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Mirror Symmetry

2003; Cornell University; Linguagem: Inglês

Eric Zaslow, Ravi Vakil, Kentaro Hori, Richard P. Thomas, Cumrun Vafa, Albrecht Klemm, Rahul Pandharipande, Sheldon Katz,

Nonlinear Waves and Solitons

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.