A Geometrical Construction of Rational Boundary States in Linear Sigma Models
arXiv:hep-th/0203266 · doi:10.1016/S0550-3213(02)00898-2
Abstract
Starting from the geometrical construction of special Lagrangian submanifolds of a toric variety, we identify a certain subclass of A-type D-branes in the linear sigma model for a Calabi-Yau manifold and its mirror with the A- and B-type Recknagel-Schomerus boundary states of the Gepner model, by reproducing topological properties such as their labeling, intersection, and the relationships that exist in the homology lattice of the D-branes. In the non-linear sigma model phase these special Lagrangians reproduce an old construction of 3-cycles relevant for computing periods of the Calabi-Yau, and provide insight into other results in the literature on special Lagrangian submanifolds on compact Calabi-Yau manifolds. The geometrical construction of rational boundary states suggests several ways in which new Gepner model boundary states may be constructed.
45 pages, 8 Postscript figures, LaTeX2e. v2: the construction reproduces a larger set of CFT boundary states; clarified discussion of instanton contributions and moduli; other minor improvements; references added . v3: version accepted for publication in Nuclear Physics B (minor changes)
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