Running shear viscosities in anisotropic holographic superfluids

  • Jae-Hyuk Oh


We have examined holographic renormalization group (RG) flows of the shear viscosities in anisotropic holographic superfluids via their gravity duals, Einstein-SU(2) Yang-Mills system. In anisotropic phase, below the critical temperature Tc, the SO(3) isometry(spatial rotation) in the dual gravity system is broken down to the residual SO(2). The shear viscosities in the symmetry broken directions of the conformal fluids defined on AdS boundary present non-universal values which depend on the chemical potential μ and temperature T of the system and also satisfy non-trivial holographic RG-flow equations. The shear viscosities flow down to the specific values in IR region, in fact which are given by the ratios of the metric components in the symmetry unbroken directions to those in the broken directions, evaluated at the black brane horizon in the dual gravity system.


Gauge-gravity correspondence AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 


  1. [1]
    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].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    C. Herzog and D. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    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].ADSCrossRefGoogle Scholar
  4. [4]
    A. Buchel, On universality of stress-energy tensor correlation functions in supergravity, Phys. Lett. B 609 (2005) 392 [hep-th/0408095] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    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].ADSGoogle Scholar
  7. [7]
    A. Buchel, Shear viscosity of CFT plasma at finite coupling, Phys. Lett. B 665 (2008) 298 [arXiv:0804.3161] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Buchel, R.C. Myers and A. Sinha, Beyond ηs = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    A. Sinha and R.C. Myers, The viscosity bound in string theory, Nucl. Phys. A 830 (2009) 295C-298C [arXiv:0907.4798] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].MathSciNetADSGoogle Scholar
  12. [12]
    S.-J. Sin and Y. Zhou, Holographic Wilsonian RG flow and sliding membrane paradigm, JHEP 05 (2011) 030 [arXiv:1102.4477] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    Y. Matsuo, S.-J. Sin and Y. Zhou, Mixed RG flows and hydrodynamics at finite holographic screen, JHEP 01 (2012) 130 [arXiv:1109.2698] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Hard-gapped holographic superconductors, Phys. Lett. B 689 (2010) 45 [arXiv:0911.4999] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    M. Ammon, J. Erdmenger, V. Grass, P. Kerner and A. O’Bannon, On holographic p-wave superfluids with back-reaction, Phys. Lett. B 686 (2010) 192 [arXiv:0912.3515] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J. Erdmenger, P. Kerner and H. Zeller, Non-universal shear viscosity from Einstein gravity, Phys. Lett. B 699 (2011) 301 [arXiv:1011.5912] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    M. Natsuume and M. Ohta, The shear viscosity of holographic superfluids, Prog. Theor. Phys. 124 (2010) 931 [arXiv:1008.4142] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  19. [19]
    P. Basu and J.-H. Oh, Analytic approaches to an-isotropic holographic superfluids, arXiv:1109.4592 [INSPIRE].
  20. [20]
    R. Manvelyan, E. Radu and D. Tchrakian, New AdS non abelian black holes with superconducting horizons, Phys. Lett. B 677 (2009) 79 [arXiv:0812.3531] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    S.S. Gubser, Colorful horizons with charge in Anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    M.F. Paulos, Transport coefficients, membrane couplings and universality at extremality, JHEP 02 (2010) 067 [arXiv:0910.4602] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    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].ADSGoogle Scholar
  27. [27]
    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].ADSCrossRefGoogle Scholar
  28. [28]
    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].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    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].ADSGoogle Scholar
  30. [30]
    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].ADSGoogle Scholar
  31. [31]
    S. Cremonini, The shear viscosity to entropy ratio: a status report, Mod. Phys. Lett. B 25 (2011)1867 [arXiv:1108.0677] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    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].ADSCrossRefGoogle Scholar
  33. [33]
    S. Cremonini and P. Szepietowski, Generating temperature flow for η s with higher derivatives: from Lifshitz to AdS, JHEP 02 (2012) 038 [arXiv:1111.5623] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Harish-Chandra Research InstituteAllahabadIndia

Personalised recommendations