Skip to main content
SpringerLink
Log in

Hydrodynamics of cold holographic matter

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We show that at any temperature, the low-energy (with respect to the chemical potential) collective excitations of the transverse components of the energy-momentum tensor and the global U(1) current in the field theory dual to the planar RN-AdS4 black hole are simply those of hydrodynamics. That is, hydrodynamics is applicable even at energy scales much greater than the temperature. It is applicable even at zero temperature. Specifically, we find that there is always a diffusion mode with diffusion constant proportional to the ratio of entropy density to energy density. At low temperatures, the leading order momentum and temperature dependences of the dispersion relation of this mode are controlled by the dimension of an operator in the thermal CFT1 dual to the near-horizon Schwarzschild-AdS2 geometry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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].

    MathSciNet  ADS  MATH  Google Scholar 

  2. 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].

    MathSciNet  ADS  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  4. 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].

    Article  ADS  Google Scholar 

  5. 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].

  6. V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, arXiv:1107.5780 [INSPIRE].

  7. L. Landau and E. Lifshitz, Course of theoretical physics volume 6: Fluid mechanics, second edition, Butterworth-Heinemann, (1987).

  8. P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  9. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. 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].

    Article  MathSciNet  ADS  Google Scholar 

  11. C.P. Herzog, The Hydrodynamics of M-theory, JHEP 12 (2002) 026 [hep-th/0210126] [INSPIRE].

    Article  ADS  Google Scholar 

  12. C.P. Herzog, The Sound of M-theory, Phys. Rev. D 68 (2003) 024013 [hep-th/0302086] [INSPIRE].

    ADS  Google Scholar 

  13. 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].

    Article  ADS  Google Scholar 

  14. P. Kovtun, D. Son and A. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].

    Article  ADS  Google Scholar 

  15. A. Buchel, On universality of stress-energy tensor correlation functions in supergravity, Phys. Lett. B 609 (2005) 392 [hep-th/0408095] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  16. 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].

    ADS  Google Scholar 

  17. S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].

    Article  ADS  Google Scholar 

  18. N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].

    Article  ADS  Google Scholar 

  19. M. Rangamani, Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. S. Bhattacharyya, S. Lahiri, R. Loganayagam and S. Minwalla, Large rotating AdS black holes from fluid mechanics, JHEP 09 (2008) 054 [arXiv:0708.1770] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. A. Abrikosov and I. Khalatnikov, The theory of a Fermi liquid (the properties of 3 He at low temperatures), Rept. Prog. Phys. 22 (1959) 329.

    Article  ADS  Google Scholar 

  22. C. Pethick, Attenuation of zero sound in a normal Fermi liquid, Phys. Rev. 185 (1969) 384.

    Article  ADS  Google Scholar 

  23. D. Pines and P. Nozières, The theory of quantum liquids, W.A. Benjamin, New York U.S.A. (1966).

  24. G. Baym and C. Pethick, Landau Fermi-liquid theory, Wiley-VCH, New York U.S.A. (2004).

    Google Scholar 

  25. A. Karch, D. Son and A. Starinets, Zero Sound from Holography, arXiv:0806.3796 [INSPIRE].

  26. M. Kulaxizi and A. Parnachev, Comments on Fermi Liquid from Holography, Phys. Rev. D 78 (2008) 086004 [arXiv:0808.3953] [INSPIRE].

    ADS  Google Scholar 

  27. M. Kulaxizi and A. Parnachev, Holographic Responses of Fermion Matter, Nucl. Phys. B 815 (2009) 125 [arXiv:0811.2262] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. L.-Y. Hung and A. Sinha, Holographic quantum liquids in 1+1 dimensions, JHEP 01 (2010) 114 [arXiv:0909.3526] [INSPIRE].

    Article  ADS  Google Scholar 

  29. C. Hoyos-Badajoz, A. O’Bannon and J.M. Wu, Zero Sound in Strange Metallic Holography, JHEP 09 (2010) 086 [arXiv:1007.0590] [INSPIRE].

    Article  ADS  Google Scholar 

  30. B.-H. Lee, D.-W. Pang and C. Park, Zero Sound in Effective Holographic Theories, JHEP 11 (2010) 120 [arXiv:1009.3966] [INSPIRE].

    Article  ADS  Google Scholar 

  31. O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].

    Article  ADS  Google Scholar 

  32. M. Ammon et al., On Stability and Transport of Cold Holographic Matter, JHEP 09 (2011) 030 [arXiv:1108.1798] [INSPIRE].

    Article  ADS  Google Scholar 

  33. R.A. Davison and A.O. Starinets, Holographic zero sound at finite temperature, Phys. Rev. D 85 (2012) 026004 [arXiv:1109.6343] [INSPIRE].

    ADS  Google Scholar 

  34. M. Goykhman, A. Parnachev and J. Zaanen, Fluctuations in finite density holographic quantum liquids, JHEP 10 (2012) 045 [arXiv:1204.6232] [INSPIRE].

    Article  ADS  Google Scholar 

  35. D.K. Brattan, R.A. Davison, S.A. Gentle and A. O’Bannon, Collective Excitations of Holographic Quantum Liquids in a Magnetic Field, JHEP 11 (2012) 084 [arXiv:1209.0009] [INSPIRE].

    Article  ADS  Google Scholar 

  36. N. Jokela, M. Jarvinen and M. Lippert, Fluctuations and instabilities of a holographic metal, JHEP 02 (2013) 007 [arXiv:1211.1381] [INSPIRE].

    Article  ADS  Google Scholar 

  37. M. Edalati, J.I. Jottar and R.G. Leigh, Shear Modes, Criticality and Extremal Black Holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Edalati, J.I. Jottar and R.G. Leigh, Holography and the sound of criticality, JHEP 10 (2010) 058 [arXiv:1005.4075] [INSPIRE].

    Article  ADS  Google Scholar 

  39. D.K. Brattan and S.A. Gentle, Shear channel correlators from hot charged black holes, JHEP 04 (2011) 082 [arXiv:1012.1280] [INSPIRE].

    Article  ADS  Google Scholar 

  40. R.A. Davison and N.K. Kaplis, Bosonic excitations of the AdS 4 Reissner-Nordstrom black hole, JHEP 12 (2011) 037 [arXiv:1111.0660] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. T. Faulkner and N. Iqbal, Friedel oscillations and horizon charge in 1D holographic liquids, arXiv:1207.4208 [INSPIRE].

  42. M. Edalati, J.I. Jottar and R.G. Leigh, Transport Coefficients at Zero Temperature from Extremal Black Holes, JHEP 01 (2010) 018 [arXiv:0910.0645] [INSPIRE].

    Article  ADS  Google Scholar 

  43. E. Imeroni and A. Sinha, Non-relativistic metrics with extremal limits, JHEP 09 (2009) 096 [arXiv:0907.1892] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. M.F. Paulos, Transport coefficients, membrane couplings and universality at extremality, JHEP 02 (2010) 067 [arXiv:0910.4602] [INSPIRE].

    Article  ADS  Google Scholar 

  45. R.-G. Cai, Y. Liu and Y.-W. Sun, Transport Coefficients from Extremal Gauss-Bonnet Black Holes, JHEP 04 (2010) 090 [arXiv:0910.4705] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. S.K. Chakrabarti, S. Jain and S. Mukherji, Viscosity to entropy ratio at extremality, JHEP 01 (2010) 068 [arXiv:0910.5132] [INSPIRE].

    Article  ADS  Google Scholar 

  47. O. Saremi, The viscosity bound conjecture and hydrodynamics of M2-brane theory at finite chemical potential, JHEP 10 (2006) 083 [hep-th/0601159] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. X.-H. Ge, K. Jo and S.-J. Sin, Hydrodynamics of RN AdS 4 black hole and Holographic Optics, JHEP 03 (2011) 104 [arXiv:1012.2515] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].

    ADS  Google Scholar 

  50. T. Faulkner and J. Polchinski, Semi-Holographic Fermi Liquids, JHEP 06 (2011) 012 [arXiv:1001.5049] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].

    Article  ADS  Google Scholar 

  52. J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  53. A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  54. M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].

    Article  ADS  Google Scholar 

  55. F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  56. J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. A. Donos and J.P. Gauntlett, Superfluid black branes in AdS 4 × S 7, JHEP 06 (2011) 053 [arXiv:1104.4478] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. R. Wald, General Relativity, The University of Chicago Press, Chicago U.S.A. (1984).

    Book  MATH  Google Scholar 

  60. P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].

    ADS  Google Scholar 

  61. 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].

    Article  MathSciNet  ADS  Google Scholar 

  62. M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [INSPIRE].

    Article  ADS  Google Scholar 

  63. H. Kodama and A. Ishibashi, Master equations for perturbations of generalized static black holes with charge in higher dimensions, Prog. Theor. Phys. 111 (2004) 29 [hep-th/0308128] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  64. R.A. Davison and A. Parnachev, work in progress.

  65. E.W. Leaver, Quasinormal modes of Reissner-Nordstrom black holes, Phys. Rev. D 41 (1990) 2986 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  66. F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, Phys. Rev. D 80 (2009) 126016 [arXiv:0908.1788] [INSPIRE].

    ADS  Google Scholar 

  67. S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS 5, Phys. Rev. D 81 (2010) 046001 [arXiv:0911.2898] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  68. S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].

Download references

Author information

Authors and Affiliations

  1. Instituut-Lorentz for Theoretical Physics, Niels Bohrweg 2, Leiden, NL-2333 CA, The Netherlands

    Richard A. Davison & Andrei Parnachev

Authors
  1. Richard A. Davison
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrei Parnachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard A. Davison.

Additional information

ArXiv ePrint: 1303.6334

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davison, R.A., Parnachev, A. Hydrodynamics of cold holographic matter. J. High Energ. Phys. 2013, 100 (2013). https://doi.org/10.1007/JHEP06(2013)100

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2013)100

Keywords

Search

Navigation