Generalized Calabi-Yau manifolds and the chiral de Rham complex

TL;DR

This paper demonstrates that the chiral de Rham complex on generalized Calabi-Yau manifolds exhibits N=2 supersymmetry and explores its topological twist, linking it to superalgebra constructions.

Contribution

It introduces the presence of N=2 supersymmetry in the chiral de Rham complex of generalized Calabi-Yau manifolds and connects it to algebraic structures like super-Sugawara.

Findings

Chiral de Rham complex has N=2 supersymmetry on generalized Calabi-Yau manifolds

Topological twist of the N=2 algebra is discussed

Relation to super-Sugawara and Kac-Todorov constructions established

Abstract

We show that the chiral de Rham complex of a generalized Calabi-Yau manifold carries N=2 supersymmetry. We discuss the corresponding topological twist for this N=2 algebra. We interpret this as an algebroid version of the super-Sugawara or Kac-Todorov construction.