D-branes as a Bubbling Calabi-Yau

We prove that the open topological string partition function on aD-brane configuration in a Calabi-Yau manifoldX takes the form of a closed topological string partition function on a different Calabi-Yau manifold Xb. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by closed string theory in Xb. The physical interpretation of the “bubbling” Calabi-Yau Xb is as the space obtained by letting the Dbranes inX undergo a geometric transition. This implies, in particular, that the partition function of closed topological string theory on certain bubbling Calabi-Yau manifolds are invariants of knots in the three-sphere. jgomis at perimeterinstitute.ca takuya at kitp.ucsb.edu