Linearly resummed hydrodynamics in a weakly curved spacetime

Michael Lublinsky; Yanyan Bu

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Linearly resummed hydrodynamics in a weakly curved spacetime

Yanyan Bu, Michael Lublinsky

High Energy Physics - Theory · Submitted 27 Feb 2015

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

The authors' main claim In addition to two viscosity functions discussed at length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced structures coupled to the fluid via new transport coefficient functions.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.72 · mentions code or data availability 0.02.

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We extend our study of all-order linearly resummed hydrodynamics in a flat space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically \emph{locally} $\textrm{AdS}_5$ geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref.~\cite{0905.4069}, the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We extend our study of all-order linearly resummed hydrodynamics in a flat space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces.	contribution 0.95	0.80	0.10	asserted 0.98
s1	The underlying microscopic theory is a finite temperature $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling.	background 0.86	0.09	0.03	asserted 1.00
s2	The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically \emph{locally} $\textrm{AdS}_5$ geometry to relativistic conformal fluids in a weakly curved 4D background.	background 0.85	0.10	0.09	asserted 1.00
s3	To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders.	method 0.77	0.88	0.18	asserted 1.00
s4	We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations.	contribution 0.46	0.88	0.09	asserted 0.99
s5	In addition to two viscosity functions discussed at length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced structures coupled to the fluid via new transport coefficient functions.	result 0.89	0.95	0.31	asserted 1.00
s6	In ref.~\cite{0905.4069}, the latter were referred to as gravitational susceptibilities of the fluid.	background 0.96	0.04	0.04	asserted 0.99
s7	We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.	method 0.68	0.96	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.88.

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The paper

Original abstract

We extend our study of all-order linearly resummed hydrodynamics in a flat space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically \emph{locally} $\textrm{AdS}_5$ geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref.~\cite{0905.4069}, the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

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References

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Chiral transport in curved spacetime via holography
hep-th 2020-09 conditional novelty 7.0 of 10

Using fluid/gravity duality, the authors derive analytic third-order gradient corrections to chiral transport that are controlled by the gravitational anomaly coefficient.
Hydrodynamic gradient expansion in linear response theory
hep-th 2020-07 accept novelty 7.0 of 10

The linearized hydrodynamic gradient expansion converges if and only if the fluid fields' momentum-space support stays below a critical momentum set by branch points of the dispersion relations.
Constructing higher-order hydrodynamics: The third order
hep-th 2015-07 accept novelty 7.0 of 10

The complete third-order gradient expansion of the relativistic fluid stress-energy tensor is classified, giving 20 conformal and 68 non-conformal transport coefficients, five combinations of which are computed hologr...
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All-order holographic U(1) transport in a Gauss-Bonnet brane shifts the electric and magnetic conductivities and the frequency dependence of the diffusion function, while leaving the leading diffusion constant unchang...
Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality
hep-th 2025-12 conditional novelty 5.0 of 10

Rest-frame dispersion modes can be mapped into Lorentz-boosted frames through a parametric re-parametrization; the boost-generated 'spurious' roots appear exactly when the mode count is not conserved, which the author...

How the literature uses it

17 arXiv papers cite this in 43 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 16 sentences without a confident label

Builds on it 2 papers

In particular, extending the analysis of [ref] , we will show that the chiral gravitational effect ($χ_T$ in [ref]), reported in [ref] , is in fact determined by the gravitational anomaly in holographic theories.

Chiral transport in curved spacetime via holography · Introduction · 1.00
In [ref] , we built upon the work of [ref] and linearly resummed derivative terms (see [ref] for boost invariant case) for fluids dual to pure Einstein gravity.

Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation · Introduction · 0.88

Uses its method or tool 8 papers

Following the strategy developed in [ref] ,

$U(1)$ current from the AdS/CFT: diffusion, conductivity and causality · Boundary current from the Maxwell dynamics in the bulk · 1.00
Instead of the order-by-order boundary expansion [ref] , we will collect the derivatives in a unified way, as proposed in [ref] to resum all order linear structures in $T_μν$.

Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation · Holographic setup for Einstein-Gauss-Bonnet gravity · 0.82
Now we consider the perturbations of the background metric and gauge field, closely following [ref] .

Chiral transport in curved spacetime via holography · The Holographic Model · 0.98

Compares with it 3 papers

Our construction is quite analogous to that of all-order stress-energy tensor derived in [ref] : $𝒟$ is analogous to the viscosity $η$, while $σ_e,σ_m$ play the role similar to the GSFs in the constitutive relation for the stress tensor.

$U(1)$ current from the AdS/CFT: diffusion, conductivity and causality · Introduction and Summary · 0.88
The form [ref] also indicates that the trailing effect does not seem to be directly related to the memory function formalism advocated in [ref] .]

Probing anomalous driving · Late time behavior · 0.89
This behaviour of $σ̃_χ̅$ is quite distinct from diffusion memory function $𝒟̃(t)$ and shear viscosity memory functions computed previously in [ref] , which are picked at the origin.

Gradient resummation for nonlinear chiral transport: an insight from holography · Summary of the results · 1.00

Cites it as support 1 paper

As we argued in our previous publications [ref] , only off-shell construction reveals transport properties of the system in full.

Anomalous transport from holography: Part II · Introduction and summary · 0.96

Cites it as background 7 papers

In the next section [ref], the meaning of all-order gradient resummation and its implication on the dynamics are briefly clarified, essentially quoting the discussion presented earlier in [ref] .

$U(1)$ current from the AdS/CFT: diffusion, conductivity and causality · Introduction and Summary · 0.83
As a result, the hydrodynamical behavior of gravity has been heavily investigated and a great many of works have been made [ref] .

Fluid/gravity correspondence for massive gravity · Introduction · 0.98
As mentioned in the Introduction, the TCFs could be Fourier transformed into memory functions, see an extensive discussion in e.g. [ref] .

Gradient resummation for nonlinear chiral transport: an insight from holography · Summary of the results · 0.94

What it cites · 63 sentences without a confident label

Contests 1 paper

The constitutive relation ([ref]) was introduced in [ref] , but with $ζ$- and $θ$-terms missed.

Improved Hydrodynamics from the AdS/CFT · Introduction · contest 0.86

Builds on 3 papers

In [ref] , we built upon previous work of [ref] and constructed a flat space all-order linearly resummed relativistic conformal hydrodynamics using the fluid/gravity correspondence.

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics · Introduction · 0.88
In [ref] , we built upon previous work of [ref] and constructed a flat space all-order linearly resummed relativistic conformal hydrodynamics using the fluid/gravity correspondence.

Improved Hydrodynamics from the AdS/CFT · Introduction · 0.88
In [ref] , we built upon previous work of [ref] and constructed a flat space all-order linearly resummed relativistic conformal hydrodynamics using the fluid/gravity correspondence.

All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence · Introduction · 0.88

Uses the method or tool of 5 papers

At every order in $λ$, a system of ordinary second order differential equations can be integrated [ref] .

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics · Analytical results: hydrodynamic expansion · 0.91
In particular, rather than considering order-by-order derivative expansion, we will collect all the derivative terms in a unified way [ref] .

All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence · Introduction · 0.89
Following the method of [ref] , we construct asymptotically locally $AdS_5$ solutions to the Einstein gravity with a weakly curved boundary metric.

Nonlinear Fluid Dynamics from Gravity · Introduction · 0.99

Uses data or values from 2 papers

The viscosity functions $η$ and $ζ$ were computed in [ref] , and the main results will be quoted below.

All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence · Introduction · 0.92
The viscosity functions $η$ and $ζ$ were computed in [ref] , and the main results will be quoted below.

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics · Introduction · 0.92

Compares with 12 papers

Up to normalization convention and the $θ$-terms, our expressions for two-point correlation functions are the same as those of [ref] .

Improved Hydrodynamics from the AdS/CFT · Navier-Stokes equations and correlation functions · 0.93
We also reproduce the plots [ref] (also [ref] ) for the thermal correlators using our numerical results for the viscosities and GSFs.

Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory · Navier-Stokes equations and correlation functions · 0.81
The logarithms appear starting from the fourth order in the boundary metric derivatives, in full agreement with computations of [ref] .

Asymptotically Anti-de Sitter spacetimes and their stress energy tensor · Stress-energy tensor from near the boundary analysis · 0.82

Cites as background 11 papers

In [ref] these coefficients were named gravitational susceptibility of the fluid (GSFs).

Improved Hydrodynamics from the AdS/CFT · Introduction · 0.87
The stress tensor of conformal fluid is supposed to transform covariantly under the Weyl rescaling $g_μν→e^-2ϕ g_μν$ [ref] .

Forced Fluid Dynamics from Gravity · Summary and discussion · 0.83
The stress tensor of conformal fluid is supposed to transform covariantly under the Weyl rescaling $g_μν→e^-2ϕ g_μν$ [ref] .

Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions · Summary and discussion · 0.83

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