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Holographic GB gravity in arbitrary dimensions

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Abstract

We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general D(≥ 5) dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.

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References

  1. 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].

    MATH  ADS  MathSciNet  Google Scholar 

  2. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  3. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  4. R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  5. S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].

    Article  ADS  Google Scholar 

  6. D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [SPIRES].

    Article  ADS  Google Scholar 

  7. 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].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. A. Buchel, J.T. Liu and A.O. Starinets, Coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 707 (2005) 56 [hep-th/0406264] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  11. 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].

    ADS  Google Scholar 

  12. D. Mateos, R.C. Myers and R.M. Thomson, Holographic viscosity of fundamental matter, Phys. Rev. Lett. 98 (2007) 101601 [hep-th/0610184] [SPIRES].

    Article  ADS  Google Scholar 

  13. K. Landsteiner and J. Mas, The shear viscosity of the non-commutative plasma, JHEP 07 (2007) 088 [arXiv:0706.0411] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  14. R.C. Myers, M.F. Paulos and A. Sinha, Quantum corrections to η/s, Phys. Rev. D 79 (2009) 041901 [arXiv:0806.2156] [SPIRES].

    ADS  Google Scholar 

  15. 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].

    ADS  Google Scholar 

  16. E. Imeroni and A. Sinha, Non-relativistic metrics with extremal limits, JHEP 09 (2009) 096 [arXiv:0907.1892] [SPIRES].

    Article  ADS  Google Scholar 

  17. M. Edalati, J.I. Jottar and R.G. Leigh, Transport Coefficients at Zero Temperature from Extremal Black Holes, JHEP 01 (2010) 018 [arXiv:0910.0645] [SPIRES].

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. S.K. Chakrabarti, S. Jain and S. Mukherji, Viscosity to entropy ratio at extremality, JHEP 01 (2010) 068 [arXiv:0910.5132] [SPIRES].

    Article  Google Scholar 

  20. R.G. Cai, Y. Liu and Y.W. Sun, Transport Coefficients from Extremal Gauss-Bonnet Black Holes, arXiv:0910.4705 [SPIRES].

  21. D. Teaney, Effect of shear viscosity on spectra, elliptic flow and Hanbury Brown-Twiss radii, Phys. Rev. C 68 (2003) 034913 [nucl-th/0301099] [SPIRES].

    ADS  Google Scholar 

  22. PHENIX collaboration, A. Adare et al., Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at \( \sqrt ( {s_N}N) = 200\;GeV \), Phys. Rev. Lett. 98 (2007) 172301 [nucl-ex/0611018] [SPIRES].

    Article  ADS  Google Scholar 

  23. M. Luzum and P. Romatschke, Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at \( \sqrt ( {s_N}N) = 200\;GeV \), Phys. Rev. C 78 (2008) 034915 [arXiv:0804.4015] [SPIRES].

    ADS  Google Scholar 

  24. 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] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. A. Sinha and R.C. Myers, The viscosity bound in string theory, Nucl. Phys. A 830 (2009) 295c–298c [arXiv:0907.4798] [SPIRES].

    ADS  Google Scholar 

  27. R.C. Myers, M.F. Paulos and A. Sinha, Holographic Hydrodynamics with a Chemical Potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [SPIRES].

    Article  ADS  Google Scholar 

  28. 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] [SPIRES].

    ADS  Google Scholar 

  29. 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] [SPIRES].

    Article  ADS  Google Scholar 

  30. X.H. Ge and S.J. Sin, Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant, JHEP 05 (2009) 051 [arXiv:0903.2527] [SPIRES].

    Article  ADS  Google Scholar 

  31. R.G. Cai, Z.Y. Nie and Y.W. Sun, Shear Viscosity from Effective Couplings of Gravitons, Phys. Rev. D 78 (2008) 126007 [arXiv:0811.1665] [SPIRES].

    ADS  Google Scholar 

  32. 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] [SPIRES].

    ADS  Google Scholar 

  33. J. de Boer, M. Kulaxizi and A. Parnachev, AdS 7/CFT 6 , Gauss-Bonnet Gravity and Viscosity Bound, arXiv:0910.5347 [SPIRES].

  34. D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [SPIRES].

    Article  ADS  Google Scholar 

  35. X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, arXiv:0911.3160 [SPIRES].

  36. R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [SPIRES].

    ADS  Google Scholar 

  37. D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656 [SPIRES].

    Article  ADS  Google Scholar 

  38. R.C. Myers and B. Robinson, Black Holes in Quasi-topological Gravity, in preparation.

  39. M.J. Duff, Observations on Conformal Anomalies, Nucl. Phys. B 125 (1977) 334 [SPIRES].

    Article  ADS  Google Scholar 

  40. M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  41. M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  42. R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, in preparation.

  43. J. Erdmenger and H. Osborn, Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  44. H. Osborn and A.C. Petkou, Implications of Conformal Invariance in Field Theories for General Dimensions, Ann. Phys. 231 (1994) 311 [hep-th/9307010] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  45. G. Arutyunov and S. Frolov, Three-point Green function of the stress-energy tensor in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 026004 [hep-th/9901121] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  46. H. Liu and A.A. Tseytlin, D = 4 super Yang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity, Nucl. Phys. B 533 (1998) 88 [hep-th/9804083] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  47. D.M. Hofman, Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [SPIRES].

    ADS  Google Scholar 

  50. 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] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  51. X.H. Ge, Y. Matsuo, F.W. Shu, S.J. Sin and T. Tsukioka, Viscosity Bound, Causality Violation and Instability with Stringy Correction and Charge, JHEP 10 (2008) 009 [arXiv:0808.2354] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  52. P. Romatschke, New Developments in Relativistic Viscous Hydrodynamics, Int. J. Mod. Phys. E 19 (2010) 1 [arXiv:0902.3663] [SPIRES].

    ADS  Google Scholar 

  53. W.A. Hiscock and L. Lindblom, Stability and causality in dissipative relativistic fluids, Annals Phys. 151 (1983) 466 [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  54. W.A. Hiscock and L. Lindblom, Linear plane waves in dissipative relativistic fluids, Phys. Rev. D 35 (1987) 3723 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  55. W.A. Hiscock and L. Lindblom, Generic instabilities in first-order dissipative relativistic fluid theories, Phys. Rev. D 31 (1985) 725 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  56. I. Müller, Zum Paradoxon der Wärmeleitungstheorie, Z. Phys. 198 (1967) 329.

    Article  MATH  ADS  Google Scholar 

  57. W. Israel, Nonstationary irreversible thermodynamics: A Causal relativistic theory, Ann. Phys. 100 (1976) 310 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  58. W. Israel and J.M. Stewart, Thermodynamics of nonstationary and transient effects in a relativistic gas, Phys. Lett. A 58 (1976) 213.

    ADS  Google Scholar 

  59. W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. 118 (1979) 341 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  60. A. Muronga, Causal Theories of DissiPative Relativistic Fluid Dynamics for Nuclear Collisions, Phys. Rev. C 69 (2004) 034903 [nucl-th/0309055] [SPIRES].

    ADS  Google Scholar 

  61. L. Brillouin, Wave Propagation and Group Velocity, Academic Press, New York U.S.A. (1960).

    MATH  Google Scholar 

  62. R. Fox, C.G. Kuper and S.G. Lipson, Faster-than-light group velocities and causality violation, Proc. Roy. Soc. Lond. A 316 (1970) 515.

    ADS  Google Scholar 

  63. E. Krotscheck and W. Kundt, Causality Criteria, Commun. Math. Phys. 60 (1978) 171.

    Article  ADS  MathSciNet  Google Scholar 

  64. D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  65. A. Buchel, R.C. Myers, M.F. Paulos and A. Sinha, Universal holographic hydrodynamics at finite coupling, Phys. Lett. B 669 (2008) 364 [arXiv:0808.1837] [SPIRES].

    ADS  Google Scholar 

  66. J. Noronha, M. Gyulassy and G. Torrieri, Constraints on AdS/CFT Gravity Dual Models of Heavy Ion Collisions, arXiv:0906.4099 [SPIRES].

  67. A. Buchel, M.P. Heller and R.C. Myers, sQGP as hCFT, Phys. Lett. B 680 (2009) 521 [arXiv:0908.2802] [SPIRES].

    ADS  Google Scholar 

  68. S. Sachdev, Polylogarithm identities in a conformal field theory in three-dimensions, Phys. Lett. B 309 (1993) 285 [hep-th/9305131] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  69. A.H. Castro Neto and E.H. Fradkin, The Thermodynamics of quantum systems and generalizations of Zamolodchikov’s C theorem, Nucl. Phys. B 400 (1993) 525 [cond-mat/9301009] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  70. P. Kovtun and A. Ritz, Black holes and universality classes of critical points, Phys. Rev. Lett. 100 (2008) 171606 [arXiv:0801.2785] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  71. P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [SPIRES].

    ADS  Google Scholar 

  72. S.S. Gubser, I.R. Klebanov and A.W. Peet, Entropy and Temperature of Black 3-Branes, Phys. Rev. D 54 (1996) 3915 [hep-th/9602135] [SPIRES].

    ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Alex Buchel, Jorge Escobedo, Robert C. Myers, Aninda Sinha & Michael Smolkin

  2. Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada

    Alex Buchel

  3. Department of Physics and Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Jorge Escobedo

  4. Department of Applied Mathematics and Theoretical Physics, Cambridge, CB3 0WA, U.K.

    Miguel F. Paulos

  5. Racah Institute of Physics, Hebrew University, Jerusalem, 91904, Israel

    Michael Smolkin

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  1. Alex Buchel
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Correspondence to Jorge Escobedo.

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ArXiv ePrint: 0911.4257

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Buchel, A., Escobedo, J., Myers, R.C. et al. Holographic GB gravity in arbitrary dimensions. J. High Energ. Phys. 2010, 111 (2010). https://doi.org/10.1007/JHEP03(2010)111

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