Derived Categories and Zero-Brane Stability

Abstract

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.

24 pages, no figures, LaTeX2e. (v2) Added references, fixed typos, small changes, esp. in discussions of D0-brane stability. (v3) Explanatory comments added, corrected discussion of birational invariance of derived category