Chiral de Rham complex and the half-twisted sigma-model

TL;DR

This paper links the chiral de Rham complex on Calabi-Yau manifolds to the half-twisted sigma-model, showing their cohomologies coincide and analyzing the independence of correlators from Kähler moduli.

Contribution

It establishes a precise mathematical correspondence between the chiral de Rham complex and the half-twisted sigma-model, including instanton effects.

Findings

Cohomology of the sheaf matches the infinite-volume limit of the half-twisted model

Correlators are independent of Kähler moduli in perturbation theory

Instantons can break the relation between the sheaf and the sigma-model

Abstract

On any Calabi-Yau manifold X one can define a certain sheaf of chiral N=2 superconformal field theories, known as the chiral de Rham complex of X. It depends only on the complex structure of X, and its local structure is described by a simple free field theory. We show that the cohomology of this sheaf can be identified with the infinite-volume limit of the half-twisted sigma-model defined by E. Witten more than a decade ago. We also show that the correlators of the half-twisted model are independent of the Kahler moduli to all orders in worldsheet perturbation theory, and that the relation to the chiral de Rham complex can be violated only by worldsheet instantons.