Abstract
We consider long wavelength solutions to the Einstein-dilaton system with negative cosmological constant which are dual, under the AdS/CFT correspondence, to solutions of the conformal relativistic Navier-Stokes equations with a dilaton-dependent forcing term. Certain forced fluid flows are known to exhibit turbulence; holographic duals of forced fluid dynamics are therefore of particular interest as they may aid efforts towards an explicit model of holographic steady state turbulence. In recent work, Bhattacharyya et al. have constructed long wavelength asymptotically locally AdS5 bulk space-times with a slowly varying boundary dilaton field which are dual to forced fluid flows on the 4–dimensional boundary. In this paper, we generalise their work to arbitrary space-time dimensions; we explicitly compute the dual bulk metric, the fluid dynamical stress tensor and Lagrangian to second order in a boundary derivative expansion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
S.S. Gubser and A. Karch, From gauge-string duality to strong interactions: A Pedestrian’s Guide, Ann. Rev. Nucl. Part. Sci. 59 (2009) 145 [arXiv:0901.0935] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
V.E. Hubeny and M. Rangamani, A Holographic view on physics out of equilibrium, Adv. High Energy Phys. 2010 (2010) 297916 [arXiv:1006.3675] [INSPIRE].
V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, hep-th/0404176 [INSPIRE].
I. Papadimitriou and K. Skenderis, Correlation functions in holographic RG flows, JHEP 10 (2004) 075 [hep-th/0407071] [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
N. Iqbal and H. Liu, Real-time response in AdS/CFT with application to spinors, Fortsch. Phys. 57 (2009) 367 [arXiv:0903.2596] [INSPIRE].
S. Caron-Huot, P.M. Chesler and D. Teaney, Fluctuation, dissipation and thermalization in non-equilibrium AdS 5 black hole geometries, Phys. Rev. D 84 (2011) 026012 [arXiv:1102.1073] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Holography and colliding gravitational shock waves in asymptotically AdS 5 spacetime, Phys. Rev. Lett. 106 (2011) 021601 [arXiv:1011.3562] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
L.D. Landau and E.M. Lifshitz, Fluid mechanics (course of theoretical physics), Pergamon Press, Oxford (1959).
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [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].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [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].
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].
R.A. Janik and R.B. Peschanski, Asymptotic perfect fluid dynamics as a consequence of AdS/CFT, Phys. Rev. D 73 (2006) 045013 [hep-th/0512162] [INSPIRE].
R.A. Janik, Viscous plasma evolution from gravity using AdS/CFT, Phys. Rev. Lett. 98 (2007) 022302 [hep-th/0610144] [INSPIRE].
M.P. Heller and R.A. Janik, Viscous hydrodynamics relaxation time from AdS/CFT, Phys. Rev. D 76 (2007) 025027 [hep-th/0703243] [INSPIRE].
M. Rangamani, Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, arXiv:1107.5780 [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].
M. Haack and A. Yarom, Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT, JHEP 10 (2008) 063 [arXiv:0806.4602] [INSPIRE].
S. Bhattacharyya, S. Minwalla and S.R. Wadia, The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity, JHEP 08 (2009) 059 [arXiv:0810.1545] [INSPIRE].
I. Kanitscheider and K. Skenderis, Universal hydrodynamics of non-conformal branes, JHEP 04 (2009) 062 [arXiv:0901.1487] [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 et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
J. Sonner and B. Withers, A gravity derivation of the Tisza-Landau Model in AdS/CFT, Phys. Rev. D 82 (2010) 026001 [arXiv:1004.2707] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, arXiv:1105.3733 [INSPIRE].
C.P. Herzog, N. Lisker, P. Surowka and A. Yarom, Transport in holographic superfluids, JHEP 08 (2011) 052 [arXiv:1101.3330] [INSPIRE].
R. Banerjee, P. Chakraborty, S. Dey, B.R. Majhi and A.K. Mitra, Two dimensional hydrodynamics with gauge and gravitational anomalies, arXiv:1307.1313 [INSPIRE].
S. Bhattacharyya, R. Loganayagam, S. Minwalla, S. Nampuri, S.P. Trivedi et al., Forced Fluid Dynamics from Gravity, JHEP 02 (2009) 018 [arXiv:0806.0006] [INSPIRE].
R.-G. Cai, L. Li, Z.-Y. Nie and Y.-L. Zhang, Holographic Forced Fluid Dynamics in Non-relativistic Limit, Nucl. Phys. B 864 (2012) 260 [arXiv:1202.4091] [INSPIRE].
F. Carrasco, L. Lehner, R.C. Myers, O. Reula and A. Singh, Turbulent flows for relativistic conformal fluids in 2 + 1 dimensions, Phys. Rev. D 86 (2012) 126006 [arXiv:1210.6702] [INSPIRE].
C. Eling, I. Fouxon and Y. Oz, Gravity and a Geometrization of Turbulence: An Intriguing Correspondence, arXiv:1004.2632 [INSPIRE].
C. Eling and Y. Oz, Holographic Vorticity in the Fluid/Gravity Correspondence, JHEP 11 (2013) 079 [arXiv:1308.1651] [INSPIRE].
A. Adams, P.M. Chesler and H. Liu, Holographic turbulence, arXiv:1307.7267 [INSPIRE].
R. Loganayagam, Entropy Current in Conformal Hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [INSPIRE].
P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [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: 1309.6325
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
Ashok, T. Forced fluid dynamics from gravity in arbitrary dimensions. J. High Energ. Phys. 2014, 138 (2014). https://doi.org/10.1007/JHEP03(2014)138
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2014)138