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.
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
NERFINISHED
ⓘ
Lev Rozansky NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
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
NERFINISHED
ⓘ
Lev Rozansky NERFINISHED ⓘ |
| produces |
graph cohomology classes
ⓘ
invariants valued in cohomology of the target manifold ⓘ weight systems for Vassiliev invariants ⓘ |
| quantizationType | topological ⓘ |
| relatedTo |
Chern–Simons theory
NERFINISHED
ⓘ
Donaldson–Thomas theory NERFINISHED ⓘ Gromov–Witten theory NERFINISHED ⓘ 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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.