A Geometrical Construction of Rational Boundary States in Linear Sigma Models

TL;DR

This paper geometrically constructs rational boundary states in linear sigma models, linking special Lagrangian submanifolds with D-branes and Gepner model boundary states, offering new insights and construction methods.

Contribution

It provides a geometric approach to construct and understand rational boundary states in linear sigma models and their relation to Gepner models, including new construction possibilities.

Findings

Identifies a subclass of A-type D-branes with Gepner model boundary states

Reproduces topological properties like labeling and intersection numbers

Suggests new methods for constructing Gepner model boundary states

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.