# Lectures on mirror symmetry, derived categories, and D-branes

@article{Kapustin2004LecturesOM, title={Lectures on mirror symmetry, derived categories, and D-branes}, author={Anton Kapustin and Dmitri O. Orlov}, journal={Russian Mathematical Surveys}, year={2004}, volume={59}, pages={907-940} }

This paper, mainly intended for a mathematical audience, is an introduction to homological mirror symmetry, derived categories, and topological D-branes. Mirror symmetry from the point of view of physics is explained, along with the relationship between symmetry and derived categories, and the reason why the Fukaya category must be extended by using co-isotropic A-branes. There is also a discussion of how to extend the definition of the Floer homology to these objects and a description of…

## 32 Citations

Stability Conditions For Topological D-branes: A Worldsheet Approach

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We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X…

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We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation…

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We consider non-compact Calabi-Yau threefolds that are fibrations over compact Riemann surfaces, the local curves, and study the dynamics of B-branes wrapped around the curves. We discuss different…

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Up to now chiral type IIA vacua have been mostly based on intersecting D6-branes wrapping special Lagrangian 3-cycles on a CY3 manifold. We argue that there are additional BPS D-branes which have so…

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We study disk-instantons ending on coisotropic branes preserved by real torus action in toric Calabi-Yau 3-folds. In particular, we find fermion zero modes on disk multi-covers ending on a…

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We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X…

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