D-branes, Categories and N=1 Supersymmetry

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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harvmac, 41 pp., 2 figures. (v4: corrected errors; added explanations)

Scientific paper

10.1063/1.1374448

We show that boundary conditions in topological open string theory on Calabi-Yau manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise criterion determining the BPS branes at any point in CY moduli space, completing the proposal of Pi-stability.

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