Abstract
It was argued by Brigante et al. [1] that the lower bound on the ratio of the shear viscosity to the entropy density in strongly coupled plasma is translated into micro-causality violation in the dual gravitational description. Since transport properties of the system characterize its infrared dynamics, while the causality of the theory is determined by its ultraviolet behavior, the viscosity bound/ microcausality link should not be applicable to theories that undergo low temperature phase transitions. We present an explicit model of AdS/CFT correspondence that confirms this fact.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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] [SPIRES].
J .M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. T heor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
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] [SPIRES].
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] [SPIRES].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [SPIRES].
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] [SPIRES].
A. Buchel, On universality of stress-energy tensor correlation functions in supergravity, Phys. Lett. B 609 (2005) 392 [hep-th/0408095] [SPIRES].
P. Benincasa, A. Buchel and R. Naryshkin, The shear viscosity of gauge theory plasma with chemical potentials, Phys. Lett. B 645 (2007) 309 [hep-th/0610145] [SPIRES].
K. Landsteiner and J. Mas, The shear viscosity of the non-commutative plasma, JHEP 07 (2007) 088 [arXiv:0706.0411] [SPIRES].
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] [SPIRES].
E.I. Buchbinder and A. Buchel, The fate of the sound and diffusion in holographic magnetic field, Phys. Rev. D 79 (2009) 046006 [arXiv:0811.4325] [SPIRES].
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] [SPIRES].
M. Luzum and P. Romatschke, Conformal relativistic viscous hydrodynamics: applications to RHIC results at \( \sqrt {{{s_{NN}}}} = 200\,GeV \), Phys. Rev. C 78 (2008) 034915 [Erratum ibid. C 79 (2009) 039903] [arXiv:0804.4015] [SPIRES].
T.D. Cohen, Is there a ’most perfect fluid’ consistent with quantum field theory?, Phys. Rev. Lett. 99 (2007) 021602 [hep-th/0702136] [SPIRES].
D.T. Son, Comment on ’Is there a ’most perfect fluid’ consistent with quantum field theory?’, Phys. Rev. Lett. 100 (2008) 029101 [arXiv:0709.4651] [SPIRES].
A. Buchel, J.T. Liu and A.O. Starinets, Coupling constant dependence of the shear viscosity in N =4 supersymmetric Yang-Mills theory, Nucl. Phys. B 707 (2005) 56 [hep-th/0406264] [SPIRES].
A. Buchel, Shear viscosity of boost invariant plasma at finite coupling, Nucl. Phys. B 802 (2008) 281 [arXiv:0801.4421] [SPIRES].
A. Buchel, Shear viscosity of CFT plasma at finite coupling, Phys. Lett. B 665 (2008) 298 [arXiv:0804.3161] [SPIRES].
A. Buchel, Resolving disagreement for η/s in a CFT plasma at finite coupling, Nucl. Phys. B 803 (2008) 166 [arXiv:0805.2683] [SPIRES].
A. Buchel, R.C. Myers, M.F. Paulos and A. Sinha, Universal holographic hydrodynamics at finite coupling, Phys. Lett. B 669 (2008) 364 [arXiv:0808.1837] [SPIRES].
R.C. Myers, M.F. Paulos and A. Sinha, Quantum corrections to η/s, Phys. Rev. D 79 (2009) 041901 [arXiv:0806.2156] [SPIRES].
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] [SPIRES].
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] [SPIRES].
A. Buchel, R.C. Myers and A. Sinha, Beyond η/s =1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [SPIRES].
M. Blau, K. S. Narain and E. Gava, “On subleading contributions to the AdS/CFT trace anomaly,” JHEP 9909 (1999) 018 [arXiv:hep-th/9904179].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055] [SPIRES].
A. Buchel and R.C. Myers, Causality of holographic hydrodynamics, JHEP 08 (2009) 016 [arXiv:0906.2922] [SPIRES].
D.M. Hofman, Higher derivative gravity, causality and positivity of energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [SPIRES].
J. de Boer, M. Kulaxizi and A. Parnachev, AdS 7 /CFT 6 , Gauss-Bonnet gravity and viscosity bound, JHEP 03 (2010) 087 [arXiv:0910.5347] [SPIRES].
X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [SPIRES].
A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [SPIRES].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Lovelock gravities and black holes, JHEP 06 (2010) 008 [arXiv:0912.1877] [SPIRES].
X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944] [SPIRES].
I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, arXiv:1006.1902 [SPIRES].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [SPIRES].
D. Berenstein, C.P. Herzog and I.R. Klebanov, Baryon spectra and AdS/CFT correspondence, JHEP 06 (2002) 047 [hep-th/0202150] [SPIRES].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [SPIRES].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [SPIRES].
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] [SPIRES].
A. Buchel, Critical phenomena in N =4 SY M plasma, Nucl. Phys. B 841 (2010) 59 [arXiv:1005.0819] [SPIRES].
O. Aharony, A. Buchel and P. Kerner, The black hole in the throat — Thermodynamics of strongly coupled cascading gauge theories, Phys. Rev. D 76 (2007) 086005 [arXiv:0706.1768] [SPIRES].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [SPIRES].
K. Behrndt, M. Cvetič and W.A. Sabra, Non-extreme black holes of five dimensional N =2 AdS supergravity, Nucl. Phys. B 553 (1999) 317 [hep-th/9810227] [SPIRES].
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] [SPIRES].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].
D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].
D.T. Son and A.O. Starinets, Hydrodynamics of R -charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [SPIRES].
S. Cremonini, J.T. Liu and P. Szepietowski, Higher derivative corrections to R -charged black holes: boundary counterterms and the mass-charge relation, JHEP 03 (2010) 042 [arXiv:0910.5159] [SPIRES].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [SPIRES].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1007.2963
Rights and permissions
About this article
Cite this article
Buchel, A., Cremonini, S. Viscosity bound and causality in superfluid plasma. J. High Energ. Phys. 2010, 26 (2010). https://doi.org/10.1007/JHEP10(2010)026
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2010)026