Abstract
We argue that the Kovtun-Son-Starinets (KSS) lower bound on the viscosity to entropy density ratio holds in fluid systems but is violated in solid materials with a nonzero shear elastic modulus. We construct explicit examples of this by applying the standard gauge/gravity duality methods to massive gravity and show that the KSS bound is clearly violated in black brane solutions whenever the massive gravity theories are of solid type. We argue that the physical reason for the bound violation relies on the viscoelastic nature of the mechanical response in these materials. We speculate on whether any real-world materials can violate the bound and discuss a possible generalization of the bound that involves the ratio of the shear elastic modulus to the pressure.
References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [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].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [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].
G. Rupak and T. Schäfer, Shear viscosity of a superfluid Fermi gas in the unitarity limit, Phys. Rev. A 76 (2007) 053607 [arXiv:0707.1520] [INSPIRE].
H. Song, S.A. Bass, U. Heinz, T. Hirano and C. Shen, 200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid, Phys. Rev. Lett. 106 (2011) 192301 [Erratum ibid. 109 (2012) 139904] [arXiv:1011.2783] [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].
S. Cremonini, The Shear Viscosity to Entropy Ratio: A Status Report, Mod. Phys. Lett. B 25 (2011) 1867 [arXiv:1108.0677] [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].
S. Jain, N. Kundu, K. Sen, A. Sinha and S.P. Trivedi, A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography, JHEP 01 (2015) 005 [arXiv:1406.4874] [INSPIRE].
R. Critelli, S.I. Finazzo, M. Zaniboni and J. Noronha, Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes, Phys. Rev. D 90 (2014) 066006 [arXiv:1406.6019] [INSPIRE].
X.-H. Ge, Y. Ling, C. Niu and S.-J. Sin, Thermoelectric conductivities, shear viscosity and stability in an anisotropic linear axion model, Phys. Rev. D 92 (2015) 106005 [arXiv:1412.8346] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [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, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
M. Baggioli and O. Pujolàs, Electron-Phonon Interactions, Metal-Insulator Transitions and Holographic Massive Gravity, Phys. Rev. Lett. 114 (2015) 251602 [arXiv:1411.1003] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
M. Taylor and W. Woodhead, Inhomogeneity simplified, Eur. Phys. J. C 74 (2014) 3176 [arXiv:1406.4870] [INSPIRE].
H. Leutwyler, Nonrelativistic effective Lagrangians, Phys. Rev. D 49 (1994) 3033 [hep-ph/9311264] [INSPIRE].
H. Leutwyler, Phonons as goldstone bosons, Helv. Phys. Acta 70 (1997) 275, hep-ph/9609466 [INSPIRE].
S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev. D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
A. Nicolis, R. Penco and R.A. Rosen, Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction, Phys. Rev. D 89 (2014) 045002 [arXiv:1307.0517] [INSPIRE].
L. Alberte, M. Baggioli, A. Khmelnitsky and O. Pujolàs, Solid Holography and Massive Gravity, JHEP 02 (2016) 114 [arXiv:1510.09089] [INSPIRE].
L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics. Vol. 7: Theory of Elasticity, sections 1, 4, 10 and 34, Pergamon Press, Oxford U.K. (1970).
P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, sections 6.4 and 8.4, Cambridge University Press, Cambridge U.K. (1995).
E.M. Lifshitz and L.P. Pitaevskii, Course of Theoretical Physics. Vol. 9: Statistical Physics Part 2, section 90, Pergamon Press, Oxford U.K. (1980).
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. II. Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [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].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [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].
L. Alberte and A. Khmelnitsky, Stability of Massive Gravity Solutions for Holographic Conductivity, Phys. Rev. D 91 (2015) 046006 [arXiv:1411.3027] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
R.S. Lakes, T. Lee, A. Berlse and Y.C. Wang, Extreme damping in composite materials with negative-stiffness inclusions, Nature 410 (2001) 565.
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
M. Mueller, J. Schmalian and L. Fritz, Graphene: A Nearly Perfect Fluid, Phys. Rev. Lett. 103 (2009) 025301 [arXiv:0903.4178].
I. Torre, A. Tomadin, A.K. Geim and M. Polini, Nonlocal transport and the hydrodynamic shear viscosity in graphene, Phys. Rev. B 92 (2015) 165433 [arXiv:1508.00363] [INSPIRE].
I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys. 8 (2005) 73 [hep-th/0404176] [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].
M. Baggioli and D.K. Brattan, Drag Phenomena from Holographic Massive Gravity, arXiv:1504.07635 [INSPIRE].
P. Kovtun, Fluctuation bounds on charge and heat diffusion, J. Phys. A 48 (2015) 265002 [arXiv:1407.0690] [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
A. Amoretti, A. Braggio, N. Magnoli and D. Musso, Bounds on charge and heat diffusivities in momentum dissipating holography, JHEP 07 (2015) 102 [arXiv:1411.6631] [INSPIRE].
S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Entropy production, viscosity bounds and bumpy black holes, JHEP 03 (2016) 170 [arXiv:1601.02757] [INSPIRE].
P. Burikham and N. Poovuttikul, Shear viscosity in holography and effective theory of transport without translational symmetry, arXiv:1601.04624 [INSPIRE].
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Alberte, L., Baggioli, M. & Pujolàs, O. Viscosity bound violation in holographic solids and the viscoelastic response. J. High Energ. Phys. 2016, 74 (2016). https://doi.org/10.1007/JHEP07(2016)074
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DOI: https://doi.org/10.1007/JHEP07(2016)074
Keywords
- Holography and condensed matter physics (AdS/CMT)
- Gauge-gravity correspondence
- Space-Time Symmetries