Traversable wormholes in AdS and bounds on information transfer
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Springer
Received: September 19, 2019 Accepted: December 16, 2019 Published: January 9, 2020
Ben Freivogel,a,b Dami´ an A. Galante,a Dora Nikolakopouloua and Antonio Rotundoa a
Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, Amsterdam, The Netherlands b GRAPPA, University of Amsterdam, Science Park 904, 1090 GL Amsterdam, The Netherlands
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We analyze the amount of information that can be sent through the traversable wormholes of Gao, Jafferis, and Wall. Although we find that the wormhole is open for a proper time shorter than the Planck time, the transmission of a signal through the wormhole can sometimes remain within the semiclassical regime. For black holes with horizons of order the AdS radius, information cannot be reliably sent through the wormhole. However, black holes with horizon radius much larger than the AdS radius do allow for the transmission of a number of quanta of order the horizon area in AdS units. More information can be sent through the wormhole by increasing the number of light fields contributing to the negative energy. Our bulk computations agree with a boundary analysis based on quantum teleportation. Keywords: AdS-CFT Correspondence, Black Holes, Gauge-gravity correspondence ArXiv ePrint: 1907.13140
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)050
JHEP01(2020)050
Traversable wormholes in AdS and bounds on information transfer
Contents 1 Introduction
1 4 4 5 10
3 Bound on information transfer 3.1 S-wave channel 3.2 A multiple shocks bound 3.3 Beyond spherical symmetry 3.4 Comparison to quantum information bounds 3.5 Generalization to d + 1 dimensions
12 14 18 21 25 27
4 Discussion and future directions
29
1
Introduction
Physicists and non-physicists have speculated about the possibility of connecting distant pieces of spacetime by creating a “shortcut” joining them [1]. A connection observers could travel through, called a traversable wormhole, remained in the realm of science fiction until a few years ago, when Gao, Jafferis and Wall (GJW) constructed traversable wormholes in the context of the AdS/CFT correspondence [2]. They began with an eternal AdS black hole, which contains an Einstein-Rosen bridge (wormhole) which is marginally non-traversable. This geometry is dual to two CFT’s entangled in the thermofield double state [3]. As we will review in the next section, they added a coupling between the two CFTs. From the gravity perspective, this is a non-local coupling between the left and right asymptotic regions. This non-local coupling allows for negative null energy and makes the wormhole traversable. The result of GJW provides a proof of existence for traversable wormholes in holography. Yet, the more fundamental question still remains to be answered: what are the general rules for traversable wormholes? In this paper we take a step towards answering this question by analyzing
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