Relativistic viscous hydrodynamics, conformal invariance, and holography

Journal of High Energy Physics (Impact Factor: 6.11). 04/2008; 2008(04):100. DOI: 10.1088/1126-6708/2008/04/100
Source: arXiv


We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled = 4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Müller-Israel-Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.

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    • "Linearization of the resulting theory reveals a single, purely decaying, non-hydrodynamic mode in addition to hydrodynamic modes [1]. This mode (which we refer to as the MIS mode) decays on a scale set by τ Π . "
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    ABSTRACT: It has recently been understood that the hydrodynamic series generated by the M\"uller-Israel-Stewart theory is divergent, and that this large order behaviour is consistent with the theory of resurgence. Furthermore, it was observed, that the physical origin of this is the presence of a purely damped nonhydrodynamic mode. It is very interesting to ask whether this picture persists in cases where the spectrum of nonhydrodynamic modes is richer. We take the first step in this direction by considering the simplest hydrodynamic theory which, instead of the purely damped mode, contains a pair of nonhydrodynamic modes of complex conjugate frequencies. This mimics the pattern of black brane quasinormal modes which appear on the gravity side of the AdS/CFT description of \symm\ plasma. We find that the resulting hydrodynamic series is divergent in a way consistent with resurgence and precisely encodes information about the nonhydrodynamic modes of the theory.
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    • "Second order transport coefficients of this system were calculated in [41]. The framework that investigates transport properties of a fluid via its corresponding gravity is called the fluid/gravity correspondence, and the most notable feature in above works [39] [40] [41] is the use of Green-Kubo formula, thus one may call it the Green-Kubo formalism of fluid/gravity correspondence. While the Green-Kubo formalism becomes popular in extracting transport properties of liquid-like plasma 2 , another systematical and powerful formalism—the boundary derivative expansion (BDE) formalism [43] [44] has been developed. "
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    ABSTRACT: We develop the framework of boundary derivative expansion (BDE) formalism of fluid/gravity correspondence in compactified D4-brane system, which is a non- conformal background used in top-down holographic QCD models. Such models contain the D4-D6 model and the Sakai-Sugimoto (SS) model, with the background of the compactified black D4 branes under the near horizon limit. By using the dimensional reduction technique, we derive a 5D Einstein gravity minimally cou- pled with 3 scalar fields from the 10D D4-brane background. Following the BDE formalism of fluid/gravity correspondence in the conformal background, we direct- ly derive all the first order transport coefficients for non-conformal gluonic matter. The results of the ratio of the bulk to shear viscosity and the sound speed agree with those obtained from the Green-Kubo method. This agreement guarantees the validity of the BDE formalism of fluid/gravity duality in the non-conformal D-brane background, which can be used to calculate the second order transport coefficients in non-conformal background.
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    • "At finite temperature and in the long wavelength regime, the dual field theory can be effectively described by fluid mechanics and it can be related to black holes in AdS space-time. The fluid/gravity correspondence was first studied using linear response theory [5] [6] [7] [8]. "
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    ABSTRACT: Non-equilibrium black hole horizons are considered in scaling theories with generic Lifshitz invariance and an unbroken U(1) symmetry. There is also a special form of hyperscaling violation associated with a non-trivial conduction exponent. The boundary stress tensor is computed and renormalized and the associated hydrodynamic equations derived. Upon a non-trivial redefinition of boundary sources associated with the U(1) gauge field, the equations are mapped to the standard non-relativistic hydrodynamics equations coupled to a mass current and an external Newton potentials in accordance with the general theory of [arXiv:1502.00228]. The shear viscosity to entropy ratio is the same as in the relativistic case.
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