Rozansky–Witten theory
E508542
Rozansky–Witten theory is a three-dimensional topological quantum field theory associated with hyperkähler manifolds that yields invariants of 3-manifolds and links via holomorphic symplectic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Rozansky–Witten theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5273891 — 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: Rozansky–Witten theory Context triple: [topological quantum field theory, example, Rozansky–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.
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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D.
Calabi–Yau manifold
A Calabi–Yau manifold is a special type of complex manifold with vanishing first Chern class that plays a central role in string theory compactifications and complex algebraic geometry.
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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: Rozansky–Witten theory Target entity description: Rozansky–Witten theory is a three-dimensional topological quantum field theory associated with hyperkähler manifolds that yields invariants of 3-manifolds and links via holomorphic symplectic geometry.
-
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.
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.
-
D.
Calabi–Yau manifold
A Calabi–Yau manifold is a special type of complex manifold with vanishing first Chern class that plays a central role in string theory compactifications and complex algebraic geometry.
-
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 (49)
| Predicate | Object |
|---|---|
| instanceOf |
3-dimensional topological quantum field theory
ⓘ
topological quantum field theory ⓘ |
| associatedWith |
3-manifolds
ⓘ
holomorphic symplectic manifolds ⓘ hyperkähler manifolds ⓘ links ⓘ |
| defines |
3-manifold invariants
ⓘ
link invariants ⓘ |
| developedBy |
Edward Witten
ⓘ
Lev Rozansky ⓘ |
| dimension | 3 ⓘ |
| field |
geometric representation theory
ⓘ
hyperkähler geometry ⓘ low-dimensional topology ⓘ mathematical physics ⓘ quantum field theory ⓘ symplectic geometry ⓘ |
| generalizes | finite-type 3-manifold invariants ⓘ |
| invariantType | topological invariant ⓘ |
| involves |
Atiyah class
ⓘ
Feynman graph weight systems ⓘ curvature tensor of the hyperkähler metric ⓘ holomorphic symplectic form ⓘ trivalent graphs ⓘ |
| mathematicalStructure | functor from 3-dimensional cobordism category to vector spaces ⓘ |
| motivation | to construct new 3-manifold invariants from hyperkähler geometry ⓘ |
| namedAfter |
Edward Witten
ⓘ
Lev Rozansky ⓘ |
| produces |
graph cohomology classes
ⓘ
invariants valued in cohomology of the target manifold ⓘ weight systems for Vassiliev invariants ⓘ |
| quantizationType | topological ⓘ |
| relatedTo |
Chern–Simons theory
ⓘ
Donaldson–Thomas theory ⓘ Gromov–Witten theory ⓘ topological sigma models ⓘ |
| studiedIn |
3-manifold topology
ⓘ
algebraic geometry ⓘ symplectic topology ⓘ |
| supersymmetryOrigin | N=4 supersymmetric sigma model in three dimensions ⓘ |
| targetSpace | hyperkähler manifold ⓘ |
| twistType | topological twist of N=4 supersymmetry ⓘ |
| uses |
Feynman diagram expansions
ⓘ
configuration space integrals ⓘ holomorphic symplectic geometry ⓘ hyperkähler geometry ⓘ supersymmetric sigma models ⓘ topological twisting ⓘ |
| yearProposed | 1996 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Rozansky–Witten theory Description of subject: Rozansky–Witten theory is a three-dimensional topological quantum field theory associated with hyperkähler manifolds that yields invariants of 3-manifolds and links via holomorphic symplectic geometry.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.