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Holography and the sound of criticality. (English) Zbl 1291.81242
Summary: 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.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81V17 Gravitational interaction in quantum theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T28 Thermal quantum field theory
83C57 Black holes
82B27 Critical phenomena in equilibrium statistical mechanics
76Q05 Hydro- and aero-acoustics
65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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