The Large N Limit of Superconformal Field Theories and Supergravity — TEI-tagged view

Juan M. Maldacena · 1998 · physics · doi:10.4310/ATMP.1998.v2.n2.a1 · full text at the source · TEI xml · tagged edition · index · concepts · authors
Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. The headline claim is a conjecture, so claim type sits between 'existence' and 'prediction'; 'existence' was chosen because what the paper demonstrates is that the supergravity sector is already present in the Hilbert space of the field theory. method is 'theoretical-derivation'; none of the suggested method values applies to an analytic string-theory argument. The scanned text contains OCR corruptions ('iV', 'JV', 'giV' for N, 'axe' for are); quotes preserve them exactly. Claim-relation targets are cited by reference number in the source, so the target strings paraphrase what the source says those references are. 2026-08-14 and 2026-08-15 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node. Update, 15 September 2026: EXCEPTION, measured with the merge gate's own predicate (Paper.locate): 6 quote(s) on this record are not found as one exact string in the current staged text - content_tags.definitions[3].evidence, content_tags.findings[3].evidence, content_tags.quantities[1].evidence, content_tags.quantities[2].evidence, content_tags.quantities[4].evidence, content_tags.variables[1].evidence. The sentence above does not hold for them as written. Where a row records why - the quote is grounded in another copy of the paper, joins two passages with an ellipsis, or differs from the staged text by extraction noise - that note stays on the row.
5 quotes on this page were cut from a different copy of this article. This project holds two extractions of this paper: the plain text every other quote here is anchored in, and the publisher’s own HTML edition, which we are not licensed to republish. They are verbatim in the second and cannot be found in the first — not because the tagging is wrong, but because the extraction damaged the passage: a page number dropped into the middle of a number, a formula moved out of its sentence, a ligature where two letters belong. The record names the copy for each one. The quote is the paper’s; the extraction is not.
Tags on this paper every tag the record carries, whether or not the words occur in the text below — a number is how many papers in the corpus carry that tag; a tag with no number is unique to this paper
AdS/CFT correspondence gauge-gravity duality holography conformal field theory string theory supergravity near horizon geometry theory24
Method, as described: theoretical-derivation

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Cross-disciplinary analysis
content-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text
phenomenonduality between large-N conformal field theories and supergravity on anti-de Sitter spacetimes— “We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories.”
claim-typeexistence— “We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds.”
method — evidence— “This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk.”
mechanismthe AdS/CFT (holographic) duality: a string/gravity theory in an anti-de Sitter spacetime is equivalent to a conformal field theory living on its lower-dimensional boundary— “We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories”mechanisms[0]
builds-on string theory and conformal field theory— “compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories”claim_relations[0]
builds-on ref. [1], the finite-temperature study of the NS fivebrane theory— “The approach is similar to that used in [1] to study the NS fivebrane theory [2] at finite temperature.”claim_relations[1]
builds-on the calculations for the 1D+5D system in refs [39, 53, 54]— “All calculations done for the 1D+5D system [39, 53, 54] are evidence for this conjecture.”claim_relations[2]
extendsWITHDRAWN AND REPLACED (RETRACTED AND RE-ADDED WITH THE IMPORTED DESCRIPTION REMOVED) · the matrix model of ref. [61], which proposed the large N limit of D0 brane quantum mechanics as a definition of eleven dimensional M-theory— “An obvious difference with the matrix model of [61] is that here JV is not interpreted as the momentum along a compact direction.”claim_relations[3]
extends the matrix model of ref. [61]— “An obvious difference with the matrix model of [61] is that here JV is not interpreted as the momentum along a compact direction.”claim_relations[4]
sensethe central result - AS A CONJECTURE, and one whose statement requires boundary conditions that are called suitable without being given: the author's word is conjecture, not correspondence— “We will conjecture that the full quantum M/string-theory on AdS space, plus suitable boundary conditions is dual to the corresponding brane theory”senses[0]
sensetrust - THE PAPER'S EPISTEMIC VERB, and it never appears without a range: a solution is not valid or proved but trusted, and trusted only as long as a stated condition holds— “At the same time we look at the near horizon geometry and we argue that the supergravity solution can be trusted as long as N is large”senses[1]
sensethe duality - ASYMMETRIC IN WHAT CAN BE COMPUTED: the regime where one side becomes untrustworthy is exactly the regime where the other can be trusted, which is what makes the pairing useful— “When the effective coupling gN becomes large we cannot trust perturbative calculations in the Yang-Mills theory but we can trust calculations in supergravity”senses[2]
retractedWITHDRAWN AND REPLACED (RETRACTED AND RE-ADDED WITH THE IMPORTED DESCRIPTION REMOVED) · the matrix model of ref. [61], which proposed the large N limit of D0 brane quantum mechanics as a definition of eleven dimensional M-theory — RETRACTED AND RE-ADDED WITH THE IMPORTED DESCRIPTION REMOVED. The target described ref [61] as 'WHICH PROPOSED THE LARGE N LIMIT OF D0 BRANE QUANTUM MECHANICS AS A DEFINITION OF ELEVEN DIMENSIONAL M-THEORY'. That is TRUE of ref [61] and this paper never says it; the span says only that JV is not the momentum along a compact direction. Being true is what made it hard to see - the same fault as putting the CO2/C mass ratio in a tag.— “An obvious difference with the matrix model of [61] is that here JV is not interpreted as the momentum along a compact direction.”— “An obvious difference with the matrix model of [61]”claim_relations[3]
auditsupergravity —part-of→ conformal field theory — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says the large N limit of certain CFTs includes a sector describing supergravity; part-of is loose.— “We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes”concept_edges[0]
for which uselimitation — every supergravity result in the paper: THE SUPERGRAVITY SOLUTION CAN BE TRUSTED AS LONG AS N IS LARGE— “the supergravity solution can be trusted as long as N is large”limitations[0]
for which uselimitation — the AdS side of the correspondence as stated here: WE ARE NOT GOING TO SPECIFY THE BOUNDARY CONDITIONS IN ADS, WE LEAVE THIS INTERESTING PROBLEM FOR THE FUTURE— “We are not going to specify the boundary conditions in AdS, we leave this interesting problem for the future.”limitations[1]
for which uselimitation — the status of the paper's predictions: WE CAN MAKE VERY NONTRIVIAL PREDICTIONS (THOUGH WE WERE NOT ABLE TO CHECK THEM)— “However we can make very nontrivial predictions (though we were not able to check them).”limitations[2]
for which uselimitation — the entropy comparison specifically: IT IS EXPECTED THAT LARGE g_YM EFFECTS CHANGE THIS NUMERICAL FACTOR, THIS PROBLEM REMAINS UNSOLVED— “This is not in disagreement with the correspondence we were suggesting, It is expected that large giV effects change this numerical factor, this problem remains unsolved.”limitations[3]
for which uselimitation — the lower-supersymmetry cases: THERE ARE SEVERAL DETAILS OF THE CONFORMAL FIELD THEORIES INVOLVED WHICH I DO NOT COMPLETELY UNDERSTAND— “This part will be more sketchy, since there are several details of the conformal field theories involved which I do not completely understand, most notably the dependence on the various moduli of the compactification.”limitations[4]
for which uselimitation — the five-dimensional black string conjecture: IT IS NOT CLEAR TO ME WHETHER THIS IS TRUE— “It is not clear to me whether this is true.”limitations[5]
for which uselimitation — the Reissner-Nordstrom section: IT IS MORE SKETCHY AND CONTAINS AN UNRESOLVED PUZZLE, SO THE READER WILL NOT MISS MUCH IF HE SKIPS IT— “This section is more sketchy and contains an unresolved puzzle, so the reader will not miss much if he skips it.”limitations[6]
for which uselimitation — the programme as a whole: WE ARE ONLY SCRATCHING THE SURFACE AND THERE ARE MANY THINGS TO BE WORKED OUT— “We are only scratching the surface and there are many things to be worked out.”limitations[7]
for which uselimitation — the cited U-duality between the AdS spacetime and the full black hole solution: this paper says that statement should be taken with caution, because in those cases the spacetime has identifications on circles that are becoming null— “However the statement in [49-51] that the AdSs x S3 spacetime is U-dual to the full black hole solution (which is asymptotic to Minkowski space) should be taken with caution”limitations[8]
for which uselimitation — the group-theoretic statements in this paper: the author notes the representation includes spinor objects so the group should be SU(4), and states that this and similar distinctions are not made in what follows— “The representation includes objects in the spinor representations, so we should be talking about SU(4), we will not make this, or similar distinctions in what follows”limitations[9]
evidential statusmechanism — the paper's own words: We conjecture that— “We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories”mechanisms[0]
replicationuntested
limitationthe supergravity description is trustworthy only in the large-N limit— “the supergravity solution can be trusted as long as N is large”limitations[0]
limitationThe boundary conditions that the AdS side requires are not specified.— “We are not going to specify the boundary conditions in AdS, we leave this interesting problem for the future.”limitations[1]
limitationThe predictions offered were not checked.— “However we can make very nontrivial predictions (though we were not able to check them).”limitations[2]
limitationThe numerical mismatch between black hole entropy and the perturbative Yang-Mills calculation is unresolved.limitations[3]
limitationThe lower-supersymmetry cases are treated sketchily and incompletely understood by the author.limitations[4]
limitationA necessary condition of the five-dimensional black string conjecture is left open.limitations[5]
limitationThe Reissner-Nordstrom section contains an unresolved puzzle.limitations[6]
limitationThe programme as a whole is preliminary.limitations[7]
limitationA published statement by others is flagged as needing caution, with the geometric reason given.
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limitations[8]
limitationA distinction the author states is the correct one is then deliberately not made anywhere in the rest of the paper.
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limitations[9]
Content tags
content-observations: finding · quantity · variable · definition · key-term — grounded in the full text
findingthe large N limit of certain CFTs contains supergravity in its Hilbert space
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content_tags.findings[0]
evidence status notefinding — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted.content_tags.findings[0]
findingM/string theory on Anti-deSitter backgrounds is conjectured dual to conformal field theories
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content_tags.findings[1]
findingthe correspondence is a strong-weak coupling correspondence
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content_tags.findings[2]
findingHawking radiation is a 1/N effect
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content_tags.findings[3]
not machine-vouchedfinding — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.findings[3]
findingfor small g and large N, the Yang-Mills theory is predicted to contain strings
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content_tags.findings[4]
quantity32 supersymmetries — maximal supersymmetry fixing the probe action
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content_tags.quantities[0]
quantityAdS5 x S5 geometry — near-horizon geometry of N D3-branes
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content_tags.quantities[1]
not machine-vouchedquantity — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.quantities[1]
quantitysqrt(4 pi g N) radius^2 / alpha' — quantized radius of the five-sphere and AdS5
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content_tags.quantities[2]
not machine-vouchedquantity — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.quantities[2]
quantity(0,2) CFT — six-dimensional theory dual to AdS7 x S4
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content_tags.quantities[3]
quantityAdS3 x S3 geometry — near-horizon geometry of the D1+D5 system
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content_tags.quantities[4]
not machine-vouchedquantity — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.quantities[4]
variableN (rank of gauge group; sets geometry size in Planck units)
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content_tags.variables[0]
variableg (type IIB string coupling, held fixed)
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content_tags.variables[1]
evidence status notevariable — marked quote-not-in-current-staged-text - today's merge gate would REFUSE this quote: Paper.locate() does not find it in the current staged text.content_tags.variables[1]
not machine-vouchedvariable — not-in-our-copy - The quote is in the original page we fetched for this paper ('fulltext.html'), but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside. This body carries no measurable character damage at all.content_tags.variables[1]
variableU (radial coordinate interpreted as gauge-theory energy scale)
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content_tags.variables[2]
variablegN (effective 't Hooft coupling controlling which description is valid)
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content_tags.variables[3]
definitionsuperconformal group
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content_tags.definitions[0]
evidence status notedefinition — QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted.content_tags.definitions[0]
definitiondecoupling limit
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content_tags.definitions[1]
definitionR-symmetry
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content_tags.definitions[2]
definition't Hooft limit
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content_tags.definitions[3]
evidence status notedefinition — marked quote-not-in-current-staged-text - today's merge gate would REFUSE this quote: Paper.locate() does not find it in the current staged text.content_tags.definitions[3]
key-termsconformal field theories, supergravity, large N limit, Anti-deSitter, super-Yang-Mills, branes, superconformal group, string theory, M-theory, near horizon geometry, duality
Concepts
terms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on CONCEPTS.html.
conceptconformal field theory
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concepts[3]
conceptstring theory
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concepts[4]
conceptsupergravity
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concepts[5]
conceptnear horizon geometry
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concepts[6]

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