Worldsheet approaches to D-branes on supersymmetric cycles

TL;DR

This paper explores D-branes on supersymmetric cycles in Calabi-Yau manifolds using worldsheet methods, linking Landau-Ginzburg models and Gepner models to understand boundary states and their target space interpretation.

Contribution

It establishes a connection between Landau-Ginzburg boundary states and Gepner model boundary states through discrete symmetries, extending the bulk correspondence to boundaries.

Findings

Boundary states constructed via Cardy's procedure in Gepner models.

Target space interpretation of boundary states in Landau-Ginzburg models.

Extension of bulk Landau-Ginzburg/Gepner correspondence to boundary cases.

Abstract

We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using the common discrete symmetries of the two descriptions. We are thus able to provide an extension to the boundary of the bulk correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner models.