Abstract
We investigate the analytic structure of thermal energy-momentum tensor correlators at large but finite coupling in quantum field theories with gravity duals. We compute corrections to the quasinormal spectra of black branes due to the presence of higher derivative $R^2$ and $R^4$ terms in the action, focusing on the dual to $\mathcal{N}=4$ SYM theory and Gauss-Bonnet gravity. We observe the appearance of new poles in the complex frequency plane at finite coupling. The new poles interfere with hydrodynamic poles of the correlators leading to the breakdown of hydrodynamic description at a coupling-dependent critical value of the wave-vector. The dependence of the critical wave vector on the coupling implies that the range of validity of the hydrodynamic description increases monotonically with the coupling. The behavior of the quasinormal spectrum at large but finite coupling may be contrasted with the known properties of the hierarchy of relaxation times determined by the spectrum of a linearized kinetic operator at weak coupling. We find that the ratio of a transport coefficient such as viscosity to the relaxation time determined by the fundamental non-hydrodynamic quasinormal frequency changes rapidly in the vicinity of infinite coupling but flattens out for weaker coupling, suggesting an extrapolation from strong coupling to the kinetic theory result. We note that the behavior of the quasinormal spectrum is qualitatively different depending on whether the ratio of shear viscosity to entropy density is greater or less than the universal, infinite coupling value of $\hbar/4\pi k_B$. In the former case, the density of poles increases, indicating a formation of branch cuts in the weak coupling limit, and the spectral function shows the appearance of narrow peaks. We also discuss the relation of the viscosity-entropy ratio to conjectured bounds on relaxation time in quantum systems.
Highlights
Nuclear matter produced in heavy ion collisions at RHIC and LHC appears to be well described by relativistic fluid dynamics at the time shortly after the collision, i.e. for t > τH, where the “hydrodynamization” time τH is of the order of 1 − 2 fm/c [1,2,3,4,5,6]
The behavior of the quasinormal spectrum at large but finite coupling may be contrasted with the known properties of the hierarchy of relaxation times determined by the spectrum of a linearized kinetic operator at weak coupling
We find that the ratio of a transport coefficient such as viscosity to the relaxation time determined by the fundamental non-hydrodynamic quasinormal frequency changes rapidly in the vicinity of infinite coupling but flattens out for weaker coupling, suggesting an extrapolation from strong coupling to the kinetic theory result
Summary
Nuclear matter produced in heavy ion collisions at RHIC and LHC appears to be well described by relativistic fluid dynamics at the time shortly after the collision, i.e. for t > τH , where the “hydrodynamization” time τH is of the order of 1 − 2 fm/c [1,2,3,4,5,6]. Recent studies (including sophisticated numerical general relativity approaches) of equilibration processes in the dual gravity models [24,25,26,27,28,29,30,31,32,33] reveal that the hydrodynamic stage of evolution is reached by a strongly coupled system long before the pressure gradients become small and that the relevant time scales are essentially determined by the lowest quasinormal frequency, even for non-conformal backgrounds [31, 34,35,36,37,38]. Extrapolating kinetic theory results to the regime of intermediate coupling was the subject of recent investigation by Romatschke [39] In holography, these questions can be studied by computing coupling constant corrections to the full quasinormal spectra using the appropriate higher derivative terms in dual gravity. Some technical issues and comments about our numerical procedures appear in the appendices
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