Generalized Calabi-Yau manifolds and the chiral de Rham complex (Q2268618)

The authors show that the chiral de Rham complex of a generalized Calabi-Yau manifold admits \(N=2\) supersymmetry, and discuss the corresponding topological twist for this algebra. They then interpret this as an algebroid version of the super-Sugawara, or Kac-Todorov construction. Contents include: Introduction (containing a review of the literature); Preliminaries on vertex algebras; Preliminaries on geometry; Sheaves of vertex algebras; \(N=2\) supersymmetry; Concluding remarks; Appendix; References (twenty-eight items).