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Black holes and random matrices

  • Jordan S. Cotler
  • Guy Gur-AriEmail author
  • Masanori Hanada
  • Joseph Polchinski
  • Phil Saad
  • Stephen H. Shenker
  • Douglas Stanford
  • Alexandre Streicher
  • Masaki Tezuka
Open Access
Regular Article - Theoretical Physics
First Online:

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.

Keywords

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

© The Author(s) 2017

Authors and Affiliations

  • Jordan S. Cotler
    • 1
  • Guy Gur-Ari
    • 1
    Email author
  • Masanori Hanada
    • 1
    • 2
    • 3
  • Joseph Polchinski
    • 4
    • 5
  • Phil Saad
    • 1
  • Stephen H. Shenker
    • 1
  • Douglas Stanford
    • 6
  • Alexandre Streicher
    • 1
    • 4
  • Masaki Tezuka
    • 7
  1. 1.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.
  2. 2.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  3. 3.The Hakubi Center for Advanced ResearchKyoto UniversityKyotoJapan
  4. 4.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  5. 5.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  6. 6.Institute for Advanced StudyPrincetonU.S.A.
  7. 7.Department of PhysicsKyoto UniversityKyotoJapan

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