Hydrodynamics of strongly coupled non-conformal fluids from gauge/gravity duality

Todd Springer

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Hydrodynamics of strongly coupled non-conformal fluids from gauge/gravity duality

Todd Springer

High Energy Physics - Theory · Submitted 11 Aug 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Analytical solutions (to order $q^4$ and $q^3$ respectively) for the shear and sound mode dispersion relations are presented for a subset of these backgrounds.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.57 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.55 · mentions code or data availability 0.02.

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The subject of relativistic hydrodynamics is explored using the tools of gauge/gravity duality. A brief literature review of AdS/CFT and gauge/gravity duality is presented first. This is followed by a pedagogical introduction to the use of these methods in determining hydrodynamic dispersion relations, $w(q)$, of perturbations in a strongly coupled fluid. Shear and sound mode perturbations are examined in a special class of gravity duals: those where the matter supporting the metric is scalar in nature. Analytical solutions (to order $q^4$ and $q^3$ respectively) for the shear and sound mode dispersion relations are presented for a subset of these backgrounds. The work presented here is based on previous publications by the same author, though some previously unpublished results are also included. In particular, the subleading term in the shear mode dispersion relation is analyzed using the AdS/CFT correspondence without any reference to the black hole membrane paradigm.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The subject of relativistic hydrodynamics is explored using the tools of gauge/gravity duality.	background 0.54	0.41	0.06	asserted 0.93
s1	A brief literature review of AdS/CFT and gauge/gravity duality is presented first.	background 0.95	0.43	0.02	asserted 0.98
s2	This is followed by a pedagogical introduction to the use of these methods in determining hydrodynamic dispersion relations, $w(q)$, of perturbations in a strongly coupled fluid.	method 0.62	0.40	0.03	asserted 0.94
s3	Shear and sound mode perturbations are examined in a special class of gravity duals: those where the matter supporting the metric is scalar in nature.	contribution 0.71	0.73	0.04	asserted 0.99
s4	Analytical solutions (to order $q^4$ and $q^3$ respectively) for the shear and sound mode dispersion relations are presented for a subset of these backgrounds.	result 0.92	0.89	0.22	asserted 1.00
s5	The work presented here is based on previous publications by the same author, though some previously unpublished results are also included.	background 0.58	0.21	0.02	asserted 1.00
s6	In particular, the subleading term in the shear mode dispersion relation is analyzed using the AdS/CFT correspondence without any reference to the black hole membrane paradigm.	contribution 0.81	0.88	0.15	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.98.

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Original abstract

The subject of relativistic hydrodynamics is explored using the tools of gauge/gravity duality. A brief literature review of AdS/CFT and gauge/gravity duality is presented first. This is followed by a pedagogical introduction to the use of these methods in determining hydrodynamic dispersion relations, $w(q)$, of perturbations in a strongly coupled fluid. Shear and sound mode perturbations are examined in a special class of gravity duals: those where the matter supporting the metric is scalar in nature. Analytical solutions (to order $q^4$ and $q^3$ respectively) for the shear and sound mode dispersion relations are presented for a subset of these backgrounds. The work presented here is based on previous publications by the same author, though some previously unpublished results are also included. In particular, the subleading term in the shear mode dispersion relation is analyzed using the AdS/CFT correspondence without any reference to the black hole membrane paradigm.

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3 arXiv papers cite this in 4 sentences

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Papers citing it

Uses its method or tool 2 papers

To see this, we rewrite the $t$- and $z$-components of the black-hole metric in an expanded form around $z_h$ as done in [ref] , [equation] and make the substitutions, [equation] making [equation] In these coordinates, the metric then appears in polar form, [equation] with the variable $τ$ and $ρ$ playing the role of the polar and radial coordinate, respectively.

The Dynamics and Thermodynamics of Soft-Wall AdS/QCD · Thermodynamics · 0.84
Let us rewrite ([ref]) in a more convenient way following [ref] .

Anisotropic D3-D5 black holes with unquenched flavors · The sound channel · 0.98

Compares with it 1 paper

([ref])), this result corresponds to having an equilibration time $τ_eff$ equal to: τ_eff = 14π T[53 + γ +ψ(85)] , which again coincides with the one found for the geometry of a D2-brane [ref] .

Anisotropic D3-D5 black holes with unquenched flavors · The sound channel · 0.97

Cites it as background 1 paper

Here, one focuses on larger classes of theories and so tries to understand the generic physics of strongly coupled theories (see for example [ref] ).

Heavy Quarks in Strongly Coupled Non-Conformal Plasmas with Anisotropy · Introduction · 0.83

What it cites · 138 sentences without a confident label

Builds on 1 paper

These results are a generalization of the results of [ref] , and include both Dp-brane, and Schwarzschild AdS black hole metrics.

Hydrodynamics from the Dp-brane · Summary · 1.00

Uses the method or tool of 2 papers

In this thesis, we use the gravitational perturbation approach similar to [ref] to compute the shear and sound mode dispersion relations for a special class of gravity duals.

Quasinormal modes and holography · Dispersion relations from gravity · 1.00
In this thesis, we use the gravitational perturbation approach similar to [ref] to compute the shear and sound mode dispersion relations for a special class of gravity duals.

Hydrodynamics from the Dp-brane · Dispersion relations from gravity · 1.00

Compares with 10 papers

Again, using ([ref]), ([ref]), ([ref]), and ([ref]), the results for the transport coefficients are: v_s^DP = √(5-p/9-p), η/s = 1 / 4 π, ζ^DP / η = 2(3-p)^2/9-p, (9-p)(1-p) τ_π^Dp = (3-p)^2 τ_Π^Dp -p/ πT(7-p)/(5-p)[1+5-p/7-p H_n(5-p/7-p)] The results for $v_s^DP$ and $ζ^DP/ η$ agree with the calculation of [ref] .

Hydrodynamics from the Dp-brane · Transport coefficients in Israel-Stewart theory · 0.98
Finally, by comparing the sound mode dispersion relation to the shear mode discussed in Chapter [ref], we were able to determine the contribution of third order hydrodynamics to the shear mode (it was pointed out that such contributions would be present in [ref] ).

Relativistic viscous hydrodynamics, conformal invariance, and holography · Summary · 0.82
Comparison with the expected dispersion relations from ([ref]),([ref]) yields formulas for the transport coefficients [ref] .

Quasinormal modes and holography · Dispersion relations from gravity · 0.92

Cites as support 2 papers

All classical Einstein gravity duals saturate the conjectured viscosity bound as shown in [ref] .

Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm · Solution for $w_2$ and shear viscosity · 0.98
Because of this fact, and the general theorem given in [ref] , all backgrounds we consider saturate the conjectured shear viscosity bound: $η/s = 1/4 π$.

Universality of the shear viscosity in supergravity · Background equations · 0.96

Cites as background 50 papers

In [ref] , a formula for the shear viscosity to entropy density ratio $η/s$ was derived which is applicable to a wide variety of gravity duals.

Holography and hydrodynamics: diffusion on stretched horizons · Introduction · 0.88
It is notable that a universal relation between second order hydrodynamic transport coefficients of a conformal theory was presented in [ref] , though it is not known whether this relation still holds for non-conformal theories.

Universality of second order transport coefficients from the gauge-string duality · Dispersion relations from gravity · 0.85
Recently, the formulation of second order hydrodynamics presented in [ref] has gained popularity, though at present it is only applicable to conformal theories.

Relativistic viscous hydrodynamics, conformal invariance, and holography · Transport coefficients in Israel-Stewart theory · 0.96

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