Fermionic screenings and line bundle twisted chiral de Rham complex on CY manifolds

We present a generalization of Borisov’s construction of the chiral de Rham complex in the case of the line-bundle-twisted chiral de Rham complex on a Calabi-Yau hypersurface in a projective space. We generalize the differential associated with a polytope Δ of the projective space ℙ ^{d − 1} by allowing nonzero modes for the screening currents forming this differential. It is shown that the numbers of screening current modes define the support function of the toric divisor of a line bundle on ℙ ^{d − 1} that twists the chiral de Rham complex on the Calabi-Yau hypersurface.