On CY-LG correspondence for (0,2) toric models
  We conjecture a description of the vertex (chiral) algebras of the (0,2) nonlinear sigma models on smooth quintic threefolds. We provide evidence in favor of the conjecture by connecting our algebras to the cohomology of a twisted chiral de Rham sheaf. We discuss CY/LG correspondence in this setting. 
Lev A. Borisov and Ralph M. Kaufmann
math.AG