Abstract
We compute all the second order transport coefficients of a hydrodynamic theory with a gravity dual which includes a Gauss-Bonnet term. We find that a particular linear combination of the second order transport coefficients, which was found to vanish in generic two derivative gravity theories with matter, remains zero even in the presence of the Gauss-Bonnet term. We contrast this behavior with the shear viscosity to entropy density ratio.
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
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].
S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [INSPIRE].
D. Anselmi and A. Kehagias, Subleading corrections and central charges in the AdS/CFT correspondence, Phys. Lett. B 455 (1999) 155 [hep-th/9812092] [INSPIRE].
A. Fayyazuddin and M. Spalinski, Large-N superconformal gauge theories and supergravity orientifolds, Nucl. Phys. B 535 (1998) 219 [hep-th/9805096] [INSPIRE].
O. Aharony, A. Fayyazuddin and J.M. Maldacena, The large-N limit of N = 2, N = 1 field theories from three-branes in F-theory, JHEP 07 (1998) 013 [hep-th/9806159] [INSPIRE].
O. Aharony, J. Pawelczyk, S. Theisen and S. Yankielowicz, A note on anomalies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 066001 [hep-th/9901134] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
M. Blau, K. Narain and E. Gava, On subleading contributions to the AdS/CFT trace anomaly, JHEP 09 (1999) 018 [hep-th/9904179] [INSPIRE].
A. Buchel, R.C. Myers and A. Sinha, Beyond η/s = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [INSPIRE].
Y. Kats and P. Petrov, Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044 [arXiv:0712.0743] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].
G. Policastro, D. Son and A. 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].
J. Erdmenger, P. Kerner and H. Zeller, Transport in anisotropic superfluids: a holographic description, JHEP 01 (2012) 059 [arXiv:1110.0007] [INSPIRE].
A. Rebhan and D. Steineder, Violation of the holographic viscosity bound in a strongly coupled anisotropic plasma, Phys. Rev. Lett. 108 (2012) 021601 [arXiv:1110.6825] [INSPIRE].
K.A. Mamo, Holographic RG flow of the shear viscosity to entropy density ratio in strongly coupled anisotropic plasma, JHEP 10 (2012) 070 [arXiv:1205.1797] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [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].
M. Haack and A. Yarom, Universality of second order transport coefficients from the gauge-string duality, Nucl. Phys. B 813 (2009) 140 [arXiv:0811.1794] [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity bound violation in higher derivative gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The viscosity bound and causality violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [INSPIRE].
A. Buchel, Shear viscosity of boost invariant plasma at finite coupling, Nucl. Phys. B 802 (2008) 281 [arXiv:0801.4421] [INSPIRE].
S. Dutta, Higher derivative corrections to locally black brane metrics, JHEP 05 (2008) 082 [arXiv:0804.2453] [INSPIRE].
R. Brustein and A. Medved, The ratio of shear viscosity to entropy density in generalized theories of gravity, Phys. Rev. D 79 (2009) 021901 [arXiv:0808.3498] [INSPIRE].
R.-G. Cai, Z.-Y. Nie, N. Ohta and Y.-W. Sun, Shear viscosity from Gauss-Bonnet gravity with a dilaton coupling, Phys. Rev. D 79 (2009) 066004 [arXiv:0901.1421] [INSPIRE].
S. Cremonini, K. Hanaki, J.T. Liu and P. Szepietowski, Higher derivative effects on η/s at finite chemical potential, Phys. Rev. D 80 (2009) 025002 [arXiv:0903.3244] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].
N. Banerjee and S. Dutta, Higher derivative corrections to shear viscosity from graviton’s effective coupling, JHEP 03 (2009) 116 [arXiv:0901.3848] [INSPIRE].
N. Banerjee and S. Dutta, Shear viscosity to entropy density ratio in six derivative gravity, JHEP 07 (2009) 024 [arXiv:0903.3925] [INSPIRE].
S. Cremonini, U. Gürsoy and P. Szepietowski, On the temperature dependence of the shear viscosity and holography, JHEP 08 (2012) 167 [arXiv:1206.3581] [INSPIRE].
R. Brustein and A. Medved, Graviton multi-point functions at the AdS boundary, Phys. Rev. D 87 (2013) 024005 [arXiv:1211.0109] [INSPIRE].
X.-H. Ge, Y. Matsuo, F.-W. Shu, S.-J. Sin and T. Tsukioka, Viscosity bound, causality violation and instability with stringy correction and charge, JHEP 10 (2008) 009 [arXiv:0808.2354] [INSPIRE].
X.-H. Ge and S.-J. Sin, Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant, JHEP 05 (2009) 051 [arXiv:0903.2527] [INSPIRE].
M.A. York and G.D. Moore, Second order hydrodynamic coefficients from kinetic theory, Phys. Rev. D 79 (2009) 054011 [arXiv:0811.0729] [INSPIRE].
O. Saremi and K.A. Sohrabi, Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT, JHEP 11 (2011) 147 [arXiv:1105.4870] [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].
R.C. Myers, Higher derivative gravity, surface terms and string theory, Phys. Rev. D 36 (1987) 392 [INSPIRE].
Y. Brihaye and E. Radu, Five-dimensional rotating black holes in Einstein-Gauss-Bonnet theory, Phys. Lett. B 661 (2008) 167 [arXiv:0801.1021] [INSPIRE].
M. Haack and A. Yarom, Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT, JHEP 10 (2008) 063 [arXiv:0806.4602] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1211.1979
Rights and permissions
About this article
Cite this article
Shaverin, E., Yarom, A. Universality of second order transport in Gauss-Bonnet gravity. J. High Energ. Phys. 2013, 13 (2013). https://doi.org/10.1007/JHEP04(2013)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2013)013