String field theory and brane superpotentials

I discuss tree-level amplitudes in cubic topological string field theory,showing that a certain family of gauge conditions leads to an A-infty algebraof tree-level string products which define a potential describing the dynamicsof physical states. Upon using results of modern deformation theory, I showthat the string moduli space admits two equivalent descriptions, one given instandard Maurer-Cartan fashion and another given in terms of a `homotopyMaurer-Cartan problem', which describes the critical set of the potential. Byapplying this construction to the topological A and B models, I obtain anintrinsic formulation of `D-brane superpotentials' in terms of string fieldtheory data. This gives a prescription for computing such quantities to allorders, and proves the equivalence of this formulation with the fundamentaldescription in terms of string field moduli. In particular, it clarifies therelation between the Chern-Simons/holomorphic Chern-Simons actions and thesuperpotential for A/B-type branes.Comment: 42 pages, 3 figure