Towards mirror symmetry à la SYZ for generalized Calabi–Yau manifolds
نویسنده
چکیده
Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal sixmanifold M with static SU(2) structure and mirror M̂ , it is argued that the product M×M̂ is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and M̂ . The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3)×SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.
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