Dirichlet branes, homological mirror symmetry, and stability

Details Dirichlet branes, homological mirror symmetry, and stability Dirichlet branes, homological mirror symmetry, and stability

2002-07-02

arxiv.org/abs/math/0207021v2

Mathematics

Algebraic Geometry

15 pp., amstex using special .sty (included). To appear in the 2002 ICM proceedings

Scientific paper

We discuss some mathematical conjectures which have come out of the Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich's homological mirror symmetry conjecture, and "physics proofs" for many of the subsequent conjectures based on it, such as the representation of Calabi-Yau monodromy by autoequivalences of the derived category.

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