Abstract
We examine the structure of the shear viscosity to entropy density ratio \( \frac{\eta }{s} \) in holographic theories of gravity coupled to a scalar field, in the presence of higher derivative corrections. Thanks to a non-trivial scalar field profile, \( \frac{\eta }{s} \) in this setup generically runs as a function of temperature. In particular, its temperature behavior is dictated by the shape of the scalar potential and of the scalar couplings to the higher derivative terms. We consider a number of dilatonic setups, but focus mostly on phenomenological models that are QCD-like. We determine the geometric conditions needed to identify local and global minima for \( \frac{\eta }{s} \) as a function of temperature, which translate to restrictions on the signs and ranges of the higher derivative couplings. Finally, such restrictions lead to an holographic argument for the existence of a global minimum for \( \frac{\eta }{s} \) in these models, at or above the deconfinement transition.
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H. Song, S.A. Bass, U. Heinz, T. Hirano and C. Shen, 200 A GeV Au + Au collisions serve a nearly perfect quark-gluon liquid, Phys. Rev. Lett. 106 (2011) 192301 [arXiv:1011.2783] [INSPIRE].
D. Teaney, The effects of viscosity on spectra, elliptic flow and HBT radii, Phys. Rev. C 68 (2003) 034913 [nucl-th/0301099] [INSPIRE].
M. Luzum and P. Romatschke, Conformal relativistic viscous hydrodynamics: applications to RHIC results at \( \sqrt {{{s_{{NN}}}{ }}} = 200\;GeV \) , Phys. Rev. C 78 (2008) 034915 [Erratum ibid. C 79 (2009)039903] [arXiv:0804.4015] [INSPIRE].
M. Luzum, Elliptic flow at energies available at the CERN Large Hadron Collider: comparing heavy-ion data to viscous hydrodynamic predictions, Phys. Rev. C 83 (2011) 044911 [arXiv:1011.5173] [INSPIRE].
J.L. Nagle, I.G. Bearden and W.A. Zajc, Quark-gluon plasma at RHIC and the LHC: perfect fluid too perfect?, New J. Phys. 13 (2011) 075004 [arXiv:1102.0680] [INSPIRE].
C. Shen, U. Heinz, P. Huovinen and H. Song, Radial and elliptic flow in Pb + Pb collisions at the Large Hadron Collider from viscous hydrodynamic, Phys. Rev. C 84 (2011) 044903 [arXiv:1105.3226] [INSPIRE].
B. Müller, J. Schukraft and B. Wyslouch, First results from Pb + Pb collisions at the LHC, arXiv:1202.3233 [INSPIRE].
G. Policastro, D. Son and A. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].
J. Erdmenger, P. Kerner and H. Zeller, Non-universal shear viscosity from Einstein gravity, Phys. Lett. B 699 (2011) 301 [arXiv:1011.5912] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [INSPIRE].
A. Adams, L.D. Carr, T. Schaefer, P. Steinberg and J.E. Thomas, Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality, arXiv:1205.5180 [INSPIRE].
A. Sinha and R.C. Myers, The viscosity bound in string theory, Nucl. Phys. A 830 (2009) 295C-298C [arXiv:0907.4798] [INSPIRE].
S. Cremonini, The shear viscosity to entropy ratio: a status report, Mod. Phys. Lett. B 25 (2011) 1867 [arXiv:1108.0677] [INSPIRE].
N. Banerjee and S. Dutta, Holographic hydrodynamics: models and methods, arXiv:1112.5345 [INSPIRE].
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] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].
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].
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].
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].
A. Buchel and S. Cremonini, Viscosity bound and causality in superfluid plasma, JHEP 10 (2010) 026 [arXiv:1007.2963] [INSPIRE].
A. Ghodsi and M. Alishahiha, Non-relativistic D3-brane in the presence of higher derivative corrections, Phys. Rev. D 80 (2009) 026004 [arXiv:0901.3431] [INSPIRE].
P. Basu and J.-H. Oh, Analytic approaches to anisotropic holographic superfluids, JHEP 07 (2012) 106 [arXiv:1109.4592] [INSPIRE].
J. Erdmenger, P. Kerner and H. Zeller, Transport in anisotropic superfluids: a holographic description, JHEP 01 (2012) 059 [arXiv:1110.0007] [INSPIRE].
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].
J.-H. Oh, Running shear viscosities in an-isotropic holographic superfluids, JHEP 06 (2012) 103 [arXiv:1201.5605] [INSPIRE].
K.A. Mamo, Holographic Wilsonian RG flow of the shear viscosity to entropy ratio in strongly coupled anisotropic plasma, arXiv:1205.1797 [INSPIRE].
L.P. Csernai, J. Kapusta and L.D. McLerran, On the strongly-interacting low-viscosity matter created in relativistic nuclear collisions, Phys. Rev. Lett. 97 (2006) 152303 [nucl-th/0604032] [INSPIRE].
S. Gavin, Transport coefficients in ultrarelativistic heavy ion collisions, Nucl. Phys. A 435 (1985) 826 [INSPIRE].
M. Prakash, M. Prakash, R. Venugopalan and G. Welke, Nonequilibrium properties of hadronic mixtures, Phys. Rept. 227 (1993) 321 [INSPIRE].
J. Noronha-Hostler, J. Noronha and C. Greiner, Transport coefficients of hadronic matter near Tc, Phys. Rev. Lett. 103 (2009) 172302 [arXiv:0811.1571] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Leading log results, JHEP 11 (2000) 001 [hep-ph/0010177] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, JHEP 05 (2003) 051 [hep-ph/0302165] [INSPIRE].
P.J. Linstrom and W.G. Mallard eds., NIST chemistry webbook, NIST standard reference database number 69, http://webbook.nist.gov/, NIST — National Institute of Standards and Technology, U.S.A. (2011).
P. Massignan, G. Bruun and H. Smith, Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit, Phys. Rev. A 71 (2005) 033607 [cond-mat/0409660] [INSPIRE].
M. Mannarelli, C. Manuel and L. Tolos, Shear viscosity in a superfluid cold Fermi gas at unitarity, arXiv:1201.4006 [INSPIRE].
H. Song, S.A. Bass, U. Heinz, T. Hirano and C. Shen, Hadron spectra and elliptic flow for 200 A GeV Au + Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade, Phys. Rev. C 83 (2011) 054910 [arXiv:1101.4638] [INSPIRE].
R.A. Lacey et al., Has the QCD critical point been signaled by observations at RHIC?, Phys. Rev. Lett. 98 (2007) 092301 [nucl-ex/0609025] [INSPIRE].
H. Niemi, G.S. Denicol, P. Huovinen, E. Molnar and D.H. Rischke, Influence of the shear viscosity of the quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions, Phys. Rev. Lett. 106 (2011) 212302 [arXiv:1101.2442] [INSPIRE].
C. Shen and U. Heinz, Hydrodynamic flow in heavy-ion collisions with large hadronic viscosity, Phys. Rev. C 83 (2011) 044909 [arXiv:1101.3703] [INSPIRE].
M. Bluhm, B. Kampfer and K. Redlich, Bulk and shear viscosities of the gluon plasma in a quasiparticle description, Phys. Rev. C 84 (2011) 025201 [arXiv:1011.5634] [INSPIRE].
P. Kovtun, G.D. Moore and P. Romatschke, The stickiness of sound: an absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics, Phys. Rev. D 84 (2011) 025006 [arXiv:1104.1586] [INSPIRE].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].
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] [INSPIRE].
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].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and thermodynamics of 5D dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [INSPIRE].
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].
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].
H. Chamblin and H. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225] [INSPIRE].
B. Gouteraux, J. Smolic, M. Smolic, K. Skenderis and M. Taylor, Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction, JHEP 01 (2012) 089 [arXiv:1110.2320] [INSPIRE].
T. Wiseman and B. Withers, Holographic renormalization for coincident Dp-branes, JHEP 10 (2008) 037 [arXiv:0807.0755] [INSPIRE].
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] [INSPIRE].
C. Charmousis, B. Gouteraux and E. Kiritsis, Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography, arXiv:1206.1499 [INSPIRE].
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] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
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] [INSPIRE].
M. Caselle et al., Thermodynamics of SU(N ) Yang-Mills theories in 2 + 1 dimensions II. The deconfined phase, JHEP 05 (2012) 135 [arXiv:1111.0580] [INSPIRE].
K. Veschgini, E. Megias and H. Pirner, Trouble finding the optimal AdS/QCD, Phys. Lett. B 696 (2011) 495 [arXiv:1009.4639] [INSPIRE].
U. Gürsoy, Continuous Hawking-Page transitions in Einstein-scalar gravity, JHEP 01 (2011) 086 [arXiv:1007.0500] [INSPIRE].
S. Caron-Huot and O. Saremi, Hydrodynamic long-time tails from Anti de Sitter space, JHEP 11 (2010) 013 [arXiv:0909.4525] [INSPIRE].
U.W. Heinz, C. Shen and H. Song, The viscosity of quark-gluon plasma at RHIC and the LHC, AIP Conf. Proc. 1441 (2012) 766 [arXiv:1108.5323] [INSPIRE].
Z. Qiu, C. Shen and U. Heinz, Hydrodynamic elliptic and triangular flow in Pb-Pb collisions at \( \sqrt {s} = 2.76\;A\;\;TeV \), Phys. Lett. B 707 (2012) 151 [arXiv:1110.3033] [INSPIRE].
A. Nakamura and S. Sakai, Transport coefficients of gluon plasma, Phys. Rev. Lett. 94 (2005) 072305 [hep-lat/0406009] [INSPIRE].
H.B. Meyer, A calculation of the shear viscosity in SU(3) gluodynamics, Phys. Rev. D 76 (2007) 101701 [arXiv:0704.1801] [INSPIRE].
B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
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Cremonini, S., Gürsoy, U. & Szepietowski, P. On the temperature dependence of the shear viscosity and holography. J. High Energ. Phys. 2012, 167 (2012). https://doi.org/10.1007/JHEP08(2012)167
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DOI: https://doi.org/10.1007/JHEP08(2012)167