Skip to main content
SpringerLink
Log in

Running shear viscosities in anisotropic holographic superfluids

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

Abstract

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.

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. 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 

  2. C. Herzog and D. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  7. A. Buchel, Shear viscosity of CFT plasma at finite coupling, Phys. Lett. B 665 (2008) 298 [arXiv:0804.3161] [INSPIRE].

    Article  ADS  Google Scholar 

  8. A. Buchel, R.C. Myers and A. Sinha, Beyond ηs = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [INSPIRE].

    Article  ADS  Google Scholar 

  9. A. Sinha and R.C. Myers, The viscosity bound in string theory, Nucl. Phys. A 830 (2009) 295C-298C [arXiv:0907.4798] [INSPIRE].

    Article  ADS  Google Scholar 

  10. I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    MathSciNet  ADS  Google Scholar 

  12. S.-J. Sin and Y. Zhou, Holographic Wilsonian RG flow and sliding membrane paradigm, JHEP 05 (2011) 030 [arXiv:1102.4477] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  14. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  18. M. Natsuume and M. Ohta, The shear viscosity of holographic superfluids, Prog. Theor. Phys. 124 (2010) 931 [arXiv:1008.4142] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  19. P. Basu and J.-H. Oh, Analytic approaches to an-isotropic holographic superfluids, arXiv:1109.4592 [INSPIRE].

  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].

    Article  MathSciNet  ADS  Google Scholar 

  21. S.S. Gubser, Colorful horizons with charge in Anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  24. R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  31. S. Cremonini, The shear viscosity to entropy ratio: a status report, Mod. Phys. Lett. B 25 (2011)1867 [arXiv:1108.0677] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India

    Jae-Hyuk Oh

Authors
  1. Jae-Hyuk Oh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jae-Hyuk Oh.

Additional information

ArXiv ePrint: 1201.5605

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oh, JH. Running shear viscosities in anisotropic holographic superfluids. J. High Energ. Phys. 2012, 103 (2012). https://doi.org/10.1007/JHEP06(2012)103

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)103

Keywords

Search

Navigation