Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
arXiv:math/0012196
Abstract
Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau three-fold is seen to have an expected adiabatic form for its induced cohomology operation only when an appropriately twisted operation resp. twisted charge is defined. Some differences with the case of as well as connections with the spectral cover construction for bundles on are pointed out. In the context of mirror symmetry Kontsevich's association of line bundle twists (resp. a certain 'diagonal' operation) with monodromies (esp. the conifold monodromy) is made explicit and checked for two example models. Interpreting this association as a relation between FM transforms and monodromies, we express the fibrewise FM transform through known monodromies. The operation of fibrewise duality as well as the notion of a certain index relevant to the computation of the moduli space of the bundle is transported to the sLag side. Finally the moduli space for D4-branes and its behaviour under the FM transform is considered with an application to the spectral cover.
47p, harvmac
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- Fibrewise T-Duality for D-Branes on Elliptic Calabi-Yau
- Derived Category Automorphisms from Mirror Symmetry
- Mirror Symmetry on Kummer Type K3 Surfaces
- Fourier Mukai Transforms and Applications to String Theory
- Quantum geometry of elliptic Calabi-Yau manifolds
- A Fourier transform for sheaves on Lagrangian families of real tori
- U(n) Vector Bundles on Calabi-Yau Threefolds for String Theory Compactifications
- On genus one fibered Calabi-Yau threefolds with 5-sections
- Extending the Geometry of Heterotic Spectral Cover Constructions
- Comments on N=1 Heterotic String Vacua
- On a relative Fourier-Mukai transform on genus one fibrations
- Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations
- Stable pairs on nodal K3 fibrations