Generalized Calabi-Yau manifolds and the chiral de Rham complex

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.

25 pages

References in corpus (11)

• Chiral de Rham complex and the half-twisted sigma-model
• Supersymmetry of the Chiral de Rham Complex
• Lectures on Generalized Complex Geometry and Supersymmetry
• Supersymmetric vertex algebras
• Generalized Kahler Geometry from supersymmetric sigma models
• Poisson sigma model on the sphere
• Vertex Algebroids II
• Supersymmetry of the chiral de Rham complex II: Commuting Sectors
• Lagrangian approach to sheaves of vertex algebras
• On the determinant bundles of abelian schemes
• Homotopy Gerstenhaber Structures and Vertex Algebras

Cited by in corpus (9)

• Mathieu Moonshine and the Geometry of K3 Surfaces
• Dilogarithms, OPE and twisted T-duality
• Superconformal structures on generalized Calabi-Yau metric manifolds
• Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
• Generalized Kähler Geometry and current algebras in $SU(2)\times U(1)$ N=2 superconformal WZW model
• Generalized K$\ddot{a}$hler Geometry and current algebras in classical N=2 superconformal WZW model
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models
• The Global Sections of Chiral de Rham Complexes on Closed Complex Curves
• Non-linear sigma models via the chiral de Rham complex