Bogolyubov Institute for Theoretical Physics,

14-b Metrologichna Str.,

Kyiv 03143,

UKRAINE

E-mail: burban@bitp.kiev.ua

**Some aspects of stability of topological D-branes**

**Abstract:**

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.