Supersymmetry of the chiral de Rham complex II: Commuting Sectors

Abstract

We construct two commuting N=2 structures on the space of sections of the chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra supersymmetry to construct a non-linear automorphism of CDR preserving these N=2 structures. Finally, we show how to extend these results to construct a commuting pair of N=4 super-vertex algebras in the Hyper-Kahler case.

arXiv comment25 pages

References in corpus (5)

• Chiral de Rham complex and the half-twisted sigma-model
• Supersymmetry of the Chiral de Rham Complex
• Instantons beyond topological theory II
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Vertex Algebroids II

Cited by in corpus (6)

• Generalized Calabi-Yau manifolds and the chiral de Rham complex
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• Lambda: A Mathematica-package for operator product expansions in vertex algebras
• Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models
• Vertex Algebras and the Equivariant Lie Algebroid Cohomology