Skip to main content
SpringerLink
Log in

Zero-viscosity limit in a holographic Gauss-Bonnet liquid

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

In recent papers, it was hypothesized that there exist dissipationless quantum liquids, i.e., liquids with zero or vanishingly small viscosity and zero entropy production, which nevertheless have nontrivial second-order transport coefficients. A natural candidate for a dissipationless liquid is the hypothetical conformal quantum liquid, whose holographically dual description in the infrared limit is given by the five-dimensional Gauss-Bonnet gravity. It is known that shear viscosity in that theory can be made arbitrarily small as the Gauss-Bonnet coupling parameter approaches a critical value. We evaluate the transport coefficients of a Gauss-Bonnet liquid (nonperturbatively in the coupling parameter; three of the six coefficients were previously unknown) and consider the zero-viscosity limit. We show that three of the five second-order coefficients are nonzero in this limit, but they do not satisfy the criterion of zero entropy production. Hence, the holographic Gauss-Bonnet liquid is not a dissipationless quantum liquid.

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. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, “Gauge/string duality, hot QCD, and heavy ion collisions,” arXiv:1101.0618v2 [hep-th] (2011).

    Google Scholar 

  2. D. T. Son and A. O. Starinets, Ann. Rev. Nucl. Part. Sci., 57, 95–118 (2007); arXiv:0704.0240v2 [hep-th] (2007).

    Article  ADS  Google Scholar 

  3. R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, and M. A. Stephanov, JHEP, 0804, 100 (2008); arXiv: 0712.2451v3 [hep-th] (2007).

    Article  ADS  MathSciNet  Google Scholar 

  4. M. Rangamani, Class. Q. Grav., 26, 224003 (2009); arXiv:0905.4352v3 [hep-th] (2009).

    Article  ADS  MathSciNet  Google Scholar 

  5. P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett., 94, 111601 (2005); arXiv:hep-th/0405231v2 (2004).

    Article  ADS  Google Scholar 

  6. A. Buchel, Phys. Lett. B, 609, 392–401 (2005); arXiv:hep-th/0408095v2 (2004).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. P. Kovtun, D. T. Son, and A. O. Starinets, JHEP, 0310, 064 (2003); arXiv:hep-th/0309213v1 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Buchel and J. T. Liu, Phys. Rev. Lett., 93, 090602 (2004); arXiv:hep-th/0311175v1 (2003).

    Article  ADS  Google Scholar 

  9. A. O. Starinets, Phys. Lett. B, 670, 442–445 (2009); arXiv:0806.3797v1 [hep-th] (2008).

    Article  ADS  MathSciNet  Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 6, Fluid Mechanics, Nauka, Moscow (1986); English transl., Pergamon, Oxford (1987).

    Google Scholar 

  11. P. Romatschke, Internat. J. Mod. Phys. E, 19, 1–53 (2010); arXiv:0902.3663v3 [hep-ph] (2009).

    Article  ADS  Google Scholar 

  12. G. Policastro, D. T. Son, and A. O. Starinets, Phys. Rev. Lett., 87, 081601 (2001); arXiv:hep-th/0104066v2 (2001).

    Article  ADS  Google Scholar 

  13. A. Buchel, J. T. Liu, and A. O. Starinets, Nucl. Phys. B, 707, 56–68 (2005); arXiv:hep-th/0406264v3 (2004).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. A. Buchel, Nucl. Phys. B, 803, 166–170 (2008); arXiv:0805.2683v1 [hep-th] (2008).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. S. Bhattacharyya, V. E. Hubeny, S. Minwalla, and M. Rangamani, JHEP, 0802, 045 (2008); arXiv:0712.2456v4 [hep-th] (2007).

    Article  ADS  Google Scholar 

  16. P. Benincasa and A. Buchel, JHEP, 0601, 103 (2006); arXiv:hep-th/0510041v1 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  17. A. Buchel, Nucl. Phys. B, 802, 281–306 (2008); arXiv:0801.4421v2 [hep-th] (2008).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. A. Buchel and M. Paulos, Nucl. Phys. B, 805, 59–71 (2008); arXiv:0806.0788v1 [hep-th] (2008).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. A. Buchel and M. Paulos, Nucl. Phys. B, 810, 40–65 (2009); arXiv:0808.1601v2 [hep-th] (2008).

    Article  ADS  MATH  Google Scholar 

  20. O. Saremi and K. A. Sohrabi, JHEP, 1111, 147 (2011); arXiv:1105.4870v2 [hep-th] (2011).

    Article  ADS  MathSciNet  Google Scholar 

  21. S. Grozdanov and A. Starinets, “Second-order transport coefficients and dissipationless liquids,” (to appear).

  22. S. C. Huot, S. Jeon, and G. D. Moore, Phys. Rev. Lett., 98, 172303 (2007); arXiv:hep-ph/0608062v2 (2006).

    Article  ADS  Google Scholar 

  23. Y. Kats and P. Petrov, JHEP, 0901, 044 (2009); arXiv:0712.0743v4 [hep-th] (2007).

    Article  ADS  MathSciNet  Google Scholar 

  24. M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, Phys. Rev. D, 77, 126006 (2008); arXiv:0712.0805v3 [hep-th] (2007).

    Article  ADS  Google Scholar 

  25. M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, Phys. Rev. Lett., 100, 191601 (2008); arXiv: 0802.3318v2 [hep-th] (2008).

    Article  ADS  Google Scholar 

  26. A. Buchel and S. Cremonini, JHEP, 1010, 026 (2010); arXiv:1007.2963v2 [hep-th] (2010).

    Article  ADS  Google Scholar 

  27. N. Banerjee and S. Dutta, “Holographic hydrodynamics: Models and methods,” arXiv:1112.5345v1 [hep-th] (2011).

    Google Scholar 

  28. A. Buchel and R. C. Myers, JHEP, 0908, 016 (2009); arXiv:0906.2922v3 [hep-th] (2009).

    Article  ADS  MathSciNet  Google Scholar 

  29. E. Shaverin and A. Yarom, JHEP, 1304, 013 (2013); arXiv:1211.1979v1 [hep-th] (2012).

    Article  ADS  MathSciNet  Google Scholar 

  30. J. Bhattacharya, S. Bhattacharyya, and M. Rangamani, JHEP, 1302, 153 (2013); arXiv:1211.1020v3 [hep-th] (2012).

    Article  ADS  MathSciNet  Google Scholar 

  31. A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, and M. Smolkin, JHEP, 1003, 111 (2010); arXiv: 0911.4257v2 [hep-th] (2009).

    Article  ADS  Google Scholar 

  32. D. T. Son and A. O. Starinets, JHEP, 0209, 042 (2002); arXiv:hep-th/0205051v2 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  33. G. Policastro, D. T. Son, and A. O. Starinets, JHEP, 0209, 043 (2002); arXiv:hep-th/0205052v2 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  34. P. K. Kovtun and A. O. Starinets, Phys. Rev. D, 72, 086009 (2005); arXiv:hep-th/0506184v2 (2005).

    Article  ADS  Google Scholar 

  35. N. Iqbal and H. Liu, Phys. Rev. D, 79, 025023 (2009); arXiv:0809.3808v2 [hep-th] (2008).

    Article  ADS  Google Scholar 

  36. G. D. Moore and K. A. Sohrabi, Phys. Rev. Lett., 106, 122302 (2011); arXiv:1007.5333v3 [hep-ph] (2010).

    Article  ADS  Google Scholar 

  37. J. S. Schwinger, J. Math. Phys., 2, 407–432 (1961).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  38. L. V. Keldysh, Soviet Phys. JETP, 20, 1018–1026 (1965).

    MathSciNet  Google Scholar 

  39. E. Wang and U. W. Heinz, Phys. Rev. D, 66, 025008 (2002); arXiv:hep-th/9809016v1 (1998).

    Article  ADS  Google Scholar 

  40. V. Balasubramanian and P. Kraus, Commun. Math. Phys., 208, 413–428 (1999); arXiv:hep-th/9902121v5 (1999).

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK

    S. Grozdanov & A. O. Starinets

Authors
  1. S. Grozdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. O. Starinets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. O. Starinets.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 182, No. 1, pp. 76–90, January, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grozdanov, S., Starinets, A.O. Zero-viscosity limit in a holographic Gauss-Bonnet liquid. Theor Math Phys 182, 61–73 (2015). https://doi.org/10.1007/s11232-015-0245-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-015-0245-7

Keywords

Search

Navigation