Results 1  10
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44
Nonlinear Fluid Dynamics from Gravity
, 2007
"... Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields – arbitrary functions of the coordinates on the boundary of AdS5 – we use Einstein’s equations together with regularity requ ..."
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Cited by 122 (4 self)
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Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields – arbitrary functions of the coordinates on the boundary of AdS5 – we use Einstein’s equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.
Entanglement entropy in higher derivative holography
, 2013
"... We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena [1] have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. C ..."
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Cited by 22 (4 self)
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We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena [1] have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For GaussBonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in GaussBonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.
Higher Derivative Corrections to Shear Viscosity from Graviton’s Effective Coupling
, 2009
"... The shear viscosity coefficient of strongly coupled boundary gauge theory plasma depends on the horizon value of the effective coupling of transverse graviton moving in black hole background. The proof for the above statement is based on the canonical form of graviton’s action. But in presence of ..."
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Cited by 21 (0 self)
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The shear viscosity coefficient of strongly coupled boundary gauge theory plasma depends on the horizon value of the effective coupling of transverse graviton moving in black hole background. The proof for the above statement is based on the canonical form of graviton’s action. But in presence of generic higher derivative terms in the bulk Lagrangian the action is no longer canonical. We give a procedure to find an effective action for graviton (to first order in coefficient of higher derivative term) in canonical form in presence of any arbitrary higher derivative terms in the bulk. From that effective action we find the effective coupling constant for transverse graviton which in general depends on the radial coordinate r. We also argue that horizon value of this effective coupling is related to the shear viscosity coefficient of the boundary fluid in higher derivative gravity. We explicitly check this procedure for two specific examples: (1) four derivative action and (2) eight derivative action (Weyl 4 term). For both cases we show that our results for shear viscosity coefficient (upto first order in coefficient of higher derivative term) completely agree with the existing results
Higher Derivative Corrections to Locally Black Brane Metrics
 JHEP
"... Abstract: In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the GaussBonnet term (with coefficient α ′) as a toy example. We find the solution to the α ′ corrected Einstein equations to first order in the boundary deri ..."
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Cited by 17 (2 self)
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Abstract: In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the GaussBonnet term (with coefficient α ′) as a toy example. We find the solution to the α ′ corrected Einstein equations to first order in the boundary derivative expansion. This allows us to find the α ′ corrections to the boundary stress tensor in the presence of the GaussBonnet term in the bulk action. We therefore obtain the ratio of shear viscosity to entropy which agrees with other methods of computation in the
Forced Fluid Dynamics from Gravity
, 2008
"... We generalise the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einsteindilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondenc ..."
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Cited by 16 (1 self)
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We generalise the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einsteindilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parametrised by fourvelocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.
Drag force at finite ’t Hooft coupling from AdS/CFT”, arXiv: hepth/0803.2890
"... We find that the drag force for a heavy quark moving through N = 4 SU(N) supersymmetric YangMills plasma is generally enhanced by the leading correction due to finite ’t Hooft coupling. For a bottom quark, the drag force increases by about 50%, whereas for a charm quark it increases by about 5%. We ..."
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Cited by 15 (1 self)
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We find that the drag force for a heavy quark moving through N = 4 SU(N) supersymmetric YangMills plasma is generally enhanced by the leading correction due to finite ’t Hooft coupling. For a bottom quark, the drag force increases by about 50%, whereas for a charm quark it increases by about 5%. We also discuss the drag force for the case of GaussBonnet gravity. 1 Introduction and Summary According to the AdS/CFT correspondence [1], the dynamics of open strings on a fivedimensional AdS black hole background are related to that of partons in the large N and large ’t Hooft coupling limit of fourdimensional N = 4 SU(N) super YangMills theory at finite temperature. There have
Thermodynamics of the MaxwellGaussBonnet antide Sitter Black Hole with Higher Derivative Gauge Corrections,” arXiv:0807.3478 [hepth
"... The local and global thermal phase structure for asymptotically antide Sitter black holes charged under an abelian gauge group, with both GaussBonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric p ..."
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Cited by 15 (0 self)
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The local and global thermal phase structure for asymptotically antide Sitter black holes charged under an abelian gauge group, with both GaussBonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric potential is held fixed. The analysis is performed in an arbitrary number of dimensions, for all three possible horizon topologies spherical, flat or hyperbolic. For spherical horizons, new metastable configurations are exhibited both for the pure GaussBonnet theory as well as the pure higher derivative gauge theory and combinations thereof. In the pure GaussBonnet theory with negative coefficient and five or more spatial dimensions, two locally thermally stable black hole solutions are found for a given temperature. Either one or both of them may be thermally favored over the antide Sitter vacuumcorresponding to a single or a double decay channel for the metastable black hole. Similar metastable configurations are uncovered for the theory with pure quartic field strength corrections, as well combinations of the two types of corrections, in three
Entropy Current in Conformal Hydrodynamics
, 2008
"... In recent work [1, 2], the energymomentum tensor for the N = 4 SYM fluid was computed up to second derivative terms using holographic methods. The aim of this note is to propose an entropy current (accurate up to second derivative terms) consistent with this energymomentum tensor and to explicate ..."
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Cited by 9 (0 self)
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In recent work [1, 2], the energymomentum tensor for the N = 4 SYM fluid was computed up to second derivative terms using holographic methods. The aim of this note is to propose an entropy current (accurate up to second derivative terms) consistent with this energymomentum tensor and to explicate its relation with the existing theories of relativistic hydrodynamics. In order to achieve this, we first develop a Weylcovariant formalism which simplifies the study of conformal hydrodynamics. This naturally leads us to a proposal for the entropy current of an arbitrary conformal fluid in any spacetime (with d> 3). In particular, this proposal translates into a definite expression for the entropy flux in the case of N = 4 SYM fluid. We conclude this note by comparing the formalism presented here with the conventional
Proof of a Universal Lower Bound on the Shear Viscosity to Entropy Density Ratio
, 2009
"... It has been conjectured, on the basis of the gaugegravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4π in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghostfree extension o ..."
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Cited by 6 (2 self)
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It has been conjectured, on the basis of the gaugegravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4π in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghostfree extension of Einstein gravity and the fieldtheory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.