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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.