Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

A.J.M. Medved; Ram Brustein

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Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

Ram Brustein, A.J.M. Medved

High Energy Physics - Theory · Submitted 28 May 2010

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The authors' main claim Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein Gravity.

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arXiv ID1005.5274 (version 3)

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CitationA.J.M. Medved, Ram Brustein. "Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity." arXiv:1005.5274 (2010). https://pith.science/paper/TDOF4IE3

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We discuss corrections to the ratio of shear viscosity to entropy density $\eta/s$ in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio $\eta/s$ remains at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, $\eta/s$ can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein Gravity.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss corrections to the ratio of shear viscosity to entropy density $\eta/s$ in higher-derivative gravity theories.	contribution 0.77	0.72	0.04	asserted 0.60
s1	Generically, these theories contain ghost modes with Planck-scale masses.	background 1.00	0.12	0.02	asserted 0.98
s2	Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish.	contribution 0.60	0.86	0.09	asserted 0.84
s3	We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio $\eta/s$ remains at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections.	result 0.71	0.95	0.40	asserted 1.00
s4	It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, $\eta/s$ can only increase from the Einstein-gravity value.	result 0.96	0.68	0.34	hedged possibility 0.65
s5	We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity.	contribution 0.52	0.50	0.05	asserted 0.77
s6	We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbative way.	result 0.41	0.40	0.06	hedged possibility 0.59
s7	Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein Gravity.	interpretation 1.00	0.69	0.68	hedged possibility 0.74

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.96.

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Original abstract

We discuss corrections to the ratio of shear viscosity to entropy density $\eta/s$ in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio $\eta/s$ remains at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, $\eta/s$ can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein Gravity.

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1 arXiv paper cite this in 14 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 · 11 sentences without a confident label

Builds on it 1 paper

Here, we extend the considerations of [ref] and propose that metric perturbations about a solution of string theory are always described by two-derivative gravity.

Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual · Introduction · 1.00

Compares with it 1 paper

The essential difference between the proposal ([ref]) and the proposal in [ref] is that, here, we are proposing to set to zero the amplitude of all the cutoff scale modes and not just the ghosts.

Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual · Extracting $η$ from higher-derivative gravity · 0.91

Cites it as background 1 paper

This issue of ghosts has been discussed in [ref] , where $η/s$ was calculated for the FT duals of four-derivative gravity theories.

Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual · Introduction · 0.80

What it cites · 53 sentences without a confident label

Uses the method or tool of 6 papers

Then, following the effective-action method [ref] , one should reduce the order of this field equation by treating the higher-derivative terms perturbatively while iteratively applying a lower-order field equation and the BC's.

Higher Derivative Corrections to Shear Viscosity from Graviton's Effective Coupling · General arguments · 1.00
It is, however, simpler to extract the kinetic term by a method proposed in [ref] , which can be viewed as a generalization of Wald's entropy formula [ref] and is tantamount to varying the Lagrangian by $R^xy_ xy$.

The ratio of shear viscosity to entropy density in generalized theories of gravity · Previous proposals · 0.97
It is, however, simpler to extract the kinetic term by a method proposed in [ref] , which can be viewed as a generalization of Wald's entropy formula [ref] and is tantamount to varying the Lagrangian by $R^xy_ xy$.

Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling · Previous proposals · 0.97

Uses data or values from 1 paper

Let us consider, for instance, the Riemann (tensor) squared model or $L=L_E+L_C = R+12 +γR_abcdR^abcd$, for which the background metric ([ref]) is appropriate and the explicit forms of $A$,$B$,$E$,$F$ are already given in Eq. (3.22) of [ref] .

Holographic Hydrodynamics with a Chemical Potential · Previous proposals · 0.88

Compares with 2 papers

We would like to be precise on how our newly proposed prescription differs from those previously used; in particular, the effective-action method [ref] and those similar to it (e.g.) [ref] .

Higher Derivative Corrections to Shear Viscosity from Graviton's Effective Coupling · Comparison to another choice of boundary conditions · 0.97
We would like to be precise on how our newly proposed prescription differs from those previously used; in particular, the effective-action method [ref] and those similar to it (e.g.) [ref] .

Holographic Hydrodynamics with a Chemical Potential · Comparison to another choice of boundary conditions · 0.97

Cites as support 5 papers

We have observed that $η$ is a gravitational coupling and any such coupling can only increase from its Einstein value in unitary theories [ref] .

Predictive Power of Strong Coupling in Theories with Large Distance Modified Gravity · Introduction · 0.99
We have observed that $η$ is a gravitational coupling and any such coupling can only increase from its Einstein value in unitary theories [ref] .

Non Pauli-Fierz Massive Gravitons · Introduction · 0.99
We have observed that $η$ is a gravitational coupling and any such coupling can only increase from its Einstein value in unitary theories [ref] .

A bound on the effective gravitational coupling from semiclassical black holes · Introduction · 0.99

Cites as background 10 papers

Let us recall the relevant discussion from [ref] .

Proof of a universal lower bound on the shear viscosity to entropy density ratio · General arguments · 0.90
The gauge–gravity duality [ref] allows one to holographically map black brane thermodynamics and hydrodynamics in the Anti-deSitter (AdS) bulk to their gauge-theory correspondents at the AdS boundary [ref] .

Large N Field Theories, String Theory and Gravity · Introduction · 1.00
The gauge–gravity duality [ref] allows one to holographically map black brane thermodynamics and hydrodynamics in the Anti-deSitter (AdS) bulk to their gauge-theory correspondents at the AdS boundary [ref] .

Anti De Sitter Space And Holography · Introduction · 1.00

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