Probing typical black hole microstates
- PDF / 2,211,988 Bytes
- 72 Pages / 595.276 x 841.89 pts (A4) Page_size
- 45 Downloads / 220 Views
Springer
Received: August 22, 2019 Accepted: December 19, 2019 Published: January 13, 2020
Probing typical black hole microstates
a
Institute for Theoretical Physics and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands b Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland c Geneva University, 24 quai Ernest-Ansermet, CH-1214 Geneva 4, Switzerland d International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturbations of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol. Keywords: AdS-CFT Correspondence, Black Holes in String Theory ArXiv ePrint: 1901.08527
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)062
JHEP01(2020)062
Jan de Boer,a Rik van Breukelen,b,c Sagar F. Lokhande,a Kyriakos Papadodimasd and Erik Verlindea
Contents 1 Introduction
1 4 4 6 10 12 13 14 14 16
3 Traversable one-sided black holes 3.1 Double-trace perturbation of the two-sided black hole 3.2 State-dependent perturbations in a single CFT 3.2.1 Energy change after the perturbation 3.2.2 Shockwaves in one-sided black hole 3.2.3 Gravitational Wilson lines and the backreacted geometry 3.3 Probing the region behind the horizon 3.3.1 Thought experiment 1 3.3.2 Thought experiment 2
17 18 20 21 23 24 25 26 28
4 The SYK model as an example 4.1 Brief review of the SYK model 4.1.1 Equilibrium and non-equilibrium states in the SYK model 4.2 Mirror operators in the SYK model 4.3 Comments on the Kourkoulou-Maldacena states 4.4 Information behind the horizon in SYK 4.5 Numerical comparison
29 29 30 31 34 36 39
5 A conjecture about quantum chaos in pure and thermal states 5.1 General comments on th
Data Loading...
