Quasinormal modes and holography

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Abstract

Quasinormal frequencies of electromagnetic and gravitational perturbations in asymptotically AdS spacetime can be identified with poles of the corresponding real-time Green's functions in a holographically dual finite temperature field theory. The quasinormal modes are defined for gauge-invariant quantities which obey incoming-wave boundary condition at the horizon and Dirichlet condition at the boundary. As an application, we explicitly find poles of retarded correlation functions of R-symmetry currents and the energy-momentum tensor in strongly coupled finite temperature N=4 supersymmetric SU(Nc) Yang-Mills theory in the limit of large Nc.

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Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics

A Starinets, D. Son, P. Kovtun (2004)

The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of \(\hbar/4\pi k_B\) for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

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Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma

, , (2010)

Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity \eta of the finite-temperature N=4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find \eta=\pi/8 N^2T^3. We conjecture that for finite 't Hooft coupling (g_YM)^2N the shear viscosity is \eta=f((g_YM)^2N) N^2T^3, where f(x) is a monotonic function that decreases from O(x^{-2}\ln^{-1}(1/x)) at small x to \pi/8 when x\to\infty.

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Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium

, (2009)

We investigate the decay of a scalar field outside a Schwarzschild anti de Sitter black hole. This is determined by computing the complex frequencies associated with quasinormal modes. There are qualitative differences from the asymptotically flat case, even in the limit of small black holes. In particular, for a given angular dependence, the decay is always exponential - there are no power law tails at late times. In terms of the AdS/CFT correspondence, a large black hole corresponds to an approximately thermal state in the field theory, and the decay of the scalar field corresponds to the decay of a perturbation of this state. Thus one obtains the timescale for the approach to thermal equilibrium. We compute these timescales for the strongly coupled field theories in three, four, and six dimensions which are dual to string theory in asymptotically AdS spacetimes.