Mirror Symmetry is T-Duality

TL;DR

The paper demonstrates that mirror symmetry for Calabi-Yau manifolds can be understood as T-duality acting on supersymmetric 3-cycles, linking the moduli spaces of cycles and their flat connections to the mirror manifold.

Contribution

It establishes that mirror symmetry corresponds to T-duality on supersymmetric 3-cycles, providing a geometric framework for understanding the moduli space of these cycles.

Findings

Mirror symmetry is equivalent to T-duality on 3-cycles.

The moduli space of supersymmetric 3-cycles with flat connections is the mirror manifold.

Several explicit examples illustrate the theoretical framework.

Abstract

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.