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Black holes and random matrices

Journal of High Energy Physics volume 2017, Article number: 118 (2017) Cite this article

An Erratum to this article was published on 03 September 2018

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A preprint version of the article is available at arXiv.

Abstract

We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.

Change history

  • 03 September 2018

    We have found a minor normalization error in some of the plots in this paper. This error has no effect on the qualitative or quantitative conclusions of the paper.

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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA, 94305, U.S.A.

    Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, Phil Saad, Stephen H. Shenker & Alexandre Streicher

  2. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

    Masanori Hanada

  3. The Hakubi Center for Advanced Research, Kyoto University, Kyoto, 606-8502, Japan

    Masanori Hanada

  4. Department of Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    Joseph Polchinski & Alexandre Streicher

  5. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    Joseph Polchinski

  6. Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Douglas Stanford

  7. Department of Physics, Kyoto University, Kyoto, 606-8501, Japan

    Masaki Tezuka

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  1. Jordan S. Cotler
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  2. Guy Gur-Ari
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  3. Masanori Hanada
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Correspondence to Guy Gur-Ari.

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ArXiv ePrint: 1611.04650

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Cotler, J.S., Gur-Ari, G., Hanada, M. et al. Black holes and random matrices. J. High Energ. Phys. 2017, 118 (2017). https://doi.org/10.1007/JHEP05(2017)118

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Keywords

  • 1/N Expansion
  • AdS-CFT Correspondence
  • Field Theories in Lower Dimensions
  • Random Systems