Donaldson–Witten theory
E508540
Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Donaldson–Witten theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5273889 — 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: Donaldson–Witten theory Context triple: [topological quantum field theory, example, Donaldson–Witten theory]
-
A.
Seiberg–Witten theory
Seiberg–Witten theory is a framework in quantum field theory and string theory that uses supersymmetry to exactly analyze strongly coupled gauge theories, leading to profound insights into dualities and four-dimensional topology.
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B.
Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
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C.
Yang–Mills theory
Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
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D.
Witten index
The Witten index is a topological invariant in supersymmetric quantum field theory that counts the difference between bosonic and fermionic zero-energy states, providing insight into supersymmetry breaking.
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E.
topological quantum field theory
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
- 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: Donaldson–Witten theory Target entity description: Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
-
A.
Seiberg–Witten theory
Seiberg–Witten theory is a framework in quantum field theory and string theory that uses supersymmetry to exactly analyze strongly coupled gauge theories, leading to profound insights into dualities and four-dimensional topology.
-
B.
Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
-
C.
Yang–Mills theory
Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
-
D.
Witten index
The Witten index is a topological invariant in supersymmetric quantum field theory that counts the difference between bosonic and fermionic zero-energy states, providing insight into supersymmetry breaking.
-
E.
topological quantum field theory
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
cohomological field theory
ⓘ
four-dimensional quantum field theory ⓘ topological quantum field theory ⓘ |
| appliesTo | smooth four-manifolds ⓘ |
| basedOn | N=2 supersymmetric Yang–Mills theory NERFINISHED ⓘ |
| computes | intersection forms on four-manifolds ⓘ |
| constructedBy | twisting N=2 supersymmetric Yang–Mills theory ⓘ |
| defines | BRST cohomology ⓘ |
| developedBy | Edward Witten NERFINISHED ⓘ |
| formulatedIn | late 1980s ⓘ |
| framework | Euclidean quantum field theory NERFINISHED ⓘ |
| hasAction | topological Yang–Mills action ⓘ |
| hasFieldContent |
fermionic fields
ⓘ
gauge field ⓘ scalar fields ⓘ |
| hasGaugeGroup |
SO(3)
NERFINISHED
ⓘ
SU(2) ⓘ |
| hasObservable |
Wilson operators
ⓘ
surface operators ⓘ topological observables ⓘ |
| hasSpacetimeDimension | 4 ⓘ |
| hasSymmetry | topological supersymmetry ⓘ |
| hasTwistType | topological twist ⓘ |
| inspired | development of Seiberg–Witten invariants ⓘ |
| invariantUnder | smooth deformations of the metric ⓘ |
| mathematicalOutput | smooth structure invariants of four-manifolds ⓘ |
| metricDependence | Q-exact up to topological terms ⓘ |
| namedAfter |
Edward Witten
NERFINISHED
ⓘ
Simon Donaldson NERFINISHED ⓘ |
| observablesClassifiedBy | BRST cohomology classes ⓘ |
| pathIntegralLocalizesOn |
anti-self-dual gauge connections
ⓘ
instantons ⓘ |
| produces | Donaldson polynomials NERFINISHED ⓘ |
| quantizationMethod | path integral quantization ⓘ |
| relatedConcept |
cohomological Yang–Mills theory
NERFINISHED
ⓘ
topological twisting ⓘ |
| relatedTo |
Donaldson theory
NERFINISHED
ⓘ
Seiberg–Witten theory NERFINISHED ⓘ Yang–Mills instantons NERFINISHED ⓘ moduli space of anti-self-dual connections ⓘ |
| requires |
Riemannian metric
ⓘ
oriented four-manifold ⓘ |
| scalarSuperchargeSquaresTo | zero ⓘ |
| studiedIn |
differential topology
ⓘ
mathematical physics ⓘ |
| twistActsOn | R-symmetry of N=2 supersymmetry ⓘ |
| twistProduces | scalar supercharge ⓘ |
| usedToCompute | Donaldson invariants NERFINISHED ⓘ |
How these facts were elicited
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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: Donaldson–Witten theory Description of subject: Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.