D-branes, Categories and N=1 Supersymmetry
Michael R. Douglas
TL;DR
This paper establishes that boundary conditions in topological open string theory on Calabi-Yau manifolds correspond to objects in the derived category of coherent sheaves, providing a mathematical framework for understanding BPS branes and Pi-stability.
Contribution
It rigorously connects boundary conditions in topological string theory with derived categories, advancing the mathematical understanding of D-branes and stability conditions.
Findings
Boundary conditions correspond to objects in the derived category.
Provides a criterion for BPS branes in CY moduli space.
Completes the Pi-stability proposal.
Abstract
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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