Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index 3 − d for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.
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V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, in Theoretical Advanced Study Institute in Elementary Particle Physics. String theory and its applications: from meV to the Planck scale, (2012), p. 348 [arXiv:1107.5780] [INSPIRE].
S.M. Diles, L.A.H. Mamani, A.S. Miranda and V.T. Zanchin, Third-order relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma, JHEP 05 (2020) 019 [arXiv:1909.05199] [INSPIRE].
T. He, R. Loganayagam, M. Rangamani and J. Virrueta, Sound and charge diffusion in holographic plasmas, work in progress (2022).
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He, T., Loganayagam, R., Rangamani, M. et al. The timbre of Hawking gravitons: an effective description of energy transport from holography. J. High Energ. Phys. 2022, 92 (2022). https://doi.org/10.1007/JHEP09(2022)092