Back reaction effects on the dynamics of heavy probes in heavy quark cloud

  • Shankhadeep Chakrabortty
  • Tanay K. Dey
Open Access
Regular Article - Theoretical Physics


We holographically study the effect of back reaction on the hydrodynamical properties of \( \mathcal{N}=4 \) strongly coupled super Yang-Mills (SYM) thermal plasma. The back reaction we consider arises from the presence of static heavy quarks uniformly distributed over \( \mathcal{N}=4 \) SYM plasma. In order to study the hydrodynamical properties, we use heavy quark as well as heavy quark-antiquark bound state as probes and compute the jet quenching parameter, screening length and binding energy. We also consider the rotational dynamics of heavy probe quark in the back-reacted plasma and analyse associated energy loss. We observe that the presence of back reaction enhances the energy-loss in the thermal plasma. Finally, we show that there is no effect of angular drag on the rotational motion of quark-antiquark bound state probing the back reacted thermal plasma.


Gauge-gravity correspondence AdS-CFT Correspondence 


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.


  1. [1]
    PHENIX collaboration, K. Adcox et al., 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].
  2. [2]
    STAR collaboration, J. Adams et al., Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [INSPIRE].
  3. [3]
    B.B. Back et al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757 (2005) 28 [nucl-ex/0410022] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    E. Shuryak, Physics of strongly coupled quark-gluon plasma, Prog. Part. Nucl. Phys. 62 (2009) 48 [arXiv:0807.3033] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    E.V. Shuryak, What RHIC experiments and theory tell us about properties of quark-gluon plasma?, Nucl. Phys. A 750 (2005) 64 [hep-ph/0405066] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B 483 (1997) 291 [hep-ph/9607355] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    K.J. Eskola, H. Honkanen, C.A. Salgado and U.A. Wiedemann, The fragility of high-p T hadron spectra as a hard probe, Nucl. Phys. A 747 (2005) 511 [hep-ph/0406319] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    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] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    G. Policastro, D.T. Son and A.O. Starinets, Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    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
  14. [14]
    A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    D. Teaney, The effects of viscosity on spectra, elliptic flow and HBT radii, Phys. Rev. C 68 (2003) 034913 [nucl-th/0301099] [INSPIRE].ADSGoogle Scholar
  16. [16]
    S.K. Chakrabarti, S. Chakrabortty and S. Jain, Proof of universality of electrical conductivity at finite chemical potential, JHEP 02 (2011) 073 [arXiv:1011.3499] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  17. [17]
    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  18. [18]
    U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    R.-G. Cai, S. He and D. Li, A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system, JHEP 03 (2012) 033 [arXiv:1201.0820] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  20. [20]
    C.P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L.G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    K.B. Fadafan, H. Liu, K. Rajagopal and U.A. Wiedemann, Stirring Strongly Coupled Plasma, Eur. Phys. J. C 61 (2009) 553 [arXiv:0809.2869] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    C. Athanasiou, P.M. Chesler, H. Liu, D. Nickel and K. Rajagopal, Synchrotron radiation in strongly coupled conformal field theories, Phys. Rev. D 81 (2010) 126001 [Erratum ibid. D 84 (2011) 069901] [arXiv:1001.3880] [INSPIRE].
  24. [24]
    H. Liu, K. Rajagopal and U.A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett. 97 (2006) 182301 [hep-ph/0605178] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    H. Liu, K. Rajagopal and U.A. Wiedemann, An AdS/CFT Calculation of Screening in a Hot Wind, Phys. Rev. Lett. 98 (2007) 182301 [hep-ph/0607062] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J. de Boer, V.E. Hubeny, M. Rangamani and M. Shigemori, Brownian motion in AdS/CFT, JHEP 07 (2009) 094 [arXiv:0812.5112] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  27. [27]
    D.T. Son and D. Teaney, Thermal Noise and Stochastic Strings in AdS/CFT, JHEP 07 (2009) 021 [arXiv:0901.2338] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    E. Caceres and A. Guijosa, Drag force in charged N = 4 SYM plasma, JHEP 11 (2006) 077 [hep-th/0605235] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    T. Matsuo, D. Tomino and W.-Y. Wen, Drag force in SYM plasma with B field from AdS/CFT, JHEP 10 (2006) 055 [hep-th/0607178] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    M. Chernicoff, D. Fernandez, D. Mateos and D. Trancanelli, Drag force in a strongly coupled anisotropic plasma, JHEP 08 (2012) 100 [arXiv:1202.3696] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. Chernicoff and A. Guijosa, Acceleration, Energy Loss and Screening in Strongly-Coupled Gauge Theories, JHEP 06 (2008) 005 [arXiv:0803.3070] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    C.P. Herzog and A. Vuorinen, Spinning Dragging Strings, JHEP 10 (2007) 087 [arXiv:0708.0609] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    J.F. Vazquez-Poritz, Drag force at finite ’t Hooft coupling from AdS/CFT, arXiv:0803.2890 [INSPIRE].
  34. [34]
    S. Roy, Holography and drag force in thermal plasma of non-commutative Yang-Mills theories in diverse dimensions, Phys. Lett. B 682 (2009) 93 [arXiv:0907.0333] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    S. Chakrabortty, Dissipative force on an external quark in heavy quark cloud, Phys. Lett. B 705 (2011) 244 [arXiv:1108.0165] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R.-G. Cai, S. Chakrabortty, S. He and L. Li, Some aspects of QGP phase in a hQCD model, JHEP 02 (2013) 068 [arXiv:1209.4512] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    J. Casalderrey-Solana and D. Teaney, Heavy quark diffusion in strongly coupled N = 4 Yang-Mills, Phys. Rev. D 74 (2006) 085012 [hep-ph/0605199] [INSPIRE].ADSGoogle Scholar
  38. [38]
    M. Chernicoff, D. Fernandez, D. Mateos and D. Trancanelli, Jet quenching in a strongly coupled anisotropic plasma, JHEP 08 (2012) 041 [arXiv:1203.0561] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    M. Chernicoff, D. Fernandez, D. Mateos and D. Trancanelli, Quarkonium dissociation by anisotropy, JHEP 01 (2013) 170 [arXiv:1208.2672] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    A. Guijosa and J.F. Pedraza, Early-Time Energy Loss in a Strongly-Coupled SYM Plasma, JHEP 05 (2011) 108 [arXiv:1102.4893] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  41. [41]
    K.B. Fadafan and H. Soltanpanahi, Energy loss in a strongly coupled anisotropic plasma, JHEP 10 (2012) 085 [arXiv:1206.2271] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S. Chakraborty and N. Haque, Holographic quark-antiquark potential in hot, anisotropic Yang-Mills plasma, Nucl. Phys. B 874 (2013) 821 [arXiv:1212.2769] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  43. [43]
    S.S. Gubser, Momentum fluctuations of heavy quarks in the gauge-string duality, Nucl. Phys. B 790 (2008) 175 [hep-th/0612143] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    J. Casalderrey-Solana and D. Teaney, Transverse Momentum Broadening of a Fast Quark in a N = 4 Yang-Mills Plasma, JHEP 04 (2007) 039 [hep-th/0701123] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    D. Giataganas, Probing strongly coupled anisotropic plasma, JHEP 07 (2012) 031 [arXiv:1202.4436] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    A.N. Atmaja, Holographic Brownian Motion in Two Dimensional Rotating Fluid, JHEP 04 (2013) 021 [arXiv:1212.5319] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    W. Fischler, J.F. Pedraza and W. Tangarife Garcia, Holographic Brownian Motion in Magnetic Environments, JHEP 12 (2012) 002 [arXiv:1209.1044] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Langevin diffusion of heavy quarks in non-conformal holographic backgrounds, JHEP 12 (2010) 088 [arXiv:1006.3261] [INSPIRE].CrossRefMATHGoogle Scholar
  49. [49]
    P. Banerjee and B. Sathiapalan, Holographic Brownian Motion in 1+1 Dimensions, Nucl. Phys. B 884 (2014) 74 [arXiv:1308.3352] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  50. [50]
    G.C. Giecold, E. Iancu and A.H. Mueller, Stochastic trailing string and Langevin dynamics from AdS/CFT, JHEP 07 (2009) 033 [arXiv:0903.1840] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  51. [51]
    S. Chakrabortty, S. Chakraborty and N. Haque, Brownian motion in strongly coupled, anisotropic Yang-Mills plasma: A holographic approach, Phys. Rev. D 89 (2014) 066013 [arXiv:1311.5023] [INSPIRE].ADSGoogle Scholar
  52. [52]
    S. Chakrabortty and B. Sathiapalan, Schwinger Effect and Negative Differential Conductivity in Holographic Models, Nucl. Phys. B 890 (2014) 241 [arXiv:1409.1383] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  53. [53]
    F. Bigazzi, A.L. Cotrone, J. Mas, D. Mayerson and J. Tarrio, D3-D7 quark-gluon Plasmas at Finite Baryon Density, JHEP 04 (2011) 060 [arXiv:1101.3560] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  54. [54]
    S.P. Kumar, Heavy quark density in N = 4 SYM: from hedgehog to Lifshitz spacetimes, JHEP 08 (2012) 155 [arXiv:1206.5140] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  56. [56]
    C. Núñez, A. Paredes and A.V. Ramallo, Unquenched Flavor in the Gauge/Gravity Correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  57. [57]
    A. Kovner and U.A. Wiedemann, Gluon radiation and parton energy loss, hep-ph/0304151 [INSPIRE].
  58. [58]
    A. Kovner and U.A. Wiedemann, Eikonal evolution and gluon radiation, Phys. Rev. D 64 (2001) 114002 [hep-ph/0106240] [INSPIRE].ADSGoogle Scholar
  59. [59]
    Y. Hatta, E. Iancu, A.H. Mueller and D.N. Triantafyllopoulos, Radiation by a heavy quark in N = 4 SYM at strong coupling, Nucl. Phys. B 850 (2011) 31 [arXiv:1102.0232] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  60. [60]
    M. Ali-Akbari and U. Gürsoy, Rotating strings and energy loss in non-conformal holography, JHEP 01 (2012) 105 [arXiv:1110.5881] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  61. [61]
    E. Kiritsis and G. Pavlopoulos, Heavy quarks in a magnetic field, JHEP 04 (2012) 096 [arXiv:1111.0314] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    K. Peeters, J. Sonnenschein and M. Zamaklar, Holographic melting and related properties of mesons in a quark gluon plasma, Phys. Rev. D 74 (2006) 106008 [hep-th/0606195] [INSPIRE].ADSGoogle Scholar
  63. [63]
    M. Chernicoff, J.A. Garcia and A. Guijosa, The Energy of a Moving Quark-Antiquark Pair in an N = 4 SYM Plasma, JHEP 09 (2006) 068 [hep-th/0607089] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  64. [64]
    M. Chernicoff and A. Guijosa, Energy Loss of Gluons, Baryons and k-Quarks in an N = 4 SYM Plasma, JHEP 02 (2007) 084 [hep-th/0611155] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  65. [65]
    C. Athanasiou, H. Liu and K. Rajagopal, Velocity Dependence of Baryon Screening in a Hot Strongly Coupled Plasma, JHEP 05 (2008) 083 [arXiv:0801.1117] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    H. Liu, K. Rajagopal and U.A. Wiedemann, Wilson loops in heavy ion collisions and their calculation in AdS/CFT, JHEP 03 (2007) 066 [hep-ph/0612168] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    A. Mikhailov, Nonlinear waves in AdS/CFT correspondence, hep-th/0305196 [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Van Swinderen Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of PhysicsSikkim Manipal Institute of TechnologyEast SikkimIndia

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