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Derived Categories and Zero-Brane Stability
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We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas proposed recently by Douglas. We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space. As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus.
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Categorified structures over moduli spaces: Anomalies, non-invertible symmetries, and exceptional holonomy
The paper conjectures that non-invertible Ising and tricritical Ising symmetries organize closed string states and D-brane categories into categorical bundles over moduli spaces of exceptional holonomy compactifications.
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