A Stochasticity Threshold in Holography and and the Instability of AdS

Basu, Prabir; Krishnan, Chethan; Saurabh, Ayush

doi:10.48550/arxiv.1408.0624

Cited by 21 publications

(68 citation statements)

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“…The three conservation laws we find form a direct parallel to the considerations of [14], where an identical mathematical structure was described for the case of a self-interacting probe scalar field in a non-dynamical AdS space. In that paper, averaging over fast oscillations was used to produce an effective Lagrangian governing the slow energy transfer.…”

Section: Introductionmentioning

confidence: 63%

Renormalization, averaging, conservation laws and AdS (in)stability

Craps

Evnin

Vanhoof

2015

J. High Energ. Phys.

207

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We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

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Section: Introductionmentioning

confidence: 63%

Renormalization, averaging, conservation laws and AdS (in)stability

Craps

Evnin

Vanhoof

2015

J. High Energ. Phys.

207

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“…We note that the Hamiltonian ( 17) could be studied in its own right as a quartic dynamical system. Classical analogs of this quantum resonant system, with various different choices of the interaction coefficients C (including the concrete problem we are considering here as a special case), have often surfaced in recent literature: resonant systems of gravitational AdS perturbations [8][9][10][11][12][13] formulated in relation to the conjectured AdS instability [14,15], resonant systems of nonlinear wave equations in AdS [16][17][18][19] and the related Gross-Pitaevskii equation for Bose-Einstein condensates [20][21][22][23], a solvable model of turbulence in the form of a specific resonant system called the cubic Szegő equation [24], as well as studies of a large class of partially solvable resonant systems [25]. Quantum resonant systems, on the other hand, have been introduced and studied in [7] from a perspective geared toward quantum chaos theory.…”

Section: Quantum Fields In Adsmentioning

confidence: 99%

Spectroscopy instead of scattering: particle experimentation in AdS spacetime

Evnin

2018

Preprint

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Particle experiments are difficult at weak coupling because interactions are rare and a huge number of collision attempts are needed to attain significant precision. One often hears that 'one Higgs boson is produced in a billion of collisions at LHC.' In this essay, we fantasize about possible advantages afforded in this regard by performing experiments in anti-de Sitter (AdS) spacetime instead of a usual collider in a nearly-flat spacetime. Being a perfectly resonant cavity, the AdS spacetime enhances all nonlinear interactions, which therefore produce effects of order one no matter how small the couplings are, provided that one waits long enough. These effects are encoded in spectroscopic data, namely, the fine splittings of the energy levels which would have been highly degenerate in AdS if no interactions were present. Over long times, such energy shifts let different components of wavefunctions drift completely out-of-phase, producing large effects for arbitrarily small interactions.

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“…In Section 4, we will apply both theorems to the AdS-(in)stability problem [1,3,4,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Currently, the main focus of this problem is indeed the consequence of the nonlinear dynamics of gravitational self-interaction, at the time scale that the leading order expansion should generically break down.…”

Section: The Ads (In)stability Problemmentioning

confidence: 99%

Conditionally extended validity of perturbation theory: Persistence of AdS stability islands

Dimitrakopoulos

Yang

2015

Phys. Rev. D

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Conditionally extended validity of perturbation theory: Persistence of AdS stability islands Dimitrakopoulos, F.; Yang, I.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Approximating nonlinear dynamics with a truncated perturbative expansion may be accurate for a while, but it, in general, breaks down at a long time scale that is one over the small expansion parameter. There are interesting cases in which such breakdown does not happen. We provide a mathematically general and precise definition of those cases, in which we prove that the validity of truncated theory trivially extends to the long time scale. This enables us to utilize numerical results, which are only obtainable within finite times, to legitimately predict the dynamics when the expansion parameter goes to zero, and thus the long time scale goes to infinity. In particular, this shows that existing noncollapsing solutions in the AdS (in)stability problem persist to the zero-amplitude limit, opposing the conjecture by Dias, Horowitz, Marolf, and Santos that predicts a shrinkage to measure zero [O. J. Dias et al., Classical Quantum Gravity 29, 235019 (2012)]. We also point out why the persistence of collapsing solutions is harder to prove, and how the recent interesting progress by Bizon, Maliborski, and Rostoworowski has not yet proven this [P. Bizon, M. Maliborski, and A. Rostworowski, arXiv:1506.03519].

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A Stochasticity Threshold in Holography and and the Instability of AdS

Cited by 21 publications

References 0 publications

Renormalization, averaging, conservation laws and AdS (in)stability

Renormalization, averaging, conservation laws and AdS (in)stability

Spectroscopy instead of scattering: particle experimentation in AdS spacetime

Conditionally extended validity of perturbation theory: Persistence of AdS stability islands

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