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Anti de Sitter space and holography
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Recently, it has been proposed by Maldacena that large N limits of certain conformal field theories in d dimensions can be described in terms of supergravity (and string theory) on the product of d 4-1dimensional AdS space with a compact manifold.Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity.In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity.As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on AdS^ x S 5 match with the chiral operators of Af = 4 super Yang-Mills theory in four dimensions.With some further assumptions, one can deduce a H'amiltonian version of the correspondence and show that the Af = 4 theory has a large N phase transition related to the thermodynamics of AdS black holes.
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“By discovering the AdS/CFT correspondence [1, 2], Maldacena definitively answered the question of whether information can escape from a black hole.It can.”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [2]
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“The Euclidean partition function (Z ) of the boundary theory is related to the on-shell bulk gravitational action (I ) as follows [2,3]:”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [3]
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“in AdS/CFT, the bulk quantum gravity theory in d + spacetime dimensions is dual to an ordinary d-dimensional conformal field theory that lives on the asymptotic boundary of the bulk spacetime.”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [2]
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“Superstring theories in asymptotically AdS spacetimes are dual to conformal field theories living on the boundary (Gubser et al., 1998;Witten, 1998;Maldacena, 1999;Aharony et al., 2000).”
From Euclidean Wormholes, Baby Universes, and Their Impact on Particle Physics and Cosmology (2018) · cites this paper as Witten, 1998
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“The AdS/CFT correspondence [6], in its strongest form, describes a duality between a theory of gravity and conformal field theory at the level of their partition functions, summarized by Gubser, Klebanov, Polyakov and Witten (GKPW) [46,47]”
From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [47]
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Metadata
- Authors
- Witten, E.
- Affiliations
- Institute for Advanced Study (US)
- Corresponding author
- Witten, Edward
- ORCID
- Witten, Edward
- Venue
- Advances in Theoretical and Mathematical Physics
- Publisher
- International Press of Boston
- Published
- 1998
- Volume
- 2
- Issue
- 2
- Pages
- 253-291
- ISSN
- 1095-0753 (ISSN-L)
- 1095-0761
- OpenAlex
- W1889142700
- Cited by
- 13,070
- References
- 53
- Citations by year
- 2026: 362 · 2025: 553 · 2024: 565 · 2023: 487 · 2022: 519 · 2021: 539 · 2020: 532 · 2019: 490 · 2018: 468 · 2017: 502 · 2016: 652 · 2015: 527 · 2014: 501 · 2013: 537 · 2012: 563
- FWCI
- 261.19
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Theoretical and Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- AdS/CFT correspondence, anti-de Sitter space, holography, large N limit, conformal field theory, supergravity, type IIB supergravity, Kaluza-Klein modes, chiral operators, N=4 supersymmetric Yang-Mills, AdS black holes, operator dimensions, correlation functions
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