A Killing vector treatment of multiboundary wormholes

Cáceres, Elena; Kundu, Arnab; Patra, Ayan K.; Shashi, Sanjit

doi:10.1007/jhep02(2020)149

Cited by 34 publications

(60 citation statements)

References 18 publications

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“…First we will give a brief review of the construction of multi-boundary wormholes. For a more detailed discussion on this topic, we refer to [58,59]. Multi-boundary wormholes can be viewed as a geometry where boundary CFTs are connected by a wormhole.…”

Section: A the Quotient Space Construction Of Wormholesmentioning

confidence: 99%

Reflected entropy for an evaporating black hole

Chu

Zhou

2020

J. High Energ. Phys.

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We study reflected entropy as a mixed state correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation, and even black hole and black hole. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and two-dimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross section. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found.We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.

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Section: A the Quotient Space Construction Of Wormholesmentioning

confidence: 99%

Reflected entropy for an evaporating black hole

Chu

Zhou

2020

J. High Energ. Phys.

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“…Recently, Ref. [41] discussed these cases in detail. Figure 6 shows the way one creates two boundaries by removing two semicircles from a pure AdS 3 slice at t ¼ 0 through a Killing vector that generates dilatation.…”

Section: B Multiboundary Wormholes and A Simple Toy Modelmentioning

confidence: 99%

“…As mentioned in the main text, there are different methods for constructing multiboundary wormholes that have been discovered in other works. In [41], a global three-boundary wormhole construction was discussed. The idea is to use the Killing vectors of AdS 3 in the t ¼ 0 slice in Poincare coordinates.…”

Section: Appendix A: More On Multiboundary Wormhole Constructionmentioning

confidence: 99%

“…For a (3,0) wormhole, the number of parameters is thus just three, all of which correspond to the horizon lengths. These three horizon lengths L 1 , L 2 , L 3 are functions of a mutually exclusive set of parameters (as found in [41]), and hence their lengths can be tuned independently in the construction. In order for our corresponding model to realize this from the subregion point of view, the same thing can be done by identifying the semicircles removed as the boundary subregions, and the entanglement of purification is then considered only for the regions in the remaining part of the boundary subregions, which correspond to the actual boundaries in the multiboundary wormhole construction.…”

Section: Appendix A: More On Multiboundary Wormhole Constructionmentioning

confidence: 99%

“…Multiboundary wormhole constructions can involve isometries, including pathologies like fixed points and closed timelike curves, in general. But these can be avoided by making suitable choices as mentioned in[41] 5. If we introduce more subregions on both sides, that would mean introducing handles in the MBW picture.…”

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Multipartite purification, multiboundary wormholes, and islands in AdS3/CFT2

Bhattacharya

2020

Phys. Rev. D

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The holographic duals of entanglement of purification (EoP) through the entanglement wedge cross section (EWCS) have been a well-discussed topic in the literature recently. More general entanglement measures involving multipartite information and their holographic duals have also been proposed. On the other hand, the recent program reproducing the Page curve in black hole entropy with the notion of islands has also been an intriguing area of interest. A toy model involving multiboundary wormholes in AdS 3 was able to capture many interesting facts about such calculations. In such a toy model, the notion of islands was intuitively connected to quantum error correction. We try to bridge the ideas of the two programs, especially in AdS 3 =CFT 2 , and give a description of the islands in terms of multipartite entanglement of purification. This clarifies a few simplified assumptions made while describing the toy model and also enables us to understand the familiar information paradox within the framework of the same model.

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Geometric secret sharing in a model of Hawking radiation

Balasubramanian

Kar

Parrikar

et al. 2021

J. High Energ. Phys.

101

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We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

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A Killing vector treatment of multiboundary wormholes

Cited by 34 publications

References 18 publications

Reflected entropy for an evaporating black hole

Reflected entropy for an evaporating black hole

Multipartite purification, multiboundary wormholes, and islands in AdS3/CFT2

Geometric secret sharing in a model of Hawking radiation

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