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

TL;DR

The work establishes a precise correspondence between the chiral de Rham complex $\Omega_X^{ch}$ on a Calabi–Yau manifold and the infinite-volume limit of the half-twisted sigma-model, via a Dolbeault resolution $\Omega_X^{ch,Dol}$ that matches the ${\bar Q}_+$-cohomology with $d_{Dol}$-cohomology. It proves that, perturbatively, the half-twisted model is independent of the Kähler moduli to all orders, with nonperturbative corrections arising from worldsheet instantons, akin to the A-model but retaining dependence on complex structure. This yields a holomorphic, algebraic description of the half-twisted theory in terms of the cohomology of the Dolbeault resolution of the chiral de Rham complex, and connects local free-field descriptions to global sheaf cohomology. The paper also outlines generalizations to non-Calabi–Yau targets and heterotic-like settings under anomaly-cancellation constraints, suggesting broader applicability of the chiral-de Rham perspective.

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.