Hitchin connection
E886934
The Hitchin connection is a geometric connection on bundles of conformal blocks over Teichmüller space, central to the study of quantization, moduli spaces, and topological quantum field theory.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
geometric connection
ⓘ
mathematical concept ⓘ projectively flat connection ⓘ |
| actsOn |
Verlinde bundles
ⓘ
spaces of conformal blocks ⓘ |
| arisesFrom |
determinant line bundle with Quillen metric
ⓘ
geometric quantization of the moduli space of flat connections ⓘ variation of complex structures on a Riemann surface ⓘ |
| associatedWith |
Chern–Simons theory
NERFINISHED
ⓘ
Verlinde formula NERFINISHED ⓘ Wess–Zumino–Witten model NERFINISHED ⓘ conformal field theory ⓘ geometric quantization ⓘ mapping class group representations ⓘ modular functors ⓘ moduli spaces ⓘ quantization of character varieties ⓘ quantization of moduli of flat connections ⓘ topological quantum field theory ⓘ |
| definedFor |
compact Riemann surfaces
ⓘ
moduli of stable principal bundles ⓘ surfaces of genus at least 2 ⓘ |
| definedOn |
bundles of conformal blocks
ⓘ
moduli space of flat connections ⓘ moduli space of stable bundles ⓘ vector bundles over Teichmüller space ⓘ |
| domain |
Teichmüller space
NERFINISHED
ⓘ
moduli space of complex structures on a surface ⓘ |
| field |
algebraic geometry
ⓘ
differential geometry ⓘ low-dimensional topology ⓘ mathematical physics ⓘ |
| generalizationOf | Knizhnik–Zamolodchikov connection in genus zero NERFINISHED ⓘ |
| introducedBy | Nigel Hitchin NERFINISHED ⓘ |
| property |
compatible with the mapping class group action
ⓘ
gives parallel transport of conformal blocks ⓘ holomorphic in the Teichmüller parameter ⓘ projectively flat over Teichmüller space ⓘ |
| relatedTo |
Atiyah–Bott symplectic form
NERFINISHED
ⓘ
Goldman symplectic structure NERFINISHED ⓘ Hitchin’s connection on the moduli of bundles NERFINISHED ⓘ Hitchin’s projectively flat connection ⓘ Knizhnik–Zamolodchikov–Bernard connection NERFINISHED ⓘ Quillen connection NERFINISHED ⓘ |
| usedIn |
construction of TQFTs from conformal field theory
ⓘ
construction of quantum representations of mapping class groups ⓘ geometric interpretation of conformal blocks ⓘ study of asymptotics of quantum invariants ⓘ study of quantum Teichmüller theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.