Holography and the sound of criticality

Abstract

Using gauge/gravity duality techniques, we discuss the sound-channel retarded correlators of vector and tensor conserved currents in a class of (2+1)-dimensional strongly-coupled field theories at zero temperature and finite charge density, assumed to be holographically dual to the extremal Reissner-Nordström AdS4 black hole. Using a combination of analytical and numerical methods, we determine the quasinormal mode spectrum at finite momentum for the coupled gravitational and electromagnetic perturbations, and discuss the appropriate choice of gauge-invariant variables (master fields) in order for the black hole quasinormal frequencies to reproduce the field theory spectrum. We discuss the role of the near horizon AdS2 geometry in determining the low-frequency behavior of retarded correlators in the boundary theory, and comment on the emergence of criticality in the IR. In addition, we establish the existence of a sound mode at zero temperature and compute the speed of sound and sound attenuation constant numerically, obtaining a result consistent with the expectations from the zero temperature limit of hydrodynamics. The dispersion relation of higher resonances is also investigated.