Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

We give a systematic derivation of the consistency conditions which constrainopen-closed disk amplitudes of topological strings. They include the A-infinityrelations (which generalize associativity of the boundary product oftopological field theory), as well as certain homotopy versions ofbulk-boundary crossing symmetry and Cardy constraint. We discuss integrabilityof amplitudes with respect to bulk and boundary deformations, and write downthe analogs of WDVV equations for the space-time superpotential. We also studythe structure of these equations from a string field theory point of view. Asan application, we determine the effective superpotential for certain familiesof D-branes in B-twisted topological minimal models, as a function of bothclosed and open string moduli. This provides an exact description of tachyoncondensation in such models, which allows one to determine the truncation ofthe open string spectrum in a simple manner.Comment: 53 page