AdS isometry group SO(2,d)
E143965
The AdS isometry group SO(2,d) is the spacetime symmetry group of (d+1)-dimensional anti-de Sitter space, matching the conformal symmetry group of the dual d-dimensional field theory in the AdS/CFT correspondence.
All labels observed (2)
| Label | Occurrences |
|---|---|
| AdS isometry group SO(2,d) canonical | 1 |
| O(2,d-1) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1250471 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: AdS isometry group SO(2,d) Context triple: [AdS/CFT correspondence, hasSymmetry, AdS isometry group SO(2,d)]
-
A.
AdS/CFT correspondence
The AdS/CFT correspondence is a conjectured duality in theoretical physics that equates a gravity theory in anti-de Sitter space with a conformal field theory on its boundary, providing a powerful framework for understanding quantum gravity and strongly coupled quantum field theories.
-
B.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
C.
de Sitter spacetime
de Sitter spacetime is a maximally symmetric, curved solution of general relativity that models an expanding universe dominated by a positive cosmological constant (dark energy).
-
D.
Green–Schwarz mechanism
The Green–Schwarz mechanism is a key anomaly-cancellation process in string theory that ensures the mathematical consistency of certain superstring models by eliminating gauge and gravitational anomalies.
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E.
Lorentz group
The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: AdS isometry group SO(2,d) Target entity description: The AdS isometry group SO(2,d) is the spacetime symmetry group of (d+1)-dimensional anti-de Sitter space, matching the conformal symmetry group of the dual d-dimensional field theory in the AdS/CFT correspondence.
-
A.
AdS/CFT correspondence
The AdS/CFT correspondence is a conjectured duality in theoretical physics that equates a gravity theory in anti-de Sitter space with a conformal field theory on its boundary, providing a powerful framework for understanding quantum gravity and strongly coupled quantum field theories.
-
B.
Poincaré group
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
C.
de Sitter spacetime
de Sitter spacetime is a maximally symmetric, curved solution of general relativity that models an expanding universe dominated by a positive cosmological constant (dark energy).
-
D.
Green–Schwarz mechanism
The Green–Schwarz mechanism is a key anomaly-cancellation process in string theory that ensures the mathematical consistency of certain superstring models by eliminating gauge and gravitational anomalies.
-
E.
Lorentz group
The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
ⓘ
conformal group ⓘ isometry group ⓘ spacetime symmetry group ⓘ |
| actsOn | (d+1)-dimensional anti-de Sitter space ⓘ |
| appearsInFramework | AdS/CFT correspondence ⓘ |
| containsSubgroup |
Lorentz group SO(1,d-1)
ⓘ
linked to:
Lorentz group
Poincaré group in d dimensions ⓘ
linked to:
Poincaré group
d-dimensional dilatations ⓘ d-dimensional special conformal transformations ⓘ d-dimensional translation group ⓘ |
| dimensionFormula | (d+2)(d+1)/2 ⓘ |
| hasCenter | {±I} for even d ⓘ |
| hasFullName |
special orthogonal group SO(2,d)
ⓘ
linked to:
special orthogonal group SO(n)
|
| hasLieAlgebra | so(2,d) ⓘ |
| hasNumberOfGenerators | (d+2)(d+1)/2 ⓘ |
| hasProperty | simple Lie group for d ≥ 3 ⓘ |
| hasRole |
classifies unitary representations used for bulk fields
ⓘ
matches boundary conformal symmetry in AdS/CFT ⓘ |
| hasSignature | (2,d) ⓘ |
| hasType | orthogonal group ⓘ |
| hasUniversalCover | Spin(2,d) ⓘ |
| isBosonicSubgroupOf | AdS supergroup in supersymmetric AdS/CFT ⓘ |
| isConformalGroupOf | d-dimensional Minkowski space ⓘ |
| isConformalSymmetryGroupOf | d-dimensional CFT in AdS/CFT correspondence ⓘ |
| isConnectedComponentOf | O(2,d) ⓘ |
| isDefinedAs | group of linear transformations preserving a bilinear form of signature (2,d) ⓘ |
| isGlobalSymmetryOf | AdS_{d+1} background ⓘ |
| isIsometryGroupOf | (d+1)-dimensional anti-de Sitter space ⓘ |
| isIsomorphicTo | conformal group in d-dimensional Minkowski space ⓘ |
| isMaximalSymmetryGroupOf | AdS_{d+1} ⓘ |
| isNonCompact | true ⓘ |
| isometryGroupOf |
AdS_{d+1}
ⓘ
linked to:
anti-de Sitter space
maximally symmetric space with negative curvature ⓘ |
| isRealFormOf | complex Lie group SO(d+2,ℂ) ⓘ |
| isRelevantIn |
higher-spin theories on AdS_{d+1}
ⓘ
quantum gravity in asymptotically AdS spacetimes ⓘ string theory on AdS backgrounds ⓘ |
| isSpacetimeSymmetryGroupOf |
(d+1)-dimensional anti-de Sitter space
ⓘ
AdS_{d+1} ⓘ
linked to:
anti-de Sitter space
|
| isSymmetryOf | Einstein equations with negative cosmological constant in AdS_{d+1} ⓘ |
| isUsedToLabel |
bulk field representations in AdS_{d+1}
ⓘ
conformal primary operators in d-dimensional CFT ⓘ |
| matchesSymmetryGroupOf | d-dimensional conformal field theory ⓘ |
| preserves | quadratic form with signature (2,d) ⓘ |
| relatesToConcept |
gauge/gravity duality
ⓘ
holographic principle ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: AdS isometry group SO(2,d) Description of subject: The AdS isometry group SO(2,d) is the spacetime symmetry group of (d+1)-dimensional anti-de Sitter space, matching the conformal symmetry group of the dual d-dimensional field theory in the AdS/CFT correspondence.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: AdS isometry group SO(2,d)