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## From AdS/CFT correspondence to hydrodynamics

Venue: | J. High Energy Phys |

Citations: | 181 - 8 self |

### Citations

5612 | The Large N Limit of Superconformal Field Theories and Supergravity
- Maldacena
- 1998
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Citation Context ... A. Gauge transformations 13 1. Introduction Any finite-temperature medium conducts sound. This simple fact provides a nontrivial method to check the conjecture of gauge theory/gravity correspondence =-=[1]-=- at finite temperatures. Indeed, if one can compute the correlators of the components of the stress-energy tensor T µν using an AdS/CFT prescription [2, 3], one should recognize in them a pole corresp... |

2748 |
Gauge theory correlators from non-critical string theory,” Phys
- Gubser, Klebanov, et al.
- 1998
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Citation Context ...njecture of gauge theory/gravity correspondence [1] at finite temperatures. Indeed, if one can compute the correlators of the components of the stress-energy tensor T µν using an AdS/CFT prescription =-=[2, 3]-=-, one should recognize in them a pole corresponding to sound-wave propagation, expected from hydrodynamics [4]. The techniques necessary for performing this check have been developed in refs. [5, 6]. ... |

449 |
Quantum mechanics (Pergamon
- Landau, Lifshitz
- 1965
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Citation Context ...ators of the components of the stress-energy tensor T µν using an AdS/CFT prescription [2, 3], one should recognize in them a pole corresponding to sound-wave propagation, expected from hydrodynamics =-=[4]-=-. The techniques necessary for performing this check have been developed in refs. [5, 6]. In ref. [5] we formulated a prescription for computing the retarded Green’s functions from gravity. In ref. [6... |

382 | Anti de Sitter space and holography
- Witten
- 1998
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Citation Context ...njecture of gauge theory/gravity correspondence [1] at finite temperatures. Indeed, if one can compute the correlators of the components of the stress-energy tensor T µν using an AdS/CFT prescription =-=[2, 3]-=-, one should recognize in them a pole corresponding to sound-wave propagation, expected from hydrodynamics [4]. The techniques necessary for performing this check have been developed in refs. [5, 6]. ... |

265 |
Starinets, Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma
- Policastro, Son, et al.
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Citation Context ...e have not checked the Ward identities in this approximation. – 11 –dispersion relation is − 2i 3 η ǫ + P q2 = − iq2 6πT (3.24) where we have used the value of η/(ǫ + P) = (4πT) −1 computed in refs. =-=[11, 6]-=-. 6 Re GR 4 2 0 ω -2 -4 -6 0 0.02 0.04 0.06 0.08 0.1 Figure 1: The real part of the correlator GR tt, tt ( , ) as a function of (real) at = 1/10. 12 Im G R 10 8 6 4 2 0 0 0.02 0.04 0.06 0.08 0.1 ω Fig... |

132 |
Tseytlin, “Coupling constant dependence
- Gubser, Klebanov, et al.
- 1998
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Citation Context ... 2−3 2 ) ( 3(H 0 tt) 2 − 12(H 0 tz) 2 + 2H 0 ttH 0 ii + 2H 0 zzH 0 aa − (H 0 zz) 2 ) ] . (3.16) The constant term, −π 2 N 2 T 4 V4/8, is the free energy density (i.e., the pressure with a minus sign) =-=[10]-=-, times the four-volume. 3.3 The correlators As noticed in ref. [5], in general it is not possible to calculate the Minkowski twopoint Green’s function by differentiating the gravitational action with... |

42 | The hydrodynamics of M-theory
- Herzog
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Citation Context ...rodynamic regime of the correlators in N = 4 SYM theory at finite temperature, which is another testimony to the validity of the correspondence. The calculations of ref. [6] has been extended in ref. =-=[12]-=- to M2 and M5 branes of M-theory, where hydrodynamic behavior is also observed, although the worldvolume theories in these cases are not well understood. 6 It should be possible to find the sound wave... |

28 |
Entropy and temperature of black 3-branes
- Gubser, Klebanov, et al.
- 1996
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Citation Context ...d 4 x √ −h ⎦ . (3.14) Here κ10 = √ 8πG is the ten-dimensional gravitational constant, related to the parameter R of the non-extremal geometry and the number N of coincident branes by κ10 = 2π2√πR4 /N =-=[8]-=-. Following ref. [9], we choose a = −6/R to cancel the volume divergence in eq. (3.14). On shell, the action reduces to the surface terms, S = Shorizon + Sǫ, where Sǫ = π2 N 2 T 4 8 ∫ d 4 x [ −1 + 1 2... |

10 |
On the absorption by near-extremal black branes
- Policastro, Starinets
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Citation Context ...variant derivative in eq. (A.2) is taken with respect to the full metric, the residual 6 Methods for computing the absorption cross section by non-extremal D- and M-branes were discussed in detail in =-=[13]-=-. – 13 –gauge transformations are dependent on the fluctuations hµν. It will be useful to introduce a book-keeping parameter κ associated with the fluctuations hµν and expand both ξµ and the Christof... |

6 |
D = 4 super Yang-Mills, D = 5 gauged supergravity and
- Liu, Tseytlin
- 1998
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Citation Context ...) Here κ10 = √ 8πG is the ten-dimensional gravitational constant, related to the parameter R of the non-extremal geometry and the number N of coincident branes by κ10 = 2π2√πR4 /N [8]. Following ref. =-=[9]-=-, we choose a = −6/R to cancel the volume divergence in eq. (3.14). On shell, the action reduces to the surface terms, S = Shorizon + Sǫ, where Sǫ = π2 N 2 T 4 8 ∫ d 4 x [ −1 + 1 2 (3Htt + Hii) + 1 ( ... |

2 | Hydrodynamic fluctuations in relativistic theories - Yaffe - 1992 |