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Bulk viscosity at extreme limits: from kinetic theory to strings

  • Alina Czajka
  • Keshav DasguptaEmail author
  • Charles Gale
  • Sangyong Jeon
  • Aalok Misra
  • Michael Richard
  • Karunava Sil
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we study bulk viscosity in a thermal QCD model with large number of colors at two extreme limits: the very weak and the very strong ’t Hooft couplings. The weak coupling scenario is based on kinetic theory, and one may go to the very strong coupling dynamics via an intermediate coupling regime. Although the former has a clear description in terms of kinetic theory, the intermediate coupling regime, which uses lattice results, suffers from usual technical challenges that render an explicit determination of bulk viscosity somewhat difficult. On the other hand, the very strong ’t Hooft coupling dynamics may be studied using string theories at both weak and strong string couplings using gravity duals in type IIB as well as M-theory respectively. In type IIB we provide the precise fluctuation modes of the metric in the gravity dual responsible for bulk viscosity, compute the speed of sound in the medium and analyze the ratio of the bulk to shear viscosities. In M-theory, where we uplift the type IIA mirror dual of the UV complete type IIB model, we study and compare both the bulk viscosity and the sound speed by analyzing the quasi-normal modes in the system at strong IIA string coupling. By deriving the spectral function, we show the consistency of our results both for the actual values of the parameters involved as well for the bound on the ratio of bulk to shear viscosities.

Keywords

Holography and quark-gluon plasmas M-Theory Quark-Gluon Plasma 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    D. Teaney, J. Lauret and E.V. Shuryak, Flow at the SPS and RHIC as a quark gluon plasma signature, Phys. Rev. Lett. 86 (2001) 4783 [nucl-th/0011058] [INSPIRE].
  2. [2]
    P. Huovinen et al., Radial and elliptic flow at RHIC: Further predictions, Phys. Lett. B 503 (2001) 58 [hep-ph/0101136] [INSPIRE].
  3. [3]
    P.F. Kolb et al., Centrality dependence of multiplicity, transverse energy and elliptic flow from hydrodynamics, Nucl. Phys. A 696 (2001) 197 [hep-ph/0103234] [INSPIRE].
  4. [4]
    T. Hirano and K. Tsuda, Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freezeout, Phys. Rev. C 66 (2002) 054905 [nucl-th/0205043] [INSPIRE].
  5. [5]
    P.F. Kolb and R. Rapp, Transverse flow and hadrochemistry in Au+Au collisions at \( \sqrt{S_{NN}} \) = 200 GeV, Phys. Rev. C 67 (2003) 044903 [hep-ph/0210222] [INSPIRE].
  6. [6]
    P. Romatschke and U. Romatschke, Viscosity information from relativistic nuclear collisions: how perfect is the fluid observed at RHIC?, Phys. Rev. Lett. 99 (2007) 172301 [arXiv:0706.1522] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    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].
  8. [8]
    K. Dusling and D. Teaney, Simulating elliptic flow with viscous hydrodynamics, Phys. Rev. C 77 (2008) 034905 [arXiv:0710.5932] [INSPIRE].ADSGoogle Scholar
  9. [9]
    H. Song and U.W. Heinz, Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions, Phys. Rev. C 77 (2008) 064901 [arXiv:0712.3715] [INSPIRE].ADSGoogle Scholar
  10. [10]
    PHENIX collaboration, Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757 (2005) 184 [nucl-ex/0410003] [INSPIRE].
  11. [11]
    B.B. Back et al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757 (2005) 28 [nucl-ex/0410022] [INSPIRE].
  12. [12]
    BRAHMS collaboration, Quark gluon plasma and color glass condensate at RHIC? The Perspective from the BRAHMS experiment, Nucl. Phys. A 757 (2005) 1 [nucl-ex/0410020] [INSPIRE].
  13. [13]
    STAR collaboration, Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaborations critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [INSPIRE].
  14. [14]
    E. Shuryak, Physics of strongly coupled quark-gluon plasma, Prog. Part. Nucl. Phys. 62 (2009) 48 [arXiv:0807.3033] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    C. Gale, S. Jeon and B. Schenke, Hydrodynamic modeling of heavy-ion collisions, Int. J. Mod. Phys. A 28 (2013) 1340011 [arXiv:1301.5893] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci. 63 (2013) 123 [arXiv:1301.2826] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    P. Romatschke, New developments in relativistic viscous hydrodynamics, Int. J. Mod. Phys. E 19 (2010) 1 [arXiv:0902.3663] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    W. Florkowski, M.P. Heller and M. Spalinski, New theories of relativistic hydrodynamics in the LHC era, Rept. Prog. Phys. 81 (2018) 046001 [arXiv:1707.02282] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    S. Jeon and U. Heinz, Introduction to hydrodynamics, Int. J. Mod. Phys. E 24 (2015) 1530010 [arXiv:1503.03931] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  21. [21]
    D.A. Teaney, Viscous hydrodynamics and the quark gluon plasma, arXiv:0905.2433 [INSPIRE].
  22. [22]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    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].
  25. [25]
    N. Christiansen, M. Haas, J.M. Pawlowski and N. Strodthoff, Transport coefficients in Yang-Mills theory and QCD, Phys. Rev. Lett. 115 (2015) 112002 [arXiv:1411.7986] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    A. Nakamura and S. Sakai, Transport coefficients of gluon plasma, Phys. Rev. Lett. 94 (2005) 072305 [hep-lat/0406009] [INSPIRE].
  27. [27]
    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].
  28. [28]
    M. Prakash, M. Prakash, R. Venugopalan and G. Welke, Nonequilibrium properties of hadronic mixtures, Phys. Rept. 227 (1993) 321.ADSCrossRefGoogle Scholar
  29. [29]
    R. Lang, N. Kaiser and W. Weise, Shear viscosity of a hot pion gas, Eur. Phys. J. A 48 (2012) 109 [arXiv:1205.6648] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    P.B. Arnold, C. Dogan and G.D. Moore, The bulk viscosity of high-temperature QCD, Phys. Rev. D 74 (2006) 085021 [hep-ph/0608012] [INSPIRE].
  31. [31]
    A. Buchel, Bulk viscosity of gauge theory plasma at strong coupling, Phys. Lett. B 663 (2008) 286 [arXiv:0708.3459] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S. Jeon, Hydrodynamic transport coefficients in relativistic scalar field theory, Phys. Rev. D 52 (1995) 3591 [hep-ph/9409250] [INSPIRE].
  33. [33]
    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] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    S. Borsányi et al., Recent results on the equation of state of QCD, PoS(LATTICE 2014) 224 [arXiv:1410.7917] [INSPIRE].
  35. [35]
    A. Bazavov, P. Petreczky and J.H. Weber, Equation of state in 2 + 1 flavor QCD at high temperatures, Phys. Rev. D 97 (2018) 014510 [arXiv:1710.05024] [INSPIRE].ADSGoogle Scholar
  36. [36]
    D. Kharzeev and K. Tuchin, Bulk viscosity of QCD matter near the critical temperature, JHEP 09 (2008) 093 [arXiv:0705.4280] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    F. Karsch, D. Kharzeev and K. Tuchin, Universal properties of bulk viscosity near the QCD phase transition, Phys. Lett. B 663 (2008) 217 [arXiv:0711.0914] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    G.D. Moore and O. Saremi, Bulk viscosity and spectral functions in QCD, JHEP 09 (2008) 015 [arXiv:0805.4201] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    S.S. Gubser, A. Nellore, S.S. Pufu and F.D. Rocha, Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics, Phys. Rev. Lett. 101 (2008) 131601 [arXiv:0804.1950] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    J. Noronha-Hostler, J. Noronha and C. Greiner, Transport coefficients of hadronic matter near T c, Phys. Rev. Lett. 103 (2009) 172302 [arXiv:0811.1571] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    G.S. Denicol, T. Kodama, T. Koide and P. Mota, Effect of bulk viscosity on elliptic flow near QCD phase transition, Phys. Rev. C 80 (2009) 064901 [arXiv:0903.3595] [INSPIRE].ADSGoogle Scholar
  42. [42]
    H. Song and U.W. Heinz, Extracting the QGP viscosity from RHIC dataA status report from viscous hydrodynamics, J. Phys. G 36 (2009) 064033 [arXiv:0812.4274] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    G.S. Denicol, T. Kodama and T. Koide, The effect of shear and bulk viscosities on elliptic flow, J. Phys. G 37 (2010) 094040 [arXiv:1002.2394] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    S. Ryu et al., Importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions, Phys. Rev. Lett. 115 (2015) 132301 [arXiv:1502.01675] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    S. Ryu et al., Effects of bulk viscosity and hadronic rescattering in heavy ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider, Phys. Rev. C 97 (2018) 034910 [arXiv:1704.04216] [INSPIRE].ADSGoogle Scholar
  46. [46]
    J.-F. Paquet et al., Production of photons in relativistic heavy-ion collisions, Phys. Rev. C 93 (2016) 044906 [arXiv:1509.06738] [INSPIRE].ADSGoogle Scholar
  47. [47]
    P. Bożek, Effect of bulk viscosity on interferometry correlations in ultrarelativistic heavy-ion collisions, Phys. Rev. C 95 (2017) 054909 [arXiv:1702.01319] [INSPIRE].ADSGoogle Scholar
  48. [48]
    A. Monnai, S. Mukherjee and Y. Yin, Phenomenological consequences of enhanced bulk viscosity near the QCD critical point, Phys. Rev. C 95 (2017) 034902 [arXiv:1606.00771] [INSPIRE].ADSGoogle Scholar
  49. [49]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Effective kinetic theory for high temperature gauge theories, JHEP 01 (2003) 030 [hep-ph/0209353] [INSPIRE].
  50. [50]
    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].
  51. [51]
    J.-S. Gagnon and S. Jeon, Leading order calculation of electric conductivity in hot quantum electrodynamics from diagrammatic methods, Phys. Rev. D 75 (2007) 025014 [Erratum ibid. D 76 (2007) 089902] [hep-ph/0610235] [INSPIRE].
  52. [52]
    J.-S. Gagnon and S. Jeon, Leading order calculation of shear viscosity in hot quantum electrodynamics from diagrammatic methods, Phys. Rev. D 76 (2007) 105019 [arXiv:0708.1631] [INSPIRE].ADSGoogle Scholar
  53. [53]
    P. Romatschke and D.T. Son, Spectral sum rules for the quark-gluon plasma, Phys. Rev. D 80 (2009) 065021 [arXiv:0903.3946] [INSPIRE].ADSGoogle Scholar
  54. [54]
    H.B. Meyer, A Calculation of the bulk viscosity in SU(3) gluodynamics, Phys. Rev. Lett. 100 (2008) 162001 [arXiv:0710.3717] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    H.B. Meyer, The bulk channel in thermal gauge theories, JHEP 04 (2010) 099 [arXiv:1002.3343] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  56. [56]
    N.Yu. Astrakhantsev, V.V. Braguta and A.Yu. Kotov, Temperature dependence of the bulk viscosity within lattice simulation of SU(3) gluodynamics, Phys. Rev. D 98 (2018) 054515 [arXiv:1804.02382] [INSPIRE].ADSGoogle Scholar
  57. [57]
    I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χ SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    P. Ouyang, Holomorphic D7 branes and flavored N = 1 gauge theories, Nucl. Phys. B 699 (2004) 207 [hep-th/0311084] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    M. Mia, K. Dasgupta, C. Gale and S. Jeon, Five easy pieces: the dynamics of quarks in strongly coupled plasmas, Nucl. Phys. B 839 (2010) 187 [arXiv:0902.1540] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  60. [60]
    M. Mia, K. Dasgupta, C. Gale and S. Jeon, Toward large N thermal QCD from dual gravity: the heavy quarkonium potential, Phys. Rev. D 82 (2010) 026004 [arXiv:1004.0387] [INSPIRE].ADSGoogle Scholar
  61. [61]
    F. Chen, L. Chen, K. Dasgupta, M. Mia and O. Trottier, Ultraviolet complete model of large N thermal QCD, Phys. Rev. D 87 (2013) 041901 [arXiv:1209.6061] [INSPIRE].ADSGoogle Scholar
  62. [62]
    K. Dasgupta, J. Elituv, M. Emelin and A.-K. Trinh, Non-Kähler deformed conifold, ultra-violet completion and supersymmetric constraints in the baryonic branch, arXiv:1805.03676 [INSPIRE].
  63. [63]
    K. Dasgupta, M. Emelin and E. McDonough, Non-Kähler resolved conifold, localized fluxes in M-theory and supersymmetry, JHEP 02 (2015) 179 [arXiv:1412.3123] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  64. [64]
    M. Dhuria and A. Misra, Towards MQGP, JHEP 11 (2013) 001 [arXiv:1306.4339] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    A. Strominger, S.-T. Yau and E. Zaslow, Mirror symmetry is T duality, Nucl. Phys. B 479 (1996) 243 [hep-th/9606040] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  66. [66]
    E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  67. [67]
    A. Buchel, Violation of the holographic bulk viscosity bound, Phys. Rev. D 85 (2012) 066004 [arXiv:1110.0063] [INSPIRE].ADSGoogle Scholar
  68. [68]
    D.J. Gross and F. Wilczek, Asymptotically free gauge theoriesI, Phys. Rev. D 8 (1973) 3633 [INSPIRE].ADSGoogle Scholar
  69. [69]
    R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Japan 12 (1957) 570.ADSMathSciNetCrossRefGoogle Scholar
  70. [70]
    S.C. Huot, S. Jeon and G.D. Moore, Shear viscosity in weakly coupled N = 4 super Yang-Mills theory compared to QCD, Phys. Rev. Lett. 98 (2007) 172303 [hep-ph/0608062] [INSPIRE].
  71. [71]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from ultrarelativistic plasmas, JHEP 11 (2001) 057 [hep-ph/0109064] [INSPIRE].
  72. [72]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon emission from quark gluon plasma: complete leading order results, JHEP 12 (2001) 009 [hep-ph/0111107] [INSPIRE].
  73. [73]
    P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon and gluon emission in relativistic plasmas, JHEP 06 (2002) 030 [hep-ph/0204343] [INSPIRE].
  74. [74]
    E. Wang and U.W. Heinz, A generalized fluctuation dissipation theorem for nonlinear response functions, Phys. Rev. D 66 (2002) 025008 [hep-th/9809016] [INSPIRE].ADSGoogle Scholar
  75. [75]
    E. Wang and U.W. Heinz, Shear viscosity of hot scalar field theory in the real time formalism, Phys. Rev. D 67 (2003) 025022 [hep-th/0201116] [INSPIRE].ADSGoogle Scholar
  76. [76]
    A. Czajka et al., Bulk viscosity of strongly interacting matter in the relaxation time approximation, Phys. Rev. C 97 (2018) 044914 [arXiv:1712.05905] [INSPIRE].ADSMathSciNetGoogle Scholar
  77. [77]
    G. ’t Hooft, Large N, in the proceedings of Phenomenology of large N c QCD, January 9–11, Tempe, U.S.A. (2002), hep-th/0204069 [INSPIRE].
  78. [78]
    O.K. Kalashnikov and V.V. Klimov, Infrared behavior of Green functions in Yang-Mills theory at finite temperatures, Sov. J. Nucl. Phys. 33 (1981) 443 [INSPIRE].Google Scholar
  79. [79]
    V.V. Klimov, Spectrum of elementary Fermi excitations in quark gluon plasma (in Russian), Sov. J. Nucl. Phys. 33 (1981) 934 [Yad. Fiz. 33 (1981) 1734] [INSPIRE].
  80. [80]
    E. Braaten and R.D. Pisarski, Soft amplitudes in hot gauge theories: a general analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    S. Caron-Huot, Asymptotics of thermal spectral functions, Phys. Rev. D 79 (2009) 125009 [arXiv:0903.3958] [INSPIRE].ADSGoogle Scholar
  82. [82]
    G. Baym and L.P. Kadanoff, Conservation laws and correlation functions, Phys. Rev. 124 (1961) 287 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  83. [83]
    J.-P. Blaizot and E. Iancu, The quark gluon plasma: collective dynamics and hard thermal loops, Phys. Rept. 359 (2002) 355 [hep-ph/0101103] [INSPIRE].
  84. [84]
    P. Danielewicz, Quantum theory of nonequilibrium processes. 1., Annals Phys. 152 (1984) 239 [INSPIRE].
  85. [85]
    J.M. Cornwall, R. Jackiw and E. Tomboulis, Effective action for composite operators, Phys. Rev. D 10 (1974) 2428 [INSPIRE].ADSzbMATHGoogle Scholar
  86. [86]
    E. Calzetta and B.L. Hu, Nonequilibrium quantum fields: closed time path effective action, Wigner function and Boltzmann equation, Phys. Rev. D 37 (1988) 2878 [INSPIRE].ADSMathSciNetGoogle Scholar
  87. [87]
    J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739 (2004) 3 [hep-ph/0409233] [INSPIRE].
  88. [88]
    E.A. Calzetta, B.L. Hu and S.A. Ramsey, Hydrodynamic transport functions from quantum kinetic theory, Phys. Rev. D 61 (2000) 125013 [hep-ph/9910334] [INSPIRE].
  89. [89]
    G. Aarts and J.M. Martinez Resco, Transport coefficients in large N f gauge theories with massive fermions, JHEP 03 (2005) 074 [hep-ph/0503161] [INSPIRE].
  90. [90]
    M.E. Carrington and E. Kovalchuk, QED electrical conductivity using the 2PI effective action, Phys. Rev. D 76 (2007) 045019 [arXiv:0705.0162] [INSPIRE].ADSGoogle Scholar
  91. [91]
    M.E. Carrington and E. Kovalchuk, Leading order QED electrical conductivity from the 3PI effective action, Phys. Rev. D 77 (2008) 025015 [arXiv:0709.0706] [INSPIRE].ADSGoogle Scholar
  92. [92]
    M.E. Carrington and E. Kovalchuk, Leading order QCD shear viscosity from the three-particle irreducible effective action, Phys. Rev. D 80 (2009) 085013 [arXiv:0906.1140] [INSPIRE].ADSGoogle Scholar
  93. [93]
    A. Arrizabalaga and J. Smit, Gauge fixing dependence of Φ derivable approximations, Phys. Rev. D 66 (2002) 065014 [hep-ph/0207044] [INSPIRE].
  94. [94]
    R. Kobes, G. Kunstatter and A. Rebhan, QCD plasma parameters and the gauge dependent gluon propagator, Phys. Rev. Lett. 64 (1990) 2992 [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    H. Van Hees and J. Knoll, Renormalization of selfconsistent approximation schemes. 2. Applications to the sunset diagram, Phys. Rev. D 65 (2002) 105005 [hep-ph/0111193] [INSPIRE].
  96. [96]
    H. van Hees and J. Knoll, Renormalization in selfconsistent approximation schemes at finite temperature. 3. Global symmetries, Phys. Rev. D 66 (2002) 025028 [hep-ph/0203008] [INSPIRE].
  97. [97]
    J. Berges, S. Borsányi, U. Reinosa and J. Serreau, Nonperturbative renormalization for 2PI effective action techniques, Annals Phys. 320 (2005) 344 [hep-ph/0503240] [INSPIRE].
  98. [98]
    U. Reinosa and J. Serreau, 2PI effective action for gauge theories: renormalization, JHEP 07 (2006) 028 [hep-th/0605023] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  99. [99]
    U. Reinosa and J. Serreau, Ward Identities for the 2PI effective action in QED, JHEP 11 (2007) 097 [arXiv:0708.0971] [INSPIRE].ADSCrossRefGoogle Scholar
  100. [100]
    D. Tong, Holographic conductivity, lectures given at the Cracow School on Theoretical Physics, June 28–July 7, Cracow, Poland (2013).Google Scholar
  101. [101]
    R. Argurio and M. Bertolini, Orientifolds and duality cascades: confinement before the wall, JHEP 02 (2018) 149 [arXiv:1711.08983] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  102. [102]
    M. Attems et al., Thermodynamics, transport and relaxation in non-conformal theories, JHEP 10 (2016) 155 [arXiv:1603.01254].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  103. [103]
    M. Attems et al., Thermodynamics, transport and relaxation in non-conformal theories, JHEP 10 (2016) 155 [arXiv:1603.01254] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  104. [104]
    K. Dasgupta, M. Emelin, C. Gale and M. Richard, Renormalization group flow, stability and bulk viscosity in a large N thermal QCD model, Phys. Rev. D 95 (2017) 086018 [arXiv:1611.07998] [INSPIRE].ADSMathSciNetGoogle Scholar
  105. [105]
    M. Mia, F. Chen, K. Dasgupta, P. Franche and S. Vaidya, Non-extremality, chemical potential and the infrared limit of large N thermal QCD, Phys. Rev. D 86 (2012) 086002 [arXiv:1202.5321] [INSPIRE].ADSGoogle Scholar
  106. [106]
    C. Eling and Y. Oz, A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation, JHEP 06 (2011) 007 [arXiv:1103.1657] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  107. [107]
    K. Ohta and T. Yokono, Deformation of conifold and intersecting branes, JHEP 02 (2000) 023 [hep-th/9912266] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  108. [108]
    K. Dasgupta, K. Oh and R. Tatar, Geometric transition, large N dualities and MQCD dynamics, Nucl. Phys. B 610 (2001) 331 [hep-th/0105066] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  109. [109]
    K. Dasgupta, K. Oh and R. Tatar, Open/closed string dualities and Seiberg duality from geometric transitions in M theory, JHEP 08 (2002) 026 [hep-th/0106040].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  110. [110]
    K. Dasgupta, K.H. Oh, J. Park and R. Tatar, Geometric transition versus cascading solution, JHEP 01 (2002) 031 [hep-th/0110050].ADSMathSciNetCrossRefGoogle Scholar
  111. [111]
    K. Dasgupta et al., Infrared dynamics of a large N QCD model, the massless string sector and mesonic spectra, JHEP 07 (2015) 122 [arXiv:1409.0559] [INSPIRE].ADSCrossRefGoogle Scholar
  112. [112]
    M. Dhuria and A. Misra, Transport coefficients of black MQGP M3-branes, Eur. Phys. J. C 75 (2015) 16 [arXiv:1406.6076] [INSPIRE].ADSCrossRefGoogle Scholar
  113. [113]
    M. Ionel and M. Min-Oo, Cohomogeneity one special lagrangian 3-folds in the deformed and the resolved conifolds, Illinois J. Math. 52 (2008) 839.MathSciNetCrossRefzbMATHGoogle Scholar
  114. [114]
    M. Becker, K. Dasgupta, A. Knauf and R. Tatar, Geometric transitions, flops and non-Kähler manifolds. I., Nucl. Phys. B 702 (2004) 207 [hep-th/0403288] [INSPIRE].
  115. [115]
    S. Alexander et al., In the realm of the geometric transitions, Nucl. Phys. B 704 (2005) 231 [hep-th/0408192].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  116. [116]
    M. Becker et al., Geometric transitions, flops and non-Kähler manifolds. II, Nucl. Phys. B 738 (2006) 124 [hep-th/0511099].
  117. [117]
    F. Chen et al., Supersymmetric configurations, geometric transitions and new non-Kähler manifolds, Nucl. Phys. B 852 (2011) 553 [arXiv:1007.5316] [INSPIRE].ADSzbMATHGoogle Scholar
  118. [118]
    K. Becker, M. Becker, K. Dasgupta and R. Tatar, Geometric transitions, non-Kahler geometries and string vacua, Int. J. Mod. Phys. A 20 (2005) 3442 [hep-th/0411039] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  119. [119]
    K. Sil and A. Misra, On aspects of holographic thermal QCD at finite coupling, Nucl. Phys. B 910 (2016) 754 [arXiv:1507.02692] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  120. [120]
    A.M. Uranga, Brane configurations for branes at conifolds, JHEP 01 (1999) 022 [hep-th/9811004] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  121. [121]
    K. Dasgupta and S. Mukhi, Brane constructions, conifolds and M-theory, Nucl. Phys. B 551 (1999) 204 [hep-th/9811139] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  122. [122]
    E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  123. [123]
    D. Tong, NS5-branes, T duality and world sheet instantons, JHEP 07 (2002) 013 [hep-th/0204186] [INSPIRE].ADSCrossRefGoogle Scholar
  124. [124]
    A. Sen, Dynamics of multiple Kaluza-Klein monopoles in M and string theory, Adv. Theor. Math. Phys. 1 (1998) 115 [hep-th/9707042] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  125. [125]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184].ADSGoogle Scholar
  126. [126]
    K. Sil, V. Yadav and A. Misra, Top-down holographic G-structure glueball spectroscopy at (N)LO in N and finite coupling, Eur. Phys. J. C 77 (2017) 381 [arXiv:1703.01306].ADSCrossRefGoogle Scholar
  127. [127]
    V. Yadav, A. Misra and K. Sil, Delocalized SYZ mirrors and confronting top-down SU(3)-structure holographic meson masses at finite g and N c with P(article) D(ata) G(roup) Values, Eur. Phys. J. C 77 (2017) 656 [arXiv:1707.02818].
  128. [128]
    K. Sil and A. Misra, New insights into properties of large-N holographic thermal QCD at finite gauge coupling at (the non-conformal/next-to) leading order in N, Eur. Phys. J. C 76 (2016) 618 [arXiv:1606.04949] [INSPIRE].ADSCrossRefGoogle Scholar
  129. [129]
    C.P. Herzog, The sound of M-theory, Phys. Rev. D 68 (2003) 024013 [hep-th/0302086] [INSPIRE].ADSMathSciNetGoogle Scholar
  130. [130]
    C.M. Bender and S.A. Orzag, Advanced mathematical methods for scientists and engineers I. Asymptotic methods and perturbation theory, Springer, Germany (1999).Google Scholar
  131. [131]
    P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  132. [132]
    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].ADSMathSciNetCrossRefGoogle Scholar
  133. [133]
    J. Casalderrey-Solana, S. Grozdanov and A.O. Starinets, Transport peak in the thermal spectral function of \( \mathcal{N} \) = 4 supersymmetric Yang-Mills plasma at intermediate coupling, Phys. Rev. Lett. 121 (2018) 191603 [arXiv:1806.10997] [INSPIRE].ADSCrossRefGoogle Scholar
  134. [134]
    T.W. Grimm, T.G. Pugh and M. Weissenbacher, On M-theory fourfold vacua with higher curvature terms, Phys. Lett. B 743 (2015) 284 [arXiv:1408.5136] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  135. [135]
    S. Caron-Huot et al., Photon and dilepton production in supersymmetric Yang-Mills plasma, JHEP 12 (2006) 015 [hep-th/0607237] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Alina Czajka
    • 1
    • 2
  • Keshav Dasgupta
    • 1
    Email author
  • Charles Gale
    • 1
  • Sangyong Jeon
    • 1
  • Aalok Misra
    • 3
  • Michael Richard
    • 4
  • Karunava Sil
    • 5
  1. 1.Department of PhysicsMcGill UniversityMontréalCanada
  2. 2.Institute of PhysicsJan Kochanowski UniversityKielcePoland
  3. 3.Department of PhysicsIndian Institute of Technology RoorkeeUttarakhandIndia
  4. 4.John Abbott CollegeQuébecCanada
  5. 5.Department of PhysicsIndian Institute of Technology RoparRupnagarIndia

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