  We compute the partition function for the topological Landau-Ginzburg B-model
on the disk. This is done by treating the worldsheet superpotential
perturbatively. We argue that this partition function as a function of bulk and
boundary perturbations may be identified with the effective D-brane
superpotential in the target spacetime. We point out the relationship of this
approach to matrix factorizations. Using these methods, we prove a conjecture
for the effective superpotential of Herbst, Lazaroiu and Lerche for the A-type
minimal models. We also consider the Landau-Ginzburg theory of the cubic torus
where we show that the effective superpotential, given by the partition
function, is consistent with the one obtained by summing up disk instantons in
the mirror A-model. This is done by explicitly constructing the open-string
mirror map.
