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Mirror Symmetry

Kentaro Hori·Cumrun Vafa
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Abstract

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type. Standard R -> 1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This provides not only a proof of mirror symmetry in the case of (local and global) Calabi-Yau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the action by holomorphic isometries.

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Kentaro Hori, Cumrun Vafa. 2000-03-31. Mirror Symmetry. https://arxiv.org/abs/hep-th/0002222

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