A Geometrical Construction of Rational Boundary States in Linear Sigma Models

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.