Information recovery from pure state geometries in 3D
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Springer
Received: January 7, Revised: March 18, Accepted: April 15, Published: June 18,
2020 2020 2020 2020
Ondˇrej Hul´ık,a,b Joris Raeymaekersa and Orestis Vasilakisa a
Institute of Physics of the Czech Academy of Sciences, CEICO, Na Slovance 2, Prague 8, 182 21 Czech Republic b Institute of Particle Physics and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holeˇsoviˇck´ ach 2, Prague 8, 180 00 Czech Republic
E-mail: [email protected], [email protected], [email protected] Abstract: It is a well-studied phenomenon in AdS3 /CFT2 that pure states often appear ‘too thermal’ in the classical gravity limit, leading to a version of the information puzzle. One example is the case of a heavy scalar primary state, whose associated classical geometry is the BTZ black hole. Another example is provided by a heavy left-moving primary, which displays late time decay in chiral correlators. In this paper we study a special class of pure state geometries which do not display such information loss. They describe heavy CFT states created by a collection of chiral operators at various positions on the complex plane. In the bulk, these take the form of multi-centered solutions from the backreaction of a collection of spinning particles, which we construct for circular distributions of particles. We compute the two-point function of probe operators in these backgrounds and show that information is retrieved. We observe that the states for which our geometric picture is reliable are highly extended star-like objects in the bulk description. This may point to limitations of semiclassical microstate geometries for understanding the information puzzle and to the need for including quantum effects. Keywords: AdS-CFT Correspondence, Black Holes, Conformal Field Theory ArXiv ePrint: 1911.12309
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)119
JHEP06(2020)119
Information recovery from pure state geometries in 3D
Contents 1 Introduction and summary
2
2 Pure states and classical geometries
4
CFT vs. geometry
4
2.2
Two heavy scalar operators
5
2.3
Particles vs. black hole microstates
7
2.4
Classical caps for extended microstates?
9
3 Left-chiral primaries and overspinning BTZ
11
3.1
Overspinning BTZ metrics
11
3.2
The Liouville throat
13
3.3
Late-time decay of two-point functions
15
3.3.1
Generic spacelike geodesics
15
3.3.2
Evaluation of geodesic length
17
3.3.3
Spin contribution to the two point function
19
3.4
Further comments
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4 Pure chiral states with a cap
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4.1
Chiral current insertions from spinning particles
22
4.2
Solution for a shell of spinning particles
25
5 Two-point function in shell background
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5.1
Simplifying assumptions
29
5.2
Geodesics in the throat
30
5.3
Geodesics in the presence of the shell
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5.4
Shell 2-point function
32
5.5
Specific examples
36
6 Discussion and outlook
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A Left-thermal geometries as quotients of global AdS3
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B Coordinate transformation between AdS
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