Journal of High Energy Physics

, 2011:95 | Cite as

Holographic bulk viscosity: GPR vs EO

  • Alex Buchel
  • Umut GürsoyEmail author
  • Elias Kiritsis
Open Access


Recently Eling and Oz (EO) proposed a formula for the holographic bulk viscosity, in arXiv:1103.1657, derived from the null horizon focusing equation. This formula seems different from that obtained earlier by Gubser, Pufu and Rocha (GPR) in arXiv:0806.0407 calculated from the IR limit of the two-point function of the trace of the stress tensor. The two were shown to agree only for some simple scaling cases. We point out that the two formulae agree in two non-trivial holographic theories describing RG flows. The first is the strongly coupled \( \mathcal{N} = {2^*} \) gauge theory plasma. The second is the semi-phenomenological model of Improved Holographic QCD.


Gauge-gravity correspondence Duality in Gauge Field Theories AdS-CFT Correspondence 


  1. [1]
    P. Benincasa, A. Buchel and A.O. Starinets, Sound waves in strongly coupled non-conformal gauge theory plasma, Nucl. Phys. B 733 (2006) 160 [hep-th/0507026] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  2. [2]
    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] [SPIRES].zbMATHADSMathSciNetGoogle Scholar
  3. [3]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    A. Buchel, Bulk viscosity of gauge theory plasma at strong coupling, Phys. Lett. B 663 (2008) 286 [arXiv:0708.3459] [SPIRES].ADSGoogle Scholar
  5. [5]
    A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    A. Buchel, On universality of stress-energy tensor correlation functions in supergravity, Phys. Lett. B 609 (2005) 392 [hep-th/0408095] [SPIRES].ADSMathSciNetGoogle Scholar
  8. [8]
    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] [SPIRES].ADSGoogle Scholar
  9. [9]
    S.S. Gubser, S.S. Pufu and F.D. Rocha, Bulk viscosity of strongly coupled plasmas with holographic duals, JHEP 08 (2008) 085 [arXiv:0806.0407] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    C. Eling and Y. Oz, A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation, JHEP 06 (2011) 007 [arXiv:1103.1657] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [SPIRES].CrossRefGoogle Scholar
  13. [13]
    U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [SPIRES].CrossRefGoogle Scholar
  14. [14]
    U. Gürsoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis and F. Nitti, Improved Holographic QCD, Lect. Notes Phys. 828 (2011) 79 [arXiv:1006.5461] [SPIRES].CrossRefGoogle Scholar
  15. [15]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Deconfinement and Gluon Plasma Dynamics in Improved Holographic QCD, Phys. Rev. Lett. 101 (2008) 181601 [arXiv:0804.0899] [SPIRES].CrossRefADSGoogle Scholar
  16. [16]
    A. Buchel, A.W. Peet and J. Polchinski, Gauge dual and noncommutative extension of an N = 2 supergravity solution, Phys. Rev. D 63 (2001) 044009 [hep-th/0008076] [SPIRES].ADSMathSciNetGoogle Scholar
  17. [17]
    N.J. Evans, C.V. Johnson and M. Petrini, The enhancon and N = 2 gauge theory/gravity RG flows, JHEP 10 (2000) 022 [hep-th/008081] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    A. Buchel and J.T. Liu, Thermodynamics of the N = 2* flow, JHEP 11 (2003) 031 [hep-th/0305064] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  19. [19]
    A. Buchel, N = 2* hydrodynamics, Nucl. Phys. B 708 (2005) 451 [hep-th/0406200] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  20. [20]
    A. Buchel, S. Deakin, P. Kerner and J.T. Liu, Thermodynamics of the N = 2* strongly coupled plasma, Nucl. Phys. B 784 (2007) 72 [hep-th/0701142] [SPIRES].CrossRefADSGoogle Scholar
  21. [21]
    A. Yarom, Notes on the bulk viscosity of holographic gauge theory plasmas, JHEP 04 (2010) 024 [arXiv:0912.2100] [SPIRES].CrossRefADSGoogle Scholar
  22. [22]
    S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [SPIRES].ADSGoogle Scholar
  23. [23]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and Thermodynamics of 5D Dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [SPIRES].CrossRefGoogle Scholar
  24. [24]
    S.S. Gubser, Curvature singularities: The good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [SPIRES].zbMATHMathSciNetGoogle Scholar
  25. [25]
    U. Gürsoy, Continuous Hawking-Page transitions in Einstein-scalar gravity, JHEP 01 (2011) 086 [arXiv:1007.0500] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    A. Buchel, On Eling-Oz formula for the holographic bulk viscosity, JHEP 05 (2011) 065 [arXiv:1103.3733] [SPIRES].CrossRefADSGoogle Scholar
  28. [28]
    O. Aharony, A. Buchel and P. Kerner, The black hole in the throat — thermodynamics of strongly coupled cascading gauge theories, Phys. Rev. D 76 (2007) 086005 [arXiv:0706.1768] [SPIRES].ADSMathSciNetGoogle Scholar
  29. [29]
    A. Buchel and C. Pagnutti, Transport at criticality, Nucl. Phys. B 834 (2010) 222 [arXiv:0912.3212] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  30. [30]
    A. Buchel and C. Pagnutti, Critical phenomena in N = 2* plasma, Phys. Rev. D 83 (2011) 046004 [arXiv:1010.3359] [SPIRES].ADSGoogle Scholar
  31. [31]
    U. Gürsoy, E. Kiritsis, G. Michalogiorgakis and F. Nitti, Thermal Transport and Drag Force in Improved Holographic QCD, JHEP 12 (2009) 056 [arXiv:0906.1890] [SPIRES].CrossRefGoogle Scholar
  32. [32]
    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] [SPIRES].ADSGoogle Scholar
  33. [33]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Improved Holographic Yang-Mills at Finite Temperature: Comparison with Data, Nucl. Phys. B 820 (2009) 148 [arXiv:0903.2859] [SPIRES].CrossRefADSGoogle Scholar
  34. [34]
    H.A. Chamblin and H.S. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225] [SPIRES].CrossRefADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Theory Group, Physics DepartmentCERNGeneva 23Switzerland
  4. 4.Crete Center for Theoretical Physics, Department of PhysicsUniversity of CreteHeraklionGreece
  5. 5.Laboratoire APCUniversité Paris-Diderot Paris 7, CNRS UMR 7164Paris Cedex 13France

Personalised recommendations