Bosonic excitations of the AdS4 Reissner-Nordstrom black hole

TL;DR

This paper analyzes the long-lived excitations in a strongly-coupled field theory dual to an AdS4 Reissner-Nordstrom black hole, revealing temperature-dependent behaviors of sound and diffusion modes in charge and energy density correlators.

Contribution

It provides a detailed study of the spectral functions and pole structures of correlators in the dual field theory, highlighting differences from Fermi liquid zero sound and temperature effects.

Findings

Sound attenuation is temperature-independent for T<ermi; decreases as 1/T for T>ermi.

Energy density spectral function is dominated by sound mode at all temperatures.

Charge density spectral function crosses over from sound to diffusion dominance with increasing temperature.

Abstract

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-Nordstrom black hole. For small momenta q<<\mu, 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 \mu=0 hydrodynamic charge diffusion mode. As the temperature is raised in the range T\lesssim\mu, the sound attenuation shows no significant temperature dependence. When T\gtrsim\mu, it quickly approaches the \mu=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 \mu^2/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<<\mu.