Aspinwall, PS, *Landau-Ginzburg to Calabi-Yau dictionary for D-branes*,
Journal of Mathematical Physics, vol. 48 no. 8
(2007),
pp. 082304 [hep-th/0610209], [doi] .
**Abstract:**

*Based on the work by Orlov (e-print arXiv:math.AG0503632), 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 with weighted projective spaces. We are able to confirm several conjectures and statements in the literature. © 2007 American Institute of Physics.*