On the Landau-Ginzburg description of Boundary CFTs and special Lagrangian submanifolds
arXiv:hep-th/0003242 · doi:10.1088/1126-6708/2000/07/016
Abstract
We consider Landau-Ginzburg (LG) models with boundary conditions preserving A-type N=2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the corresponding CFT by an explicit computation of the open-string Witten index in the LG model. We extend the linear class of boundary conditions to general non-linear boundary conditions and determine their consistency with A-type N=2 supersymmetry. This enables us to provide a microscopic description of special Lagrangian submanifolds in C^n due to Harvey and Lawson. We generalise this construction to the case of hypersurfaces in P^n. We find that the boundary conditions must necessarily have vanishing Poisson bracket with the combination (W(ϕ)-\bar{W}(\barϕ)), where W(ϕ) is the appropriate superpotential for the hypersurface. An interesting application considered is the T^3 supersymmetric cycle of the quintic in the large complex structure limit.
arXiv comment28+1 pages; no figures; requires JHEP.cls, amssymb; (v2) typo corrected; (v3) references added
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