Abstract
We continue our construction of a hydrodynamical description of a holographic model with broken translation invariance. Using the fluid/gravity correspondence we derive the constitutive relations of the boundary theory in the presence of a magnetic field. This allows us to obtain novel results for the low-frequency magnetothermoelectric response coefficients. We discuss the DC limit of our hydrodynamics in detail, and show that our approach is equivalent to the ‘horizon-fluid’ of Donos and Gauntlett.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Further evidence for lattice-induced scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].
S.A. Hartnoll and D.M. Hofman, Locally critical resistivities from Umklapp scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
M. Blake and D. Tong, Universal resistivity from holographic massive gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
M. Blake, D. Tong and D. Vegh, Holographic lattices give the graviton an effective mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
B. Gouteraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
A. Donos, B. Gouteraux and E. Kiritsis, Holographic metals and insulators with helical symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Thermo-electric transport in gauge/gravity models with momentum dissipation, JHEP 09 (2014) 160 [arXiv:1406.4134] [INSPIRE].
M. Blake, Momentum relaxation from the fluid/gravity correspondence, JHEP 09 (2015) 010 [arXiv:1505.06992] [INSPIRE].
A. Lucas, Conductivity of a strange metal: from holography to memory functions, JHEP 03 (2015) 071 [arXiv:1501.05656] [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].
A. Lucas and S. Sachdev, Memory matrix theory of magnetotransport in strange metals, Phys. Rev. B 91 (2015) 195122 [arXiv:1502.04704] [INSPIRE].
R.A. Davison and B. Gouteraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
R.A. Davison and B. Gouteraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Coherent/incoherent metal transition in a holographic model, JHEP 12 (2014) 170 [arXiv:1409.8346] [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
T.R. Chien, Z.Z. Wang and N.P. Ong, Effect of Zn Impurities on the normal-state Hall angle in single crystal YBa 2 Cu 3−x Zn x O 7−δ , Phys. Rev. Lett. 67 (1991) 2088.
M. Blake and A. Donos, Quantum critical transport and the Hall angle, Phys. Rev. Lett. 114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].
V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, arXiv:1107.5780 [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [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].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
S. Bhattacharyya, R. Loganayagam, S. Minwalla, S. Nampuri, S.P. Trivedi and S.R. Wadia, Forced fluid dynamics from gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [INSPIRE].
M. Blake, A. Donos and N. Lohitsiri, Magnetothermoelectric response from holography, JHEP 08 (2015) 124 [arXiv:1502.03789] [INSPIRE].
A. Amoretti and D. Musso, Magneto-transport from momentum dissipating holography, JHEP 09 (2015) 094 [arXiv:1502.02631] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Thermoelectric conductivities at finite magnetic field and the Nernst effect, JHEP 07 (2015) 027 [arXiv:1502.05386] [INSPIRE].
A. Donos and J.P. Gauntlett, Navier-Stokes on black hole horizons and DC thermoelectric conductivity, arXiv:1506.01360 [INSPIRE].
E. Banks, A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities and Stokes flows on black hole horizons, arXiv:1507.00234 [INSPIRE].
M.J. Bhaseen, A. G. Green, S. L. Sondhi, Magnetothermoelectric response at a superfluid-Mott insulator transition, Phys. Rev. Lett. 98 (2007) 179901 [cond-mat/0610687].
M.J. Bhaseen, A.G. Green and S.L. Sondhi, Magnetothermoelectric response near quantum critical points, Phys. Rev. B 79 (2009) 094502 [arXiv:0811.0269].
M.M. Caldarelli, O.J.C. Dias and D. Klemm, Dyonic AdS black holes from magnetohydrodynamics, JHEP 03 (2009) 025 [arXiv:0812.0801] [INSPIRE].
J. Hansen and P. Kraus, Nonlinear magnetohydrodynamics from gravity, JHEP 04 (2009) 048 [arXiv:0811.3468] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].
Y.-P. Hu and J.-H. Zhang, Gravity/fluid correspondence and its application on bulk gravity with U(1) gauge field, Adv. High Energy Phys. 2014 (2014) 483814 [arXiv:1311.3974] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
L. D. Landau and E. M. Lifshitz, The classical theory of fields, Butterworth-Heinemann, Oxford U.K. (1987).
L.P. Kadanoff and P.C. Martin, Hydrodynamic equations and correlation functions, Ann. Phys. 24 (1963) 419.
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].
J. Lindgren, I. Papadimitriou, A. Taliotis and J. Vanhoof, Holographic Hall conductivities from dyonic backgrounds, JHEP 07 (2015) 094 [arXiv:1505.04131] [INSPIRE].
A. Lucas, Hydrodynamic transport in strongly coupled disordered quantum field theories, arXiv:1506.02662 [INSPIRE].
S. Grozdanov, A. Lucas, S. Sachdev and K. Schalm, Absence of disorder-driven metal-insulator transitions in simple holographic models, arXiv:1507.00003 [INSPIRE].
C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev. D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].
K. Goldstein, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi and A. Westphal, Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [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: 1507.04870
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Blake, M. Magnetotransport from the fluid/gravity correspondence. J. High Energ. Phys. 2015, 78 (2015). https://doi.org/10.1007/JHEP10(2015)078
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2015)078