Journal of High Energy Physics

, 2019:32 | Cite as

Exotic holographic dispersion

  • U. GranEmail author
  • M. Tornsö
  • T. Zingg
Open Access
Regular Article - Theoretical Physics


For strongly interacting systems, where perturbation theory is not applicable, holographic duality is a powerful framework for computing e.g. dispersion relations. Using the standard Reissner-Nordström black hole as a holographic model for a (strange) metal, we obtain exotic dispersion relations for both plasmon modes and quasinormal modes for certain intermediate values of the charge of the black hole.

The obtained dispersion relations show dissipative behavior which we compare to the generic expectations from the Caldeira-Leggett model for quantum dissipation. Based on these considerations, we investigate how holography can predict higher order corrections for strongly coupled physics.


Holography and condensed matter physics (AdS/CMT) AdS-CFT Correspondence Gauge-gravity 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]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    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].
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    U. Gran, M. Tornsö and T. Zingg, Holographic Plasmons, JHEP 11 (2018) 176 [arXiv:1712.05672] [INSPIRE].
  5. [5]
    U. Gran, M. Tornsö and T. Zingg, Plasmons in Holographic Graphene, arXiv:1804.02284 [INSPIRE].
  6. [6]
    D. Pines and P. Nozières, The Theory of Quantum Liquids, W.A. Benjamin Inc., (1966).Google Scholar
  7. [7]
    E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
  8. [8]
    W. Mueck, An improved correspondence formula for AdS/CFT with multitrace operators, Phys. Lett. B 531 (2002) 301 [hep-th/0201100] [INSPIRE].
  9. [9]
    J. Zaanen, Y.-W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, (2015).Google Scholar
  10. [10]
    A.O. Caldeira and A.J. Leggett, Path integral approach to quantum Brownian motion, Physica A 121 (1983) 587.Google Scholar
  11. [11]
    A.O. Caldeira and A.J. Leggett, Quantum tunneling in a dissipative system, Annals Phys. 149 (1983) 374 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Mitrano et al., Singular density fluctuations in the strange metal phase of a copper-oxide superconductor, Proc. Nat. Acad. Sci. 115 (2018) 5392 [arXiv:1708.01929].ADSCrossRefGoogle Scholar
  13. [13]
    L. Alberte, M. Ammon, M. Baggioli, A. Jiménez and O. Pujolàs, Black hole elasticity and gapped transverse phonons in holography, JHEP 01 (2018) 129 [arXiv:1708.08477] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    N. Jokela, G. Lifschytz and M. Lippert, Magnetic effects in a holographic Fermi-like liquid, JHEP 05 (2012) 105 [arXiv:1204.3914] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    B. Wang, C.-Y. Lin and E. Abdalla, Quasinormal modes of Reissner-Nordström anti-de Sitter black holes, Phys. Lett. B 481 (2000) 79 [hep-th/0003295] [INSPIRE].
  16. [16]
    E. Berti and K.D. Kokkotas, Quasinormal modes of Reissner-Nordström-anti-de Sitter black holes: Scalar, electromagnetic and gravitational perturbations, Phys. Rev. D 67 (2003) 064020 [gr-qc/0301052] [INSPIRE].
  17. [17]
    M. Edalati, J.I. Jottar and R.G. Leigh, Holography and the sound of criticality, JHEP 10 (2010) 058 [arXiv:1005.4075] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  18. [18]
    R.A. Davison and N.K. Kaplis, Bosonic excitations of the AdS 4 Reissner-Nordström black hole, JHEP 12 (2011) 037 [arXiv:1111.0660] [INSPIRE].
  19. [19]
    W. Witczak-Krempa and S. Sachdev, Dispersing quasinormal modes in 2+1 dimensional conformal field theories, Phys. Rev. B 87 (2013) 155149 [arXiv:1302.0847] [INSPIRE].
  20. [20]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].
  21. [21]
    V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    S.A. Hartnoll and P. Petrov, Electron star birth: A continuous phase transition at nonzero density, Phys. Rev. Lett. 106 (2011) 121601 [arXiv:1011.6469] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    J. Lucietti, K. Murata, H.S. Reall and N. Tanahashi, On the horizon instability of an extreme Reissner-Nordström black hole, JHEP 03 (2013) 035 [arXiv:1212.2557] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  24. [24]
    S. Aretakis, Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I, Commun. Math. Phys. 307 (2011) 17 [arXiv:1110.2007] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    S. Aretakis, Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II, Annales Henri Poincaré 12 (2011) 1491 [arXiv:1110.2009] [INSPIRE].
  26. [26]
    U. Gran, M. Tornsö and T. Zingg, Holographic Response of Electron Clouds, arXiv:1810.11416 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics, Division for Theoretical PhysicsChalmers University of TechnologyGöteborgSweden
  2. 2.Nordita, Stockholm University and KTH Royal Institute of TechnologyStockholmSweden

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