Mirror symmetry is \(T\)-duality. (English) Zbl 0896.14024

Summary: It is argued that every Calabi-Yau manifold \(X\) with a mirror \(Y\) admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space \(Y\). The mirror transformation is equivalent to \(T\)-duality on the 3-cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed.


14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14M30 Supervarieties
14J30 \(3\)-folds
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