Fourier Mukai Transforms and Applications to String Theory
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.
Cite
@article{arxiv.math/0412328,
title = {Fourier Mukai Transforms and Applications to String Theory},
author = {Bjorn Andreas and Daniel Hernandez Ruiperez},
journal= {arXiv preprint arXiv:math/0412328},
year = {2007}
}
Comments
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