Longitudinal sound and diffusion in holographic massive gravity

  • Martin Ammon
  • Matteo BaggioliEmail author
  • Séan Gray
  • Sebastian Grieninger
Open Access
Regular Article - Theoretical Physics


We consider a simple class of holographic massive gravity models for which the dual field theories break translational invariance spontaneously. We study, in detail, the longitudinal sector of the quasi-normal modes at zero charge density. We identify three hydrodynamic modes in this sector: a pair of sound modes and one diffusion mode. We numerically compute the dispersion relations of the hydrodynamic modes. The obtained speed and the attenuation of the sound modes are in agreement with the hydrodynamic predictions. On the contrary, we surprisingly find disagreement in the case of the diffusive mode; its diffusion constant extracted from the quasi-normal mode data does not agree with the expectations from hydrodynamics. We confirm our numerical results using ana- lytic tools in the decoupling limit and we comment on some possible reasons behind the disagreement. Finally, we extend the analysis of the collective longitudinal modes beyond the hydrodynamic limit by displaying the dynamics of the higher quasi-normal modes at large frequencies and momenta.


Holography and condensed matter physics (AdS/CMT) Space-Time Sym- metries 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


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Theoretisch-Physikalisches InstitutJenaGermany
  2. 2.Instituto de Fisica Teorica UAM/CSICMadridSpain
  3. 3.Department of PhysicsUniversity of WashingtonSeattleU.S.A.

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