The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes

TL;DR

This paper provides a detailed correspondence between B-type D-branes in Landau-Ginzburg models and objects in the derived category of Calabi-Yau manifolds, confirming several theoretical conjectures.

Contribution

It offers a precise recipe for mapping D-branes between Landau-Ginzburg models and Calabi-Yau geometries, extending previous work with explicit examples.

Findings

Confirmed several conjectures in the literature.

Mapped D-branes in Landau-Ginzburg models to derived categories.

Provided examples involving quotient singularities and weighted projective spaces.

Abstract

Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories correspond to matrix factorizations and the D-branes on the Calabi-Yau manifolds are objects in the derived category. We give several examples including branes on quotient singularities associated to weighted projective spaces. We are able to confirm several conjectures and statements in the literature.