Strominger–Yau–Zaslow conjecture
E551966
The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
conjecture in mirror symmetry
ⓘ
mathematical conjecture ⓘ |
| aimsToExplain |
exchange of complex and symplectic geometry under mirror symmetry
ⓘ
matching of Hodge numbers of mirror Calabi–Yau manifolds ⓘ |
| alsoKnownAs | SYZ conjecture NERFINISHED ⓘ |
| appliesTo |
Calabi–Yau manifolds
NERFINISHED
ⓘ
mirror pairs of Calabi–Yau manifolds ⓘ |
| context | compactification of type II string theory on Calabi–Yau manifolds ⓘ |
| coreIdea | mirror pairs of Calabi–Yau manifolds arise as dual special Lagrangian torus fibrations ⓘ |
| dimensionStatement | fibers are real n-dimensional tori for n-dimensional Calabi–Yau manifolds ⓘ |
| explains | geometric origin of mirror symmetry ⓘ |
| field |
algebraic geometry
ⓘ
mathematical physics ⓘ mathematics ⓘ string theory ⓘ symplectic geometry ⓘ |
| hasAspect |
semi-flat case without singular fibers
ⓘ
singular fibers over discriminant locus ⓘ |
| hasConsequence |
geometric description of D-branes via special Lagrangian submanifolds
ⓘ
interpretation of mirror symmetry as T-duality along torus fibers ⓘ |
| influenced |
development of tropical geometry in mirror symmetry
ⓘ
geometric approaches to mirror symmetry ⓘ study of Lagrangian torus fibrations ⓘ |
| involves |
SYZ fibration
NERFINISHED
ⓘ
base of real dimension equal to complex dimension of Calabi–Yau ⓘ |
| mirrorConstruction | mirror obtained by fiberwise dualizing special Lagrangian tori ⓘ |
| motivatedBy | mirror symmetry in string theory ⓘ |
| namedAfter |
Andrew Strominger
NERFINISHED
ⓘ
Eric Zaslow NERFINISHED ⓘ Shing-Tung Yau NERFINISHED ⓘ |
| predicts | existence of special Lagrangian torus fibrations on Calabi–Yau manifolds ⓘ |
| proposedBy |
Andrew Strominger
NERFINISHED
ⓘ
Eric Zaslow NERFINISHED ⓘ Shing-Tung Yau NERFINISHED ⓘ |
| publishedIn | paper "Mirror Symmetry is T-Duality" ⓘ |
| publishedInJournal | Nuclear Physics B NERFINISHED ⓘ |
| relatedTo |
Gross–Siebert program
NERFINISHED
ⓘ
Gross–Wilson work on K3 surfaces ⓘ SYZ transforms between A-model and B-model data ⓘ |
| relatesTo | homological mirror symmetry conjecture NERFINISHED ⓘ |
| status | open problem ⓘ |
| subfield | mirror symmetry ⓘ |
| usesConcept |
Lagrangian fibrations
ⓘ
T-duality ⓘ dual torus fibrations ⓘ special Lagrangian submanifolds ⓘ torus fibrations ⓘ |
| yearProposed | 1996 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.