CoChat
Sign Up
Cited by 101

The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.

Gravity/ensemble duality

Bousso, Raphael, Wildenhain, Elizabeth·2020·Physical Review D
DOI 10.1103/physrevd.102.066005
Open this paper in CoChat — free account

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevd.102.066005

Cites

19 of 19 references verified0 citation errors · 0 not checkable

Statistics

Figures

Image 1
CC-BY · From the PDF
FIG. 2 Examples of holographic duality. Left: the solid bulk Md is dual to a holographic CFT d -1 on Md -1 (blue boundary). Right: in this example, Md -1 is a manifold with boundary, so the boundary theory is a BCFT d -1 and Md contains an end of the world brane EOW d . (Despite the appearance of a BCFT this is a ' singly holographic ' example. In Secs. IV and V we will consider a doubly holographic setting where the EOW d is a braneworld that localizes gravity and contains a holographic CFT d .)
FIG. 2 Examples of holographic duality. Left: the solid bulk Md is dual to a holographic CFT d -1 on Md -1 (blue boundary). Right: in this example, Md -1 is a manifold with boundary, so the boundary theory is a BCFT d -1 and Md contains an end of the world brane EOW d . (Despite the appearance of a BCFT this is a ' singly holographic ' example. In Secs. IV and V we will consider a doubly holographic setting where the EOW d is a braneworld that localizes gravity and contains a holographic CFT d .)CC-BY · From the PDF
FIG. 3 RT prescription, applied in the setting shown on the right of Fig. 2. The entropy of the boundary region Rd -1 is given by the generalized entropy of its entanglement wedge EW ð Rd -1 Þ . γ d is the quantum extremal surface.
FIG. 3 RT prescription, applied in the setting shown on the right of Fig. 2. The entropy of the boundary region Rd -1 is given by the generalized entropy of its entanglement wedge EW ð Rd -1 Þ . γ d is the quantum extremal surface.CC-BY · From the PDF
Image 4
CC-BY · From the PDF
Image 5
CC-BY · From the PDF
FIG. 6 Here we assume the gravity/ensemble interpretation, in the examples studied in Sec. II C (left) and Sec. II D (right). This resolves the state paradox. The RT prescription (yellow) computes the ensemble averaged entropy h S i of the full boundary (left) or of Rd -1 (right). The extrapolate dictionary (blue) yields the average state of the ensemble, h ρ i , in these regions.
FIG. 6 Here we assume the gravity/ensemble interpretation, in the examples studied in Sec. II C (left) and Sec. II D (right). This resolves the state paradox. The RT prescription (yellow) computes the ensemble averaged entropy h S i of the full boundary (left) or of Rd -1 (right). The extrapolate dictionary (blue) yields the average state of the ensemble, h ρ i , in these regions.CC-BY · From the PDF
FIG. 7 Hawking radiation escapes into an auxiliary system without gravity. The RT prescription can be applied to the boundary Md -1 , yielding the dark green entanglement wedge. A version of the RT prescription for AUX can be developed by requiring consistency with the analysis in Sec. II D. One finds that EW(AUX) (light green) includes AUX itself, and after the Page time, it also the bulk region I complementary to EW ð Md -1 Þ . The state paradox arises in AUX: the entropy must follow Hawking ' s rising curve for the island I to be part of EW(AUX), but with I included, RT yields the Page curve for AUX.
FIG. 7 Hawking radiation escapes into an auxiliary system without gravity. The RT prescription can be applied to the boundary Md -1 , yielding the dark green entanglement wedge. A version of the RT prescription for AUX can be developed by requiring consistency with the analysis in Sec. II D. One finds that EW(AUX) (light green) includes AUX itself, and after the Page time, it also the bulk region I complementary to EW ð Md -1 Þ . The state paradox arises in AUX: the entropy must follow Hawking ' s rising curve for the island I to be part of EW(AUX), but with I included, RT yields the Page curve for AUX.CC-BY · From the PDF
FIG. 8 Double holography without a bath. Md (purple surface) is the bulk dual of a holographic CFT d -1 (left) or BCFT d -1 (right) on Md -1 (dark green rim). So far this is identical to (a time slice of) the setups shown in Fig. 2. But we now assume that Md contains a holographic CFT d . This gives rise to a doubly-holographic bulk dual Md þ 1 (the solid interior). From the d þ 1 bulk perspective, Md is a Karch-Randall braneworld.
FIG. 8 Double holography without a bath. Md (purple surface) is the bulk dual of a holographic CFT d -1 (left) or BCFT d -1 (right) on Md -1 (dark green rim). So far this is identical to (a time slice of) the setups shown in Fig. 2. But we now assume that Md contains a holographic CFT d . This gives rise to a doubly-holographic bulk dual Md þ 1 (the solid interior). From the d þ 1 bulk perspective, Md is a Karch-Randall braneworld.CC-BY · From the PDF
FIG. 9 Examples of the doubly holographic entanglement wedge EW 2 ð Rd -1 Þ for a ð B Þ CFT d -1 region Rd -1 . As before, the light purple surface Md is the bulk dual of a holographic CFT d -1 (left) or BCFT d -1 (middle, right) on Md -1 (dark green rim). In each case, the doubly holographic entanglement wedge is bounded in part by the surface γ d þ 1 , shown in dark purple.
FIG. 9 Examples of the doubly holographic entanglement wedge EW 2 ð Rd -1 Þ for a ð B Þ CFT d -1 region Rd -1 . As before, the light purple surface Md is the bulk dual of a holographic CFT d -1 (left) or BCFT d -1 (middle, right) on Md -1 (dark green rim). In each case, the doubly holographic entanglement wedge is bounded in part by the surface γ d þ 1 , shown in dark purple.CC-BY · From the PDF
FIG. 10 A doubly holographic CFT d -1 on Md -1 is coupled to holographic bath: a CFT d on M d . The first holographic dual is Md ∪ M d , where Md contains the same CFT d coupled to gravity. The second holographic dual is Md þ 1 (solid interior). We consider a state which, in the first dual, corresponds to an evaporating black hole in Md with radiation escaping to M d . The von Neumann entropy of the radiation in the subregion R d ⊂ M d can be computed using the single or double RT prescription.
FIG. 10 A doubly holographic CFT d -1 on Md -1 is coupled to holographic bath: a CFT d on M d . The first holographic dual is Md ∪ M d , where Md contains the same CFT d coupled to gravity. The second holographic dual is Md þ 1 (solid interior). We consider a state which, in the first dual, corresponds to an evaporating black hole in Md with radiation escaping to M d . The von Neumann entropy of the radiation in the subregion R d ⊂ M d can be computed using the single or double RT prescription.CC-BY · From the PDF
FIG. 11 Entanglement wedges of the bath region R d before (left) and after (right) the Page time, when EW ð R d Þ has a disconnected island I . Each top figure is simply the bottom figure rotated around the axis. The ' squared ' entanglement wedge EW 2 is always connected. It can be found iteratively as EW ð EW ð R d ÞÞ , or in one step from Eq. (5.8) [42,43]. As in Sec. V C, γ d is a quantum extremal surface, but γ d þ 1 is an ordinary extremal surface.
FIG. 11 Entanglement wedges of the bath region R d before (left) and after (right) the Page time, when EW ð R d Þ has a disconnected island I . Each top figure is simply the bottom figure rotated around the axis. The ' squared ' entanglement wedge EW 2 is always connected. It can be found iteratively as EW ð EW ð R d ÞÞ , or in one step from Eq. (5.8) [42,43]. As in Sec. V C, γ d is a quantum extremal surface, but γ d þ 1 is an ordinary extremal surface.CC-BY · From the PDF
FIG. 12 Bulk dual of the state paradox. Left: we regard R d as a BCFT d subregion (top level). The homology rule following Eq. (5.8) applies: γ d þ 1 is allowed to end on the braneworld which here appears as an EOW brane. At late times, A ð γ d þ 1 Þ → 0 , resulting in the Page curve for S ð R d Þ . Right: we consider R d as a subregion of the CFT d on Md ∪ M d . The homology rule following Eq. (4.10) applies. The braneworld Md is now part of the boundary; since we are computing the entropy only for the region R d , γ 0 d þ 1 is not allowed to end on Md . A ð γ 0 d þ 1 Þ grows monotonically, resulting in Hawking ' s curve.
FIG. 12 Bulk dual of the state paradox. Left: we regard R d as a BCFT d subregion (top level). The homology rule following Eq. (5.8) applies: γ d þ 1 is allowed to end on the braneworld which here appears as an EOW brane. At late times, A ð γ d þ 1 Þ → 0 , resulting in the Page curve for S ð R d Þ . Right: we consider R d as a subregion of the CFT d on Md ∪ M d . The homology rule following Eq. (4.10) applies. The braneworld Md is now part of the boundary; since we are computing the entropy only for the region R d , γ 0 d þ 1 is not allowed to end on Md . A ð γ 0 d þ 1 Þ grows monotonically, resulting in Hawking ' s curve.CC-BY · From the PDF

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 19 references

Research works printed but not linked: 38

  1. J. Polchinski, 2017, The Black Hole Information Problem, 10.1142/9789813149441_0006 · DOI
  2. 10.1103/PhysRevD.13.191 · DOI · Paper page
  3. 10.4310/ATMP.1998.v2.n2.a1 · DOI · Paper page
  4. 10.1007/JHEP12(2019)063 · DOI · Paper page
  5. 10.1007/JHEP08(2013)090 · DOI · Paper page
  6. 10.1088/1126-6708/2006/08/045 · DOI · Paper page
  7. 10.1007/JHEP11(2013)074 · DOI · Paper page
  8. 10.1007/JHEP03(2014)068 · DOI
  9. 10.1007/JHEP02(2013)062 · DOI · Paper page
  10. 10.1007/JHEP07(2020)022 · DOI
  11. 10.1103/PhysRevD.15.2752 · DOI · Paper page
  12. 10.1007/JHEP08(2020)032 · DOI
  13. 10.1016/0370-2693(83)90012-6 · DOI · Paper page
  14. 10.1016/0550-3213(85)90448-1 · DOI · Paper page
  15. 10.1007/JHEP03(2020)152 · DOI
  16. 10.21468/SciPostPhys.9.1.001 · DOI
  17. J. Cardy, 2006, Encyclopedia of Mathematical Physics
  18. 10.1103/PhysRevLett.67.161 · DOI
  19. 10.1103/PhysRevLett.107.101602 · DOI · Paper page
  20. 10.1007/JHEP11(2011)043 · DOI · Paper page
  21. 10.1088/1126-6708/2006/06/012 · DOI · Paper page
  22. 10.1007/JHEP06(2013)013 · DOI
  23. 10.1103/PhysRevLett.111.171301 · DOI · Paper page
  24. 10.1007/JHEP09(2013)018 · DOI · Paper page
  25. 10.1103/PhysRevD.87.124023 · DOI · Paper page
  26. 10.1103/PhysRevD.88.084035 · DOI
  27. 10.1103/PhysRevLett.112.041102 · DOI
  28. 10.1103/PhysRevLett.83.3370 · DOI · Paper page
  29. 10.1007/JHEP07(2019)065 · DOI
  30. 10.1007/JHEP01(2015)073 · DOI · Paper page
  31. 10.1007/BF02757029 · DOI · Paper page
  32. 10.1103/PhysRevD.52.6997 · DOI
  33. 10.1103/PhysRevD.74.066009 · DOI · Paper page
  34. 10.1088/0264-9381/31/22/225007 · DOI · Paper page
  35. 10.1007/JHEP06(2016)004 · DOI · Paper page
  36. 10.1103/PhysRevLett.117.021601 · DOI · Paper page
  37. 10.1088/1126-6708/2001/05/008 · DOI · Paper page
  38. 10.1088/1126-6708/2002/04/057 · DOI

Cited by

Sorted by citations

Metadata

Authors
Bousso, R., & Wildenhain, E.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2020-09-16
Volume
102
Issue
6
ISSN
  • 2470-0010
  • 2470-0029
DOI
10.1103/physrevd.102.066005
Cited by
101
References
19
Language
en
Licence
creativecommons.org/licenses/by/4.0/ (vor)
Funders
  • U.S. Department of Energy (DE-SC0019380, DE-AC02-05CH11231)
  • National Science Foundation (PHY1820912)
  • Berkeley Center for Theoretical Physics

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review