Landau-Ginzburg realization of open string TFT

We investigate B-type topological Landau-Ginzburg theory with one variable,with D2-brane boundary conditions. We find that the allowed braneconfigurations are determined in terms of the possible factorizations of thesuperpotential, and compute the corresponding open string chiral rings. Theseare characterized by bosonic and fermionic generators that satisfy certainrelations. Moreover we show that the disk correlators, being continuousfunctions of deformation parameters, satisfy the topological sewingconstraints, thereby proving consistency of the theory. In addition we showthat the open string LG model is, in its content, equivalent to a certaintriangulated category introduced by Kontsevich, and thus may be viewed as aconcrete physical realization of it.Comment: Latex, 29p, 1 fig, refs added, various minor corrections, example section droppe