Mirror symmetry realized by T-duality

Show that mirror symmetry is realized by a T-duality map on appropriate fibrations of Calabi–Yau manifolds that model the compact dimensions of two string theories, thereby establishing the proposed geometric mechanism underlying mirror symmetry.

Background

The discussion of T-duality includes its role in relating Type IIA and Type IIB string theories and its broader implications for compactifications on Calabi–Yau manifolds.

The authors highlight the Strominger–Yau–Zaslow proposal that mirror symmetry can be understood via T-duality applied to special fibrations, presenting this as a conjectural realization that links string-theoretic dualities to deep mathematical structures.