{"work":{"id":"3559baf4-a73f-4ab9-924e-dc5290a82643","openalex_id":null,"doi":null,"arxiv_id":"hep-th/9802150","raw_key":null,"title":"Anti De Sitter Space And Holography","authors":null,"authors_text":"Edward Witten","year":1998,"venue":"hep-th","abstract":"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 $d+1$-dimensional $AdS$ 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 $AdS_5\\times {\\bf S}^5$ match with the chiral operators of $\\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.","external_url":"https://arxiv.org/abs/hep-th/9802150","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-06-29T13:23:28.638781+00:00","pith_arxiv_id":"hep-th/9802150","created_at":"2026-05-09T05:45:21.712307+00:00","updated_at":"2026-06-29T13:23:28.638781+00:00","title_quality_ok":true,"display_title":"Anti De Sitter Space And Holography","render_title":"Anti De Sitter Space And Holography"},"hub":{"state":{"work_id":"3559baf4-a73f-4ab9-924e-dc5290a82643","tier":"super_hub","tier_reason":"100+ Pith inbound or 10,000+ external citations","pith_inbound_count":153,"external_cited_by_count":null,"distinct_field_count":7,"first_pith_cited_at":"2009-05-19T05:15:43+00:00","last_pith_cited_at":"2026-06-25T04:55:03+00:00","author_build_status":"needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-06-29T16:09:01.003660+00:00","tier_text":"super_hub"},"tier":"super_hub","role_counts":[{"context_role":"background","n":56},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":51},{"context_polarity":"support","n":3},{"context_polarity":"unclear","n":2},{"context_polarity":"use_method","n":1}],"runs":{"ask_index":{"job_type":"ask_index","status":"succeeded","result":{"title":"Anti De Sitter Space And Holography","claims":[{"claim_text":"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 $d+1$-dimensional $AdS$ 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","claim_type":"abstract","evidence_strength":"source_metadata"},{"claim_text":"5148 [hep-th]. 3, 17 [7] N. Seiberg, \"The Power of holomorphy: Exact results in 4-D SUSY field theories,\" in Particles, Strings, and Cosmology (PASCOS 94), pp. 0357-369. 5, 1994. arXiv:hep-th/9408013. 3 [8] J. M. Maldacena, \"The LargeNlimit of superconformal field theories and supergravity,\" Adv. Theor. Math. Phys.2(1998) 231-252,arXiv:hep-th/9711200. 3 [9] E. Witten, \"Anti de Sitter space and holography,\"Adv. Theor. Math. Phys.2(1998) 253-291,arXiv:hep-th/9802150. 3 [10] S. S. Gubser, I. R. Kle","claim_type":"background","confidence":0.95,"evidence_strength":"citation_context"},{"claim_text":"branes [1]. While the fundamental string usually provides perturbative degrees of freedom en- 2 coding dynamics of the theory, branes generate and support a background in a non-perturbative fashion. One of the well known examples of such applications of Dp-branes is the AdS/CFT holography first suggested in [2] and then developed in more details in [3,4]. Given the amazing power of holography for investigation of the strong coupling dynamics of quantum field theo- ries, huge amount of various re","claim_type":"background","confidence":0.95,"evidence_strength":"citation_context"},{"claim_text":"69(1992) 1849-1851, [hep-th/9204099]. [2] M. Banados, M. Henneaux, C. Teitelboim, and J. Zanelli,Geometry of the (2+1) black hole, Phys. Rev. D48(1993) 1506-1525, [gr-qc/9302012]. [Erratum: Phys.Rev.D 88, 069902 (2013)]. - 32 - [3] J. M. Maldacena,The LargeNlimit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231-252, [hep-th/9711200]. [4] E. Witten,Anti de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253-291, [hep-th/9802150]. [5] S. S. Gubser, I.","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"\u0012 T4 −T 3 ϵ \u0013 .(49) 32 References [1] J. M. Maldacena, \"The Large N limit of superconformal field theories and supergravity,\" Int. J. Theor. Phys.38(1999) 1113-1133,arXiv:hep-th/9711200. [2] S. Gubser, I. R. Klebanov, and A. M. Polyakov, \"Gauge theory correlators from noncritical string theory,\"Phys. Lett. B428(1998) 105-114,arXiv:hep-th/9802109. [3] E. Witten, \"Anti-de Sitter space and holography,\"Adv. Theor. Math. Phys.2(1998) 253-291,arXiv:hep-th/9802150. [4] S. Ryu and T. 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Polyakov,Gauge theory correlators from noncritical string theory,Phys. Lett. B428(1998) 105-114, [hep-th/9802109]. [3] E. Witten,Anti de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253-291, [hep-th/9802150]. 17 [4] S. Corley, A. Jevicki, and S. R","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"}],"why_cited":"Pith tracks Anti De Sitter Space And Holography because it crossed a citation-hub threshold. 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Maldacena,The LargeNlimit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231-252, [hep-th/9711200]. [4] E. Witten,Anti de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253-291, [hep-th/9802150]. [5] S. S. Gubser, I.","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"},{"claim_text":"\u0012 T4 −T 3 ϵ \u0013 .(49) 32 References [1] J. M. Maldacena, \"The Large N limit of superconformal field theories and supergravity,\" Int. J. Theor. Phys.38(1999) 1113-1133,arXiv:hep-th/9711200. [2] S. Gubser, I. R. Klebanov, and A. M. Polyakov, \"Gauge theory correlators from noncritical string theory,\"Phys. Lett. B428(1998) 105-114,arXiv:hep-th/9802109. [3] E. Witten, \"Anti-de Sitter space and holography,\"Adv. Theor. Math. Phys.2(1998) 253-291,arXiv:hep-th/9802150. [4] S. Ryu and T. 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Polyakov,Gauge theory correlators from noncritical string theory,Phys. Lett. B428(1998) 105-114, [hep-th/9802109]. [3] E. Witten,Anti de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253-291, [hep-th/9802150]. 17 [4] S. Corley, A. Jevicki, and S. R","claim_type":"background","confidence":0.9,"evidence_strength":"citation_context"}],"why_cited":"Pith tracks Anti De Sitter Space And Holography because it crossed a citation-hub threshold. 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