Black holes and random matrices

By Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, J. Polchinski, Phil Saad, S. Shenker, D. Stanford, Alexandre Streicher, Masaki Tezuka. 2016

937 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/800a2c548ebd8eeb672471aa0c0e5bd418860dbd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. D. Stanford
2. Phil Saad
3. Zhenbin Yang
4. K. Jensen
5. S. Shenker
6. Jordan S. Cotler
7. G. Turiaci
8. D. Harlow

In Statistical and Nonlinear Physics

1. D. Stanford
2. Phil Saad
3. Zhenbin Yang
4. G. Turiaci
5. K. Jensen
6. Jordan S. Cotler
7. S. Shenker
8. E. Witten

Citations in the corpus

• AdS3 gravity and random CFT (2020, methodology): “This “ramp” is, in random matrix theory, a consequence of eigenvalue repulsion, and it leads to linear growth with a universal slope that exactly matches our gravitational result [7, 12, 35, 36].”
• Power-law out of time order correlation functions in the SYK model (2017, background): “[10] in the limit of a large number of interacting fermions and more recently in Ref.”
• On the evolution of operator complexity beyond scrambling (2019, background): “It would be interesting to study the consequences of this randomization on the long time behavior of correlation functions, along the lines of [9, 19–21].”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “, calculations of Renyi entropies [41, 50], the spectral form factor [122, 125], correlation functions [90, 126], and overlap of black hole microstate wavefunctions [41, 50].”
• A primer on resurgent transseries and their asymptotics (2018, neutral): “So far, most fully worked-out physical problems seem to remain within height one and depth one83, but there are recent results pointing towards the need to include (at the very least) height-two contributions in the Sachdev–Ye–Kitaev model describing AdS black holes [75], and in Yang–Mills/QCD theor”
• Hyperuniform states of matter (2018, background): “Since this seminal work, random matrices have found applications in a host of fields including quantum chaos [13, 218], nuclear physics [219], black holes [220, 221], quantitative finance [222, 223], complex energy landscapes [224] and number theory [211, 215].”
• Quantum chaos and the complexity of spread of states (2022, neutral): “As shown in [15], the dip (i.e., minimum) in the spectral form factor occurs at a time of O ( √ N ), while the complexity peak occurs at a time of O ( N ) (see Fig.”
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, background): “ term on the right-hand side of equation (17), N 2ˇ2 S(J) 1 , is simply the value of the Schwarzian action (14) for ’(˝) = 2ˇ˝=. The (J) 2 term (with the coecient given in Table1) was reported in [25,26]. We will derive it from a correction to the Schwarzian action that is non-local in time. Note th”
• Pure states in the SYK model and nearly-$AdS_2$ gravity (2017, neutral): “For a detailed analysis of the long time behavior in SYK see [16].”
• JT gravity and the ensembles of random matrix theory (2019, methodology): “The contribution of a particular topology to the path (1)This has included many different derivations of the exact path integral [12, 13, 14, 15, 16, 17, 18, 19, 20], studies of the Hilbert space structure [21, 18, 22, 23], correlation functions [24, 25, 26], the physical symmetry charges [27], and ”
• Quantum chaos and holographic tensor models (2016, methodology): “5See section 8 of [6] and our discussions later for a precise definition of the running time average.”
• A theory of reparameterizations for AdS3 gravity (2018, methodology): “This result paves the way for future discussions [20] of traversable wormholes [21, 22] and perhaps even a semiclassical “ramp” [23, 24] in AdS3 gravity using this boundary field theory.”
• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, methodology): “Some representative examples of such systems include (i) models that are (or are thought to be) holographically dual to black holes[19, 21, 22], including the Sachdev-Ye-Kitaev (SYK) model[24, 25] and chains of coupled SYK dots at large N [29], (ii) large-N gauge”