Fourier Mukai Transforms and Applications to String Theory
arXiv:math/0412328
Abstract
We give an introductory review of Fourier-Mukai transforms and their application to various aspects of moduli problems, string theory and mirror symmetry. We develop the necessary mathematical background for Fourier-Mukai transforms such as aspects of derived categories and integral functors as well as their relative version which becomes important for making precise the notion of fiberwise T-duality on elliptic Calabi-Yau threefolds. We discuss various applications of the Fourier-Mukai transform to D-branes on Calabi-Yau manifolds as well as homological mirror symmetry and the construction of vector bundles for heterotic string theory.
52 pages. To appear in Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. Minor changes, reference of conjecture in section 7.5 changed, references updated
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Cited by in corpus (10)
- The Swampland Distance Conjecture for Kahler moduli
- A worldsheet extension of O(d,d;Z)
- Heterotic Non-Kahler Geometries via Polystable Bundles on Calabi-Yau Threefolds
- Curve counting on elliptic Calabi-Yau threefolds via derived categories
- Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
- The Spectral Construction for a (1,8)-Polarized Family of Abelian Varieties
- Heterotic Models without Fivebranes
- Undoing Orbifold Quivers
- On genus one fibered Calabi-Yau threefolds with 5-sections
- Fourier-Mukai transforms for coherent systems on elliptic curves