Skip to main content
SpringerLink
Log in

Transport in anisotropic superfluids: a holographic description

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

Abstract

We study transport phenomena in p-wave superfluids in the context of gauge/gravity duality. Due to the spacetime anisotropy of this system, the tensorial structure of the transport coefficients is non-trivial in contrast to the isotropic case. In particular, there is an additional shear mode which leads to a non-universal value of the shear viscosity even in an Einstein gravity setup. In this paper, we present a complete study of the helicity two and helicity one fluctuation modes. In addition to the non-universal shear viscosity, we also investigate the thermoelectric effect, i.e. the mixing of electric and heat current. Moreover, we also find an additional effect due to the anisotropy, the so-called flexoelectric effect.

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. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. G. Lifschytz and M. Lippert, Anomalous conductivity in holographic QCD, Phys. Rev. D 80 (2009) 066005 [arXiv:0904.4772] [INSPIRE].

    ADS  Google Scholar 

  5. A. Gynther, K. Landsteiner, F. Pena-Benitez and A. Rebhan, Holographic Anomalous Conductivities and the Chiral Magnetic Effect, JHEP 02 (2011) 110 [arXiv:1005.2587] [INSPIRE].

    Article  ADS  Google Scholar 

  6. T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].

    Article  ADS  Google Scholar 

  7. C. Hoyos, T. Nishioka and A. O’Bannon, A Chiral Magnetic Effect from AdS/CFT with Flavor, JHEP 10 (2011) 084 [arXiv:1106.4030] [INSPIRE].

    Article  ADS  Google Scholar 

  8. D. Mateos and D. Trancanelli, Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].

    Article  ADS  Google Scholar 

  9. A. Rebhan and D. Steineder, Electromagnetic signatures of a strongly coupled anisotropic plasma, JHEP 08 (2011) 153 [arXiv:1106.3539] [INSPIRE].

    Article  ADS  Google Scholar 

  10. C.P. Herzog, N. Lisker, P. Surowka and A. Yarom, Transport in holographic superfluids, JHEP 08 (2011) 052 [arXiv:1101.3330] [INSPIRE].

    Article  ADS  Google Scholar 

  11. J. Bhattacharya, S. Bhattacharyya and S. Minwalla, Dissipative Superfluid dynamics from gravity, JHEP 04 (2011) 125 [arXiv:1101.3332] [INSPIRE].

    Article  ADS  Google Scholar 

  12. J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, arXiv:1105.3733 [INSPIRE].

  13. L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics. Vol. 7: Theory of Elasticity, Pergamon Press, Oxford U.K. (1959), pg. 134.

    Google Scholar 

  14. P. de Gennes, The Physics of Liquid Crystals, Oxford University Press, Oxford U.K. (1974).

    Google Scholar 

  15. S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].

    ADS  Google Scholar 

  16. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].

    Article  ADS  Google Scholar 

  17. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. 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 

  19. M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Superconductivity from gauge/gravity duality with flavor, Phys. Lett. B 680 (2009) 516 [arXiv:0810.2316] [INSPIRE].

    ADS  Google Scholar 

  20. P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Superconductivity from D3/D7: Holographic Pion Superfluid, JHEP 11 (2009) 070 [arXiv:0810.3970] [INSPIRE].

    Article  ADS  Google Scholar 

  21. M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Flavor Superconductivity from Gauge/Gravity Duality, JHEP 10 (2009) 067 [arXiv:0903.1864] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. 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].

    ADS  Google Scholar 

  23. 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 

  24. A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].

    Article  ADS  Google Scholar 

  25. 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 

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

    Article  ADS  Google Scholar 

  27. S. Cremonini, The Shear Viscosity to Entropy Ratio: A Status Report, Mod. Phys. Lett. B 25 (2011) 1867 [arXiv:1108.0677] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. J. Erdmenger, P. Kerner and H. Zeller, Non-universal shear viscosity from Einstein gravity, Phys. Lett. B 699 (2011) 301 [arXiv:1011.5912] [INSPIRE].

    ADS  Google Scholar 

  29. 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 

  30. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. 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].

    Article  ADS  MATH  Google Scholar 

  34. P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Hard-gapped Holographic Superconductors, Phys. Lett. B 689 (2010) 45 [arXiv:0911.4999] [INSPIRE].

    ADS  Google Scholar 

  35. S.S. Gubser, F.D. Rocha and A. Yarom, Fermion correlators in non-abelian holographic superconductors, JHEP 11 (2010) 085 [arXiv:1002.4416] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. 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 

  37. C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].

    Google Scholar 

  38. R.C. Myers, A.O. Starinets and R.M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, JHEP 11 (2007) 091 [arXiv:0706.0162] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Buchel and R.C. Myers, Causality of Holographic Hydrodynamics, JHEP 08 (2009) 016 [arXiv:0906.2922] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. P. Basu and J.-H. Oh, Analytic Approaches to An-Isotropic Holographic Superfluids, arXiv:1109.4592 [INSPIRE].

  41. J. Erdmenger, M. Kaminski, P. Kerner and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP 11 (2008) 031 [arXiv:0807.2663] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. S. Barisch, M. Haack, S. Nampuri and G. Policastro, to appear.

  43. F.M. Leslie, Some Constitutive Equations For Anisotropic Fluids, Quart. J. Mech. Appl. Math. 19 (1966) 357.

    Article  MathSciNet  MATH  Google Scholar 

  44. K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  45. B. Sahoo and H.-U. Yee, Electrified plasma in AdS/CFT correspondence, JHEP 11 (2010) 095 [arXiv:1004.3541] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. D. Son and M.A. Stephanov, QCD at finite isospin density, Phys. Rev. Lett. 86 (2001) 592 [hep-ph/0005225] [INSPIRE].

    Article  ADS  Google Scholar 

  47. 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 

  48. 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 

  49. L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics. Vol. 6: Fluid Mechanics, Pergamon Press, Oxford U.K. (1959), pg. 134.

    Google Scholar 

  50. C. Pujol and D. Davesne, Relativistic dissipative hydrodynamics with spontaneous symmetry breaking, Phys. Rev. C 67 (2003) 014901 [hep-ph/0204355] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805, München, Germany

    Johanna Erdmenger, Patrick Kerner & Hansjörg Zeller

Authors
  1. Johanna Erdmenger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick Kerner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hansjörg Zeller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hansjörg Zeller.

Additional information

ArXiv ePrint: 1110.0007

Rights and permissions

Reprints and permissions

About this article

Cite this article

Erdmenger, J., Kerner, P. & Zeller, H. Transport in anisotropic superfluids: a holographic description. J. High Energ. Phys. 2012, 59 (2012). https://doi.org/10.1007/JHEP01(2012)059

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2012)059

Keywords

Search

Navigation