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Dirichlet branes, homological mirror symmetry, and stability

Michael R. Douglas
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Abstract

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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Michael R. Douglas. 2002-07-05. Dirichlet branes, homological mirror symmetry, and stability. https://arxiv.org/abs/math/0207021

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