We study the long-lived modes of the charge density and energy density correlators in the strongly-coupled, finite density field theory dual to the AdS4 Reissner-Nordström black hole. For small momenta q ≪ μ, these correlators contain a pole due to sound propagation, as well as a pole due to a long-lived, purely imaginary mode analogous to the μ = 0 hydrodynamic charge diffusion mode. As the temperature is raised in the range T ≲ μ, the sound attenuation shows no significant temperature dependence. When T & μ, it quickly approaches the μ = 0 hydrodynamic result where it decreases like 1=T . It does not share any of the temperature-dependent properties of the 'zero sound' of Landau Fermi liquids observed in the strongly-coupled D3/D7 field theory. For such small momenta, the energy density spectral function is dominated by the sound mode at all temperatures, whereas the charge density spectral function undergoes a crossover from being dominated by the sound mode at low temperatures to being dominated by the diffusion mode when T ∼ μ2/q. This crossover occurs due to the changing residue at each pole. We also compute the momentum dependence of these spectral functions and their corresponding long-lived poles at fixed, low temperatures T ≪ μ.
- Black holes in string theory
- Gauge-gravity correspondence
- Holography and condensed matter physics (AdS/CMT)
ASJC Scopus subject areas
- Nuclear and High Energy Physics