Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy

By Aron C. Wall. 2012

630 citations recorded by the source corpus.

The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. This extremal surface can be obtained by a maximin construction, allowing many new results to be proven. On manifolds obeying the null curvature condition, these extremal surfaces: (i) always lie outside the causal wedge of R, (ii) have less area than the bifurcation surface of the causal wedge, (iii) move away from the boundary as R grows, and (iv) obey strong subadditivity and monogamy of mutual information. These results suggest that the information in R allows the bulk to be reconstructed all the way up to the extremal area surface. The maximin surfaces are shown to exist on spacetimes without horizons, and on black hole spacetimes with Kasner-like singularities.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2445a494b9b003762607f39c6b6e02e7ace250e4

How researchers see this paper

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In Applied Mathematics

1. R. Myers
2. D. Harlow
3. Mark Van Raamsdonk
4. H. Chen
5. Joshua Sandor
6. Dominik Neuenfeld
7. I. Reyes
8. V. Hubeny

In Geometry and Topology

1. R. Myers
2. V. Hubeny
3. D. Harlow
4. M. Rangamani
5. Xi Dong
6. D. Stanford
7. M. Headrick
8. Aitor Lewkowycz

In Nuclear and High Energy Physics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. V. Hubeny
5. J. Maldacena
6. T. Takayanagi
7. S. Raju
8. S. Shenker

Citations in the corpus

• The holographic entropy cone (2015, background): “The work [46] implies that at least under certain conditions on the structure of an inequality, it is possible to reduce to individual time slices, so that our proofs by contraction become applicable.”
• Replica wormholes and the black hole interior (2019, background): “This resonates with the longstanding suspicion that some small corrections to the Hawking calculation (of order e−SBH) could be responsible for making black (1)For example [4, 5, 6, 7, 8, 9]; for a review see [10].”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “Returning to the issue of extracting information from the island, entanglement wedge reconstruction [24, 131–137] allows us to recover information about the island with data from the boundary CFT in the corresponding boundary subregion.”
• Relative entropy equals bulk relative entropy (2015, neutral): “RC is generically smaller than Rb [41, 35].”
• Information flow in black hole evaporation (2019, background): “By entanglement wedge reconstruction [1, 25–30], this implies that after some time, QML plus the bath contain information about the interior of the black hole.”
• Entanglement wedge reconstruction and the information paradox (2019, background): “It is also needed to prove that the classical entanglement wedge contains the causal wedge [20].”
• Entropy, extremality, euclidean variations, and the equations of motion (2017, result): “ent entropy is defined with respect to the bulk spatial region between the RT surface X and the boundary region R. The domain of dependence of this region defines the notation of the entanglement wedge [18, 19, 20]. It is worth noting that after extremization Xis known as the quantum extremal surface.”
• Causality & holographic entanglement entropy (2014, background): “It is known, based on properties of extremal surfaces, that EA lies outside the causal wedgesWC[A] andWC[A] [12, 22, 23].”
• The AdS/CFT correspondence (2014, background): “While harder to prove, this covariant prescription has however also passed many non-trivial checks; for example, it implies strong subadditivity [56] and it is non-trivially consistent with field theory causality [57].”