Adding new branches to the “Christmas tree” of the quasinormal spectrum of black branes

  • Sašo GrozdanovEmail author
  • Andrei O. Starinets
Open Access
Regular Article - Theoretical Physics


In holography, quasinormal spectra of black branes coincide with the poles of retarded finite-temperature correlation functions of a dual quantum field theory in the limit of infinite number of relevant degrees of freedom such as colours. For asymptotically antide Sitter backgrounds, the spectra form a characteristic pattern in the complex frequency plane, colloquially known as the “Christmas tree”. At infinite coupling, the tree has only one pair of branches. At large but finite coupling, the branches become more dense and lift up towards the real axis, consistent with the expectation of forming a branch cut in the limit of zero coupling. However, it is known that at zero coupling, the corresponding correlators generically have not one but multiple branch cuts separated by intervals proportional to the Matsubara frequency. This suggests the existence of multiple branches of the “Christmas tree” spectrum in dual gravity. In this note, we show numerically how these additional branches of the spectrum can emerge from the dual gravitational action with higher-derivative terms. This phenomenon appears to be robust, yet, reproducing the expected weak coupling behaviour of the correlators quantitatively implies the existence of certain constraints on the coefficients of the higher-derivative terms of the dual gravity theory.


AdS-CFT Correspondence Black Holes in String Theory Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) 


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]
    S. Kalyana Rama and B. Sathiapalan, On the role of chaos in the AdS/CFT connection, Mod. Phys. Lett. A 14 (1999) 2635 [hep-th/9905219] [INSPIRE].
  2. [2]
    G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
  3. [3]
    D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    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
  5. [5]
    A.O. Starinets, Quasinormal modes of near extremal black branes, Phys. Rev. D 66 (2002) 124013 [hep-th/0207133] [INSPIRE].
  6. [6]
    A. Núñez and A.O. Starinets, AdS/CFT correspondence, quasinormal modes and thermal correlators in N = 4 SYM, Phys. Rev. D 67 (2003) 124013 [hep-th/0302026] [INSPIRE].
  7. [7]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
  8. [8]
    E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    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] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S.A. Hartnoll and S.P. Kumar, AdS black holes and thermal Yang-Mills correlators, JHEP 12 (2005) 036 [hep-th/0508092] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    G.D. Moore, Stress-stress correlator in ϕ 4 theory: poles or a cut?, JHEP 05 (2018) 084 [arXiv:1803.00736] [INSPIRE].
  12. [12]
    P. Romatschke, Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions, Eur. Phys. J. C 76 (2016) 352 [arXiv:1512.02641] [INSPIRE].
  13. [13]
    A. Kurkela and U.A. Wiedemann, Analytic structure of nonhydrodynamic modes in kinetic theory, arXiv:1712.04376 [INSPIRE].
  14. [14]
    S. Grozdanov, K. Schalm and V. Scopelliti, Kinetic theory for classical and quantum many-body chaos, Phys. Rev. E 99 (2019) 012206 [arXiv:1804.09182] [INSPIRE].
  15. [15]
    L.G. Yaffe, private communication (2002).Google Scholar
  16. [16]
    S.A. Stricker, Holographic thermalization in N = 4 Super Yang-Mills theory at finite coupling, Eur. Phys. J. C 74 (2014) 2727 [arXiv:1307.2736] [INSPIRE].
  17. [17]
    S. Waeber, A. Schäfer, A. Vuorinen and L.G. Yaffe, Finite coupling corrections to holographic predictions for hot QCD, JHEP 11 (2015) 087 [arXiv:1509.02983] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S. Grozdanov, N. Kaplis and A.O. Starinets, From strong to weak coupling in holographic models of thermalization, JHEP 07 (2016) 151 [arXiv:1605.02173] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    A. Buchel, Sensitivity of holographic \( \mathcal{N}=4 \) SYM plasma hydrodynamics to finite coupling corrections, Phys. Rev. D 98 (2018) 061901 [arXiv:1807.05457] [INSPIRE].
  20. [20]
    S. Grozdanov and A.O. Starinets, Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid, JHEP 03 (2017) 166 [arXiv:1611.07053] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    R.A. Davison and A.O. Starinets, Holographic zero sound at finite temperature, Phys. Rev. D 85 (2012) 026004 [arXiv:1109.6343] [INSPIRE].
  22. [22]
    S. Grozdanov and N. Poovuttikul, Generalized global symmetries in states with dynamical defects: The case of the transverse sound in field theory and holography, Phys. Rev. D 97 (2018) 106005 [arXiv:1801.03199] [INSPIRE].
  23. [23]
    N.I. Gushterov, A. O’Bannon and R. Rodgers, Holographic Zero Sound from Spacetime-Filling Branes, JHEP 10 (2018) 076 [arXiv:1807.11327] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    N.I. Gushterov, Quasinormal Modes and Correlators in the Shear Channel of Spacetime-Filling Branes, arXiv:1807.11390 [INSPIRE].
  25. [25]
    S. Grozdanov and W. van der Schee, Coupling Constant Corrections in a Holographic Model of Heavy Ion Collisions, Phys. Rev. Lett. 119 (2017) 011601 [arXiv:1610.08976] [INSPIRE].
  26. [26]
    B.S. DiNunno, S. Grozdanov, J.F. Pedraza and S. Young, Holographic constraints on Bjorken hydrodynamics at finite coupling, JHEP 10 (2017) 110 [arXiv:1707.08812] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Grozdanov, A. Lucas and N. Poovuttikul, Holography and hydrodynamics with weakly broken symmetries, arXiv:1810.10016 [INSPIRE].
  28. [28]
    S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [hep-th/9805156] [INSPIRE].
  29. [29]
    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].
  30. [30]
    S. Grozdanov and A.O. Starinets, Zero-viscosity limit in a holographic Gauss-Bonnet liquid, Theor. Math. Phys. 182 (2015) 61 [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    S. Grozdanov and A.O. Starinets, On the universal identity in second order hydrodynamics, JHEP 03 (2015) 007 [arXiv:1412.5685] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    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].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  2. 2.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.

Personalised recommendations