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 (3)
| Label | Occurrences |
|---|---|
| Donaldson–Witten theory canonical | 1 |
| Witten’s topological quantum field theory | 1 |
| cohomological Yang–Mills theory | 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.
-
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
- 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
ⓘ
linked to:
Seiberg–Witten theory
|
| computes | intersection forms on four-manifolds ⓘ |
| constructedBy | twisting N=2 supersymmetric Yang–Mills theory ⓘ |
| defines | BRST cohomology ⓘ |
| developedBy | Edward Witten ⓘ |
| formulatedIn | late 1980s ⓘ |
| framework | Euclidean quantum field theory ⓘ |
| hasAction | topological Yang–Mills action ⓘ |
| hasFieldContent |
fermionic fields
ⓘ
gauge field ⓘ scalar fields ⓘ |
| hasGaugeGroup |
SO(3)
ⓘ
linked to:
rotation group SO(3)
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
ⓘ
Simon Donaldson ⓘ |
| observablesClassifiedBy | BRST cohomology classes ⓘ |
| pathIntegralLocalizesOn |
anti-self-dual gauge connections
ⓘ
instantons ⓘ |
| produces |
Donaldson polynomials
ⓘ
linked to:
Donaldson invariants
|
| quantizationMethod | path integral quantization ⓘ |
| relatedConcept |
cohomological Yang–Mills theory
ⓘ
linked to:
Donaldson–Witten theory
topological twisting ⓘ |
| relatedTo |
Donaldson theory
ⓘ
Seiberg–Witten theory ⓘ Yang–Mills instantons ⓘ
linked to:
Yang–Mills theory
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 ⓘ |
How these facts were elicited
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Instruction
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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 (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Donaldson–Witten theory
linked to: Donaldson–Witten theory