On the Landau-Ginzburg description of boundary CFTs and special lagrangian submanifolds

We consider Landau-Ginzburg (LG) models with boundary conditions preservingA-type N=2 supersymmetry. We show the equivalence of a linear class of boundaryconditions in the LG model to a particular class of boundary states in thecorresponding CFT by an explicit computation of the open-string Witten index inthe LG model. We extend the linear class of boundary conditions to generalnon-linear boundary conditions and determine their consistency with A-type N=2supersymmetry. This enables us to provide a microscopic description of specialLagrangian submanifolds in C^n due to Harvey and Lawson. We generalise thisconstruction to the case of hypersurfaces in P^n. We find that the boundaryconditions must necessarily have vanishing Poisson bracket with the combination(W(\phi)-\bar{W}(\bar{\phi})), where W(\phi) is the appropriate superpotentialfor the hypersurface. An interesting application considered is the T^3supersymmetric cycle of the quintic in the large complex structure limit.Comment: 28+1 pages; no figures; requires JHEP.cls, amssymb; (v2) typo corrected; (v3) references adde