Proof of a universal lower bound on the shear viscosity to entropy density ratio

A.J.M. Medved; Ram Brustein

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Proof of a universal lower bound on the shear viscosity to entropy density ratio

Ram Brustein, A.J.M. Medved

High Energy Physics - Theory · Submitted 11 Aug 2009

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

The authors' main claim Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof.

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.37 · randomized assignment 0.01 · states quantitative result 0.94 · compares with prior results 0.67 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/ 4 pi in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory 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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/ 4 pi in units of the Planck constant divided by the Boltzmann constant.	background 1.00	0.03	0.07	speculative 0.98
s1	Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof.	contribution 0.72	0.96	0.85	asserted 1.00
s2	Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value.	method 0.88	0.56	0.08	asserted 0.95
s3	Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity.	result 0.54	0.74	0.32	asserted 1.00
s4	Meanwhile, we show that the entropy density can always be calibrated to its Einstein value.	result 0.53	0.92	0.06	asserted 1.00
s5	Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.	method 0.51	0.90	0.03	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/ 4 pi in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory 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.

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References

Forward citations

Cited by 2 Pith papers

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

Transport in holographic superfluids
hep-th 2011-01 conditional novelty 6.0 of 10

In a holographic superfluid at large scalar charge, the condensate shear viscosity vanishes, charge diffusion is continuous across the phase transition, and the third bulk viscosity diverges at the critical temperature.
Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
hep-th 2014-09 accept novelty 5.0 of 10

Using holography, the authors derive closed-form equations for two momentum-dependent viscosity functions that resum all-order derivative terms in the linearized stress tensor of a strongly coupled fluid.

How the literature uses it

8 arXiv papers cite this in 15 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 2 papers

In these theories therefore there is no lower bound for the shear viscosity to entropy density ratio, in contrast to the predictions coming from the AdS/CFT correspondence.

Viscosity to entropy density ratio: violation of the lower bound at small temperatures · 0.95
The resulting ratio can take on values above or below 1/4\pi\ and is consistent with all the previous calculations, even though our reasoning is substantially different.

Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual · 0.82

Papers citing it · 11 sentences without a confident label

Uses its method or tool 1 paper

The most convenient way to evaluate it is, as explained in [ref] and reviewed in Appendix B, to use a particular choice of field redefinition.

Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual · Calculating the ratio $η/s$ · 0.97

Cites it as background 3 papers

Let us recall the relevant discussion from [ref] .

Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity · General arguments · 0.90
A great progress alone this line appeared several months ago when the authors of [ref] gave a proof for the existence of a universal bound of $η/s$ for any ghost-free extension of Einstein theory.

The Quantum Viscosity Bound In Lovelock Gravity · Introduction · 0.81
These findings led to a series of new works, see e.g. [ref] related to Lovelock gravity.

Shock waves and Birkhoff's theorem in Lovelock gravity · introduction · 0.85

What it cites · 14 sentences without a confident label

Uses the method or tool of 6 papers

For a general theory$X$that extends Einstein gravity, the entropy is given by Wald's formula [ref] and can be expressed as a correction to the Einstein value: S_X = V_ r_h^p/4G_X = V_ r_h^p/4G_E+λδG + O[λ^2] .$

Black Hole Entropy is Noether Charge · Introduction · 0.93
For a general theory$X$that extends Einstein gravity, the entropy is given by Wald's formula [ref] and can be expressed as a correction to the Einstein value: S_X = V_ r_h^p/4G_X = V_ r_h^p/4G_E+λδG + O[λ^2] .$

On Black Hole Entropy · Introduction · 0.93
For a general theory$X$that extends Einstein gravity, the entropy is given by Wald's formula [ref] and can be expressed as a correction to the Einstein value: S_X = V_ r_h^p/4G_X = V_ r_h^p/4G_E+λδG + O[λ^2] .$

Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy · Introduction · 0.93

Cites as support 1 paper

For a ghost-free theory, all of the couplings must remain positive at all energy scales [ref] ; meaning that the propagator can only increase relative to its Einstein value.

Predictive Power of Strong Coupling in Theories with Large Distance Modified Gravity · Introduction · 0.98

Cites as background 8 papers

Kovtun, Son and Starinets (KSS) have proposed that the ratio of the shear viscosity $η$ to the entropy density $s$ should be universally bounded from below by $1/4π$ in units of the Planck constant divided by the Boltzmann constant $ħ/k_B$ [ref] .

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics · Introduction · 0.83
The gauge–gravity duality [ref] provides a hydrodynamic description of strongly coupled field theories in terms of the hydrodynamics of a black brane in an asymptotically anti-de Sitter (AdS) spacetime [ref] .

Holography and hydrodynamics: diffusion on stretched horizons · Introduction · 0.98
The gauge–gravity duality [ref] provides a hydrodynamic description of strongly coupled field theories in terms of the hydrodynamics of a black brane in an asymptotically anti-de Sitter (AdS) spacetime [ref] .

Large N Field Theories, String Theory and Gravity · Introduction · 0.98

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