  We give a systematic derivation of the consistency conditions which constrain
open-closed disk amplitudes of topological strings. They include the A-infinity
relations (which generalize associativity of the boundary product of
topological field theory), as well as certain homotopy versions of
bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability
of amplitudes with respect to bulk and boundary deformations, and write down
the analogs of WDVV equations for the space-time superpotential. We also study
the structure of these equations from a string field theory point of view. As
an application, we determine the effective superpotential for certain families
of D-branes in B-twisted topological minimal models, as a function of both
closed and open string moduli. This provides an exact description of tachyon
condensation in such models, which allows one to determine the truncation of
the open string spectrum in a simple manner.

High Energy Physics - Theory;Quantum Algebra