A moving mirror in AdS space as a toy model for holographic thermalization

Johanna Erdmenger; Shu Lin; Thanh Hai Ngo

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A moving mirror in AdS space as a toy model for holographic thermalization

Johanna Erdmenger, Shu Lin, Thanh Hai Ngo

High Energy Physics - Theory · Submitted 28 Jan 2011

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The authors' main claim We test our method on two sample trajectories for the mirror, and find that the singularity structure of the two-point functions is in agreement with geometric optics.

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arXiv ID1101.5505 (version 2)

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CitationJohanna Erdmenger, Shu Lin, Thanh Hai Ngo. "A moving mirror in AdS space as a toy model for holographic thermalization." arXiv:1101.5505 (2011). https://pith.science/paper/CAADWWMB

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It is expected that thermalization may be described within gauge/gravity duality by considering time-dependent configurations on the gravity side of the correspondence, for instance a gravitational collapse of a matter configuration in Anti-de Sitter space. As a step towards the ambitious goal of describing such a configuration, we investigate a simple time-dependent toy model in which a mirror moves in the radial direction of Anti-de Sitter space. For this configuration, we establish a procedure for calculating two-point functions of scalar fluctuations, based on a WKB approximation. We test our method on two sample trajectories for the mirror, and find that the singularity structure of the two-point functions is in agreement with geometric optics.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is expected that thermalization may be described within gauge/gravity duality by considering time-dependent configurations on the gravity side of the correspondence, for instance a gravitational collapse of a matter configuration in Anti-de Sitter space.	background 1.00	0.04	0.04	hedged possibility 1.00
s1	As a step towards the ambitious goal of describing such a configuration, we investigate a simple time-dependent toy model in which a mirror moves in the radial direction of Anti-de Sitter space.	contribution 0.82	0.86	0.05	asserted 0.88
s2	For this configuration, we establish a procedure for calculating two-point functions of scalar fluctuations, based on a WKB approximation.	method 0.98	0.96	0.06	asserted 1.00
s3	We test our method on two sample trajectories for the mirror, and find that the singularity structure of the two-point functions is in agreement with geometric optics.	result 1.00	0.97	0.43	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.61 · evidence from proof or derivation 0.95.

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Original abstract

It is expected that thermalization may be described within gauge/gravity duality by considering time-dependent configurations on the gravity side of the correspondence, for instance a gravitational collapse of a matter configuration in Anti-de Sitter space. As a step towards the ambitious goal of describing such a configuration, we investigate a simple time-dependent toy model in which a mirror moves in the radial direction of Anti-de Sitter space. For this configuration, we establish a procedure for calculating two-point functions of scalar fluctuations, based on a WKB approximation. We test our method on two sample trajectories for the mirror, and find that the singularity structure of the two-point functions is in agreement with geometric optics.

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Cited by 4 Pith papers

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

Extremal surfaces as bulk probes in AdS/CFT
hep-th 2012-03 accept novelty 6.0 of 10

For static asymptotically AdS spacetimes, extremal surfaces anchored on the boundary cannot penetrate a black hole horizon, and constant-time spacelike geodesics reach deepest at fixed endpoint separation.
Evolution of Two-Point Functions from Holography
hep-th 2011-09 conditional novelty 6.0 of 10

In a holographic 2D CFT thermalizing via gravitational collapse, late-time two-point functions depend on separation only through the combination l - t1 - t2, matching the quantum quench pattern.
Holographic Thermalization
hep-th 2011-03 conditional novelty 6.0 of 10

In holographic quenches across two, three, and four dimensions, short-distance observables thermalize before long-distance ones, and entanglement entropy sets the slowest equilibration time, saturating a light-speed c...
Heavy ions and string theory
hep-th 2013-04 accept novelty 2.0 of 10

Holographic duality gives a tractable model of the strongly coupled quark-gluon plasma, and this review catalogues where its outputs (viscosity, drag, multiplicity bounds, a critical point) land near heavy-ion data an...

How the literature uses it

10 arXiv papers cite this in 21 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 · 12 sentences without a confident label

Builds on it 1 paper

This work is based on the previous work [ref] by Amado and one of the present authors and [ref] by Ngo and the other two of the present authors.

Time singularities of correlators from Dirichlet conditions in AdS/CFT · Introduction · 0.80

Uses its method or tool 1 paper

Similar to the appendix of [ref] , we have: G_LO(t<t')=A_1/at'^-d+1/2$t/u_0$^d-1/2 e^iπb(d-1)/2a$2iπ/a$^cΦ(e^2iπb/a,-c,d-1/4), with $a=lnu_0+1/u_0-1, b=lnt/t'+lnu_0-1/u_0, c=d+1/2$. $Φ$ is the Lerch transcendent function.

Time singularities of correlators from Dirichlet conditions in AdS/CFT · Explicit evaluations of the correlators: scaling trajectory · 0.97

Cites it as background 6 papers

First, we will analyze the non-equilibrium evolution and equilibration of the spectral density, $ρ(Q)$, which has been studied in non-equilibrium contexts by several groups [ref] .

Heavy ions and string theory · Non-equilibrium two-point functions · 0.93
Much effort is devoted to such problems in connection with, for example, application of the AdS/CFT correspondence to QCD physics like that in the RHIC experiment, or to nonequilibrium phenomena in condensed matter physics and fluid dynamics [ref] .

Hawking temperature for near-equilibrium black holes · Introduction · 0.93
The effect of a dynamical boundary condition has also been studied in the background of a moving mirror [ref] .

Holographic Thermalization · Thermalization scenarios · 0.92

What it cites · 20 sentences without a confident label

Builds on 4 papers

Our results generalize the static mirror case considered in [ref] to the time-dependent case.

AdS black holes as reflecting cavities · Introduction · 1.00
In this paper we start a program of studying gravitational collapse of a thin matter shell beyond the quasi-static approximation, thus generalizing [ref] .

Toward the AdS/CFT Gravity Dual for High Energy Collisions. 3.Gravitationally Collapsing Shell and Quasiequilibrium · Introduction · 1.00
A direct application to [ref] with infalling boundary conditions of the wave imposed on the horizon will allow us to obtain the quasi-normal modes beyond the adiabatic approximation used in [ref] .

Asymptotic perfect fluid dynamics as a consequence of AdS/CFT · Conclusion · 0.92

Uses the method or tool of 3 papers

We will follow [ref] for the computation of the two point correlator[Note a subtlety involved in this procedure is elaborated in [ref] , but this does not affect our result for the massless scalar.].

Anti De Sitter Space And Holography · Derivation of the correlator · 1.00
We will follow [ref] for the computation of the two point correlator[Note a subtlety involved in this procedure is elaborated in [ref] , but this does not affect our result for the massless scalar.].

Correlation functions in the CFT(d)/AdS(d+1) correpondence · Derivation of the correlator · 1.00
We focus on the UV part of the correlator following the work by Amado and Hoyos [ref] .

AdS black holes as reflecting cavities · Different limits of the correlator · 0.89

Compares with 4 papers

It should be stressed that while the authors of [ref] use a static mirror in $$ which introduces an explicit scale to the boundary CFT, our mirror moves in such a way that scale invariance of the boundary CFT is still preserved.

AdS black holes as reflecting cavities · Different limits of the correlator · 0.92
Finally, let us compare our results for two-point functions of a massless scalar field with light-like separation to previous discussions of space-like separation, for instance those of [ref] .

Holographic Evolution of Entanglement Entropy · Conclusion · 1.00
Finally, let us compare our results for two-point functions of a massless scalar field with light-like separation to previous discussions of space-like separation, for instance those of [ref] .

AdS Dynamics from Conformal Field Theory · Conclusion · 1.00

Cites as background 19 papers

The authors of [ref] investigate the gravitational collapse of energy injected into Anti-de Sitter space and the formation of an event horizon by considering the evolution of locally anisotropic metric perturbations initially located near the AdS boundary.

Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma · Introduction · 0.96
So far, the collapsing shell scenario has been considered in the quasi-static approximation where the shell is considered to move adiabatically [ref] , which simplifies the calculations significantly.

Gravitational collapse and its boundary description in AdS · Introduction · 0.93
So far, the collapsing shell scenario has been considered in the quasi-static approximation where the shell is considered to move adiabatically [ref] , which simplifies the calculations significantly.

Toward the AdS/CFT Gravity Dual for High Energy Collisions. 3.Gravitationally Collapsing Shell and Quasiequilibrium · Introduction · 0.93

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