406125] [INSPIRE].
D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A 797 (2007) 67 [arXiv:0706.1026] [INSPIRE].
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] [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
D.T. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [INSPIRE].
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] [INSPIRE].
D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].
Y. Burnier, D.E. Kharzeev, J. Liao and H.-U. Yee, Chiral magnetic wave at finite baryon density and the electric quadrupole moment of quark-gluon plasma in heavy ion collisions, Phys. Rev. Lett. 107 (2011) 052303 [arXiv:1103.1307] [INSPIRE].
D.E. Kharzeev and D.T. Son, Testing the chiral magnetic and chiral vortical effects in heavy ion collisions, Phys. Rev. Lett. 106 (2011) 062301 [arXiv:1010.0038] [INSPIRE].
A. Bzdak, V. Koch and J. Liao, Charge-Dependent Correlations in Relativistic Heavy Ion Collisions and the Chiral Magnetic Effect, Lect. Notes Phys. 871 (2013) 503 [arXiv:1207.7327] [INSPIRE].
H.-U. Yee and Y. Yin, Realistic Implementation of Chiral Magnetic Wave in Heavy Ion Collisions, Phys. Rev. C 89 (2014) 044909 [arXiv:1311.2574] [INSPIRE].
ALICE collaboration, Charge-dependent flow and the search for the chiral magnetic wave in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}}=2.76 \) TeV, Phys. Rev. C 93 (2016) 044903 [arXiv:1512.05739] [INSPIRE].
CMS collaboration, Observation of charge-dependent azimuthal correlations in p-P b collisions and its implication for the search for the chiral magnetic effect, Phys. Rev. Lett. 118 (2017) 122301 [arXiv:1610.00263] [INSPIRE].
CMS collaboration, Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pP b and P bP b collisions at the CERN Large Hadron Collider, Phys. Rev. C 97 (2018) 044912 [arXiv:1708.01602] [INSPIRE].
CMS collaboration, Challenges to the chiral magnetic wave using charge-dependent azimuthal anisotropies in pPb and PbPb collisions at \( \sqrt{s_{\mathrm{NN}}}=5.02 \) TeV , arXiv:1708.08901 [INSPIRE].
X. Huang et al., Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs, Phys. Rev. X 5 (2015) 031023 [arXiv:1503.01304] [INSPIRE].
H. Li et al., Negative Magnetoresistance in Dirac Semimetal Cd3As2, Nat. Commun. 7 (2016) 10301 [arXiv:1507.06470].
Q. Li et al., Observation of the chiral magnetic effect in ZrTe5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [INSPIRE].
D.E. Kharzeev, The Chiral Magnetic Effect and Anomaly-Induced Transport, Prog. Part. Nucl. Phys. 75 (2014) 133 [arXiv:1312.3348] [INSPIRE].
X.-G. Huang, Electromagnetic fields and anomalous transports in heavy-ion collisions — A pedagogical review, Rept. Prog. Phys. 79 (2016) 076302 [arXiv:1509.04073] [INSPIRE].
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 (2016) 1 [arXiv:1511.04050] [INSPIRE].
V. Koch et al., Status of the chiral magnetic effect and collisions of isobars, Chin. Phys. C 41 (2017) 072001 [arXiv:1608.00982] [INSPIRE].
K. Landsteiner, Notes on Anomaly Induced Transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Anomalous transport properties of Dirac and Weyl semimetals (Review Article), Low Temp. Phys. 44 (2018) 487 [arXiv:1712.08947] [INSPIRE].
X.-G. Huang and J. Liao, Axial Current Generation from Electric Field: Chiral Electric Separation Effect, Phys. Rev. Lett. 110 (2013) 232302 [arXiv:1303.7192] [INSPIRE].
Y. Jiang, X.-G. Huang and J. Liao, Chiral electric separation effect in the quark-gluon plasma, Phys. Rev. D 91 (2015) 045001 [arXiv:1409.6395] [INSPIRE].
S. Pu, S.-Y. Wu and D.-L. Yang, Holographic Chiral Electric Separation Effect, Phys. Rev. D 89 (2014) 085024 [arXiv:1401.6972] [INSPIRE].
S. Pu, S.-Y. Wu and D.-L. Yang, Chiral Hall Effect and Chiral Electric Waves, Phys. Rev. D 91 (2015) 025011 [arXiv:1407.3168] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [INSPIRE].
E.V. Gorbar, I.A. Shovkovy, S. Vilchinskii, I. Rudenok, A. Boyarsky and O. Ruchayskiy, Anomalous Maxwell equations for inhomogeneous chiral plasma, Phys. Rev. D 93 (2016) 105028 [arXiv:1603.03442] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Consistent hydrodynamic theory of chiral electrons in Weyl semimetals, Phys. Rev. B 97 (2018) 121105 [arXiv:1712.01289] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms, Phys. Rev. B 97 (2018) 205119 [arXiv:1802.07265] [INSPIRE].
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Collective excitations in Weyl semimetals in the hydrodynamic regime, J. Phys. Condens. Matter 30 (2018) 275601 [arXiv:1802.10110] [INSPIRE].
A.V. Sadofyev and M.V. Isachenkov, The Chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical Conductivity with Holographic Lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
A. Gynther, K. Landsteiner, F. Pena-Benitez and A. Rebhan, Holographic Anomalous Conductivities and the Chiral Magnetic Effect, JHEP 02 (2011) 110 [arXiv:1005.2587] [INSPIRE].
Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part I, JHEP 11 (2016) 093 [arXiv:1608.08595] [INSPIRE].
Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part II, Eur. Phys. J. C 77 (2017) 194 [arXiv:1609.09054] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].
B. Müller and D.-L. Yang, Viscous Leptons in the Quark Gluon Plasma, Phys. Rev. D 91 (2015) 125010 [arXiv:1503.06967] [INSPIRE].
J. Erlich, E. Katz, D.T. Son and M.A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].
Y. Matsuo, S.-J. Sin, S. Takeuchi and T. Tsukioka, Magnetic conductivity and Chern-Simons Term in Holographic Hydrodynamics of Charged AdS Black Hole, JHEP 04 (2010) 071 [arXiv:0910.3722] [INSPIRE].
K. Landsteiner and Y. Liu, The holographic Weyl semi-metal, Phys. Lett. B 753 (2016) 453 [arXiv:1505.04772] [INSPIRE].
K. Landsteiner, Y. Liu and Y.-W. Sun, Quantum phase transition between a topological and a trivial semimetal from holography, Phys. Rev. Lett. 116 (2016) 081602 [arXiv:1511.05505] [INSPIRE].
K. Landsteiner, Y. Liu and Y.-W. Sun, Odd viscosity in the quantum critical region of a holographic Weyl semimetal, Phys. Rev. Lett. 117 (2016) 081604 [arXiv:1604.01346] [INSPIRE].
K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].
Y.-W. Sun and Q. Yang, Negative magnetoresistivity in holography, JHEP 09 (2016) 122 [arXiv:1603.02624] [INSPIRE].
Y. Seo, G. Song, P. Kim, S. Sachdev and S.-J. Sin, Holography of the Dirac Fluid in Graphene with two currents, Phys. Rev. Lett. 118 (2017) 036601 [arXiv:1609.03582] [INSPIRE].
M. Rogatko and K.I. Wysokinski, Holographic calculation of the magneto-transport coefficients in Dirac semimetals, JHEP 01 (2018) 078 [arXiv:1712.01608] [INSPIRE].
M. Rogatko and K.I. Wysokinski, Two interacting current model of holographic Dirac fluid in graphene, Phys. Rev. D 97 (2018) 024053 [arXiv:1708.08051] [INSPIRE].
M. Ammon, M. Baggioli, A. Jiménez-Alba and S. Moeckel, A smeared quantum phase transition in disordered holography, JHEP 04 (2018) 068 [arXiv:1802.08650] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
M. Blake, Momentum relaxation from the fluid/gravity correspondence, JHEP 09 (2015) 010 [arXiv:1505.06992] [INSPIRE].
M. Blake, Magnetotransport from the fluid/gravity correspondence, JHEP 10 (2015) 078 [arXiv:1507.04870] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
M. Taylor, More on counterterms in the gravitational action and anomalies, hep-th/0002125 [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
B. Sahoo and H.-U. Yee, Electrified plasma in AdS/CFT correspondence, JHEP 11 (2010) 095 [arXiv:1004.3541] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S. Bhattacharyya, R. Loganayagam, I. Mandal, S. Minwalla and A. Sharma, Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions, JHEP 12 (2008) 116 [arXiv:0809.4272] [INSPIRE].
J. Hur, K.K. Kim and S.-J. Sin, Hydrodynamics with conserved current from the gravity dual, JHEP 03 (2009) 036 [arXiv:0809.4541] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [INSPIRE].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. 2. Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [INSPIRE].
X.-H. Ge, Y. Matsuo, F.-W. Shu, S.-J. Sin and T. Tsukioka, Density Dependence of Transport Coefficients from Holographic Hydrodynamics, Prog. Theor. Phys. 120 (2008) 833 [arXiv:0806.4460] [INSPIRE].
E. Megias and F. Pena-Benitez, Holographic Gravitational Anomaly in First and Second Order Hydrodynamics, JHEP 05 (2013) 115 [arXiv:1304.5529] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1803.08389
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bu, Y., Cai, RG., Yang, Q. et al. Holographic charged fluid with chiral electric separation effect. J. High Energ. Phys. 2018, 83 (2018). https://doi.org/10.1007/JHEP09(2018)083
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2018)083