Bogolyubov Institute for Theoretical Physics,
14-b Metrologichna Str.,
Kyiv 03143,
E-mail: burban@bitp.kiev.ua

Some aspects of stability of topological D-branes

We analyze the correspondence between classical stability of vector bundles and physical stability of type IIB topological D-branes on large-radius limit of moduli space of Calabi-Yau manifold. The D-branes that are sensible away from the large-radius limit points in moduli space of complexified Kähler forms of Calabi-Yay manifold are viewed as objects of bounded derived category of coherent sheaves. The triangle structure of this category defines the rules for D-brane decay. We note particular properties of the space of stability conditions on the bounded derived category of coherent sheaves for some manifolds.