Black holes and the butterfly effect
By S. Shenker, D. Stanford. Journal of High Energy Physics, 2013
1,449 citations recorded by the source corpus.
We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/91a4e3df95505d379128e739b440629db09e18db
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Citations in the corpus
- The complex life of hydrodynamic modes (2019, background): “47) thus correctly reproduces the (maximal) Lyapunov exponent and the butterfly velocity of the dual to the BTZ black hole [72]:”
- Quantum complexity and negative curvature (2016, background): “14 from [19] we identify complexity with the geodesic length of wormhole.”
- Multiple shocks (2013, methodology): “Details of the shock wave metric are given in [6], following earlier work by [25, 26, 27, 28].”
- Chaos and complexity by design (2016, background): “It was later conjectured [2] and then proven [3, 4] that black holes are the fastest scramblers in nature, suggesting their dynamics must have much in common with random unitary evolution.”
- Disentangling Scrambling and Decoherence via Quantum Teleportation (2018, background): “While a precise definition of quantum scrambling remains elusive, a powerful proxy for characterizing its behavior is provided by out-of-time-order correlation (OTOC) functions, which take the general form hVð0ÞWðtÞVð0ÞWðtÞi, where V, W are operators that act on sufficiently small subsystems [8,10,1”
- A theory of reparameterizations for AdS3 gravity (2018, methodology): “) Conformally transforming to the thermal cylinder at inverse temperature β and performing an analytic continuation to the second sheet, this gives the identity’s contribution to the out-of-time-ordered four-point function which has been used as a definition for quantum Lyapunov growth [25, 72].”
- Multiboundary wormholes and holographic entanglement (2014, background): “meaning in the bulk quantum gravity theory; they lie within the class of wormholes discussed in [38] and are distinct from the so-called long wormholes of [39, 40].”
- Scrambling and thermalization in a diffusive quantum many-body system (2016, background): “This bound is saturated in strongly coupled field theories with a gravity dual [6] and in disordered models describing a strange metal [7, 11, 12].”
- Moving the CFT into the bulk with TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} (2016, background): “early with time with the butterfly velocity vB [24, 33].”
- TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “These are precisely the situations where there is a distinction between the causal and entanglement wedges, and the recent exciting work on chaos and traversable wormholes in large part hinges on how bulk operators move around as we change the geometry [91, 92, 93].”