Light-sheets and AdS/CFT
Open accessAbstract
One may ask whether the conformal field theory (CFT) restricted to a subset $b$ of the anti-de Sitter (AdS) boundary has a well-defined dual restricted to a subset $H(b)$ of the bulk geometry. The Poincar\'e patch is an example, but more general choices of $b$ can be considered. We propose a geometric construction of $H$. We argue that $H$ should contain the set $C$ of causal curves with both endpoints on $b$. Yet $H$ should not reach so far from the boundary that the CFT has insufficient degrees of freedom to describe it. This can be guaranteed by constructing a superset $L$ of $H$ from light-sheets off boundary slices and invoking the covariant entropy bound in the bulk. The simplest covariant choice is $L={L}^{+}\ensuremath{\cap}{L}^{\ensuremath{-}}$, where ${L}^{+}$ (${L}^{\ensuremath{-}}$) is the union of all future-directed (past-directed) light-sheets. We prove that $C=L$, so the holographic domain is completely determined by our assumptions: $H=C=L$. In situations where local bulk operators can be constructed on $b$, $H$ is closely related to the set of bulk points where this construction remains unambiguous under modifications of the CFT Hamiltonian outside of $b$. Our construction leads to a covariant geometric renormalization-group flow. We comment on the description of black hole interiors and cosmological regions via AdS/CFT.
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If AdS-Rindler reconstruction is the last word on bulk reconstruction, then the central point in the two-interval example cannot be reconstructed on A or its complement.
“If the AdS-Rindler reconstruction is the last word on bulk reconstruction [11], then the answer is clearly no; this point lies neither in W C [ A ] nor in W C [ A ].”
From Bulk locality and quantum error correction in AdS/CFT (2015) · cites this paper as [11]
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Generalized gravitational entropy
Lewkowycz, A., & Maldacena, J. (2013) · Journal of High Energy Physics · doi:10.1007/jhep08(2013)090 · Cited by 1,183 · see citing works
Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
Engelhardt, N., & Wall, A. C. (2015) · Journal of High Energy Physics · doi:10.1007/jhep01(2015)073 · Cited by 836 · see citing works
Bulk locality and quantum error correction in AdS/CFT
Almheiri, A., Dong, X., & Harlow, D. (2015) · Journal of High Energy Physics · doi:10.1007/jhep04(2015)163 · Cited by 802 · see citing works
“Can we choose a code subspace where we can realize the bulk operator in the center as an operator acting on A or A? If the AdS-Rindler reconstruction is the last word on bulk reconstruction [11], then the answer is clearly no; this point lies neither in WC [A] nor in WC [A].”
BackgroundReconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
Dong, X., Harlow, D., & Wall, A. C. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.021601 · Cited by 541 · see citing works
Relative entropy equals bulk relative entropy
Jafferis, D. L., Lewkowycz, A., Maldacena, J., & Suh, S. J. (2016) · Journal of High Energy Physics · doi:10.1007/jhep06(2016)004 · Cited by 539 · see citing works
Relative entropy equals bulk relative entropy
Jafferis, D. L., Lewkowycz, A., Maldacena, J., & Suh, S. J. (2015) · arXiv · doi:10.48550/arxiv.1512.06431 · Cited by 534
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
Wall, A. C. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/22/225007 · Cited by 545 · see citing works
Causality & holographic entanglement entropy
Headrick, M., Hubeny, V. E., Lawrence, A., & Rangamani, M. (2014) · Journal of High Energy Physics · doi:10.1007/jhep12(2014)162 · Cited by 418 · see citing works
Causal holographic information
Hubeny, V. E., & Rangamani, M. (2012) · Journal of High Energy Physics · doi:10.1007/jhep06(2012)114 · Cited by 190 · see citing works
Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
Morrison, I. A. (2014) · Journal of High Energy Physics · doi:10.1007/jhep05(2014)053 · Cited by 111 · see citing works
Holographic spacetime, black holes and quantum error correcting codes: a review
Kibe, T., Mandayam, P., & Mukhopadhyay, A. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10382-1 · Cited by 44 · see citing works
- Authors
- Bousso, R., Leichenauer, S., & Rosenhaus, V.
- Affiliations
- California Institute of Technology (US)
- Lawrence Berkeley National Laboratory (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2012-08-24
- Volume
- 86
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W1972763957
- Cited by
- 84
- References
- 6
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 1 · 2023: 7 · 2022: 5 · 2021: 5 · 2020: 5 · 2019: 3 · 2018: 6 · 2017: 7 · 2016: 9 · 2015: 9 · 2014: 10 · 2013: 5 · 2012: 7
- FWCI
- 4.46
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- U.S. Department of Energy
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- AdS/CFT correspondence, light sheet, causal curves, covariant entropy bound, Poincaré patch, bulk reconstruction, renormalization group flow, black hole interior
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