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Holography and the sound of criticality

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 AdS$_4$ 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 AdS$_{2}$ 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.