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Anti de Sitter space and holography
Open accessAbstract
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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Citations
Cites
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MethodVacuum interpolation in supergravity via superp-branes
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MethodCompact and non-compact gauged supergravity theories in five dimensions
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Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes
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String Theory and Quark Confinement
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Massless particles, conformal group, and de Sitter universe
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BackgroundSemiclassical decay of near extremal fivebranes
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Singletons, doubletons and M-theory
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Conformal Maxwell theory as a singleton field theory on AdS , IIB 3-branes and duality
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“Conversely, by a theorem of Graham and Lee [42] (see [43-46] for earlier mathematical work), any conformal structure on S that is sufficiently close to the standard one arises, by the procedure in (2.”
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Gauge fields as composite boundary excitations
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ResultU-duality between Three and Higher Dimensional Black HolesPreprint
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Background
Flagged first, then by citations
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Cited by
Sorted by citations
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Ofer Aharony, A., Gubser, S. S., MALDACENA, J. M., Ooguri, H., & Oz, Y. (2000) · Physics Reports · doi:10.1016/s0370-1573(99)00083-6 · Cited by 6,327
Ryu, S., & Takayanagi, T. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.181602 · Cited by 4,302
Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
Witten, E. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n3.a3 · Cited by 3,915
Self-citationColloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
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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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