Fermionic screenings and chiral de Rham complex on CY manifolds with line bundles

TL;DR

This paper extends Borisov's construction of the chiral de Rham complex to include line bundle twists on Calabi-Yau hypersurfaces, incorporating nonzero modes in screening currents and relating them to toric divisors.

Contribution

It introduces a generalized differential with nonzero modes for screening currents, linking these modes to line bundle twists on Calabi-Yau hypersurfaces in projective space.

Findings

Generalized Borisov's construction for line bundle twists

Established correspondence between screening modes and toric divisors

Extended the differential to include nonzero modes

Abstract

We represent a generalization of Borisov's construction of chiral de Rham complex for the case of line bundle twisted chiral de Rham complex on Calabi-Yau hypersurface in projective space. We generalize the differential associated to the polytope $\Delta$ of the projective space $\mathbb{P}^{d-1}$ 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 toric divisor of a line bundle on $\mathbb{P}^{d-1}$ that twists the chiral de Rham complex on Calabi-Yau hypersurface.