Superconformal structures on generalized Calabi-Yau metric manifolds

Abstract

We construct an embedding of two commuting copies of the N=2 superconformal vertex algebra in the space of global sections of the twisted chiral-anti-chiral de Rham complex of a generalized Calabi-Yau metric manifold, including the case when there is a non-trivial H-flux and non-vanishing dilaton. The 4 corresponding BRST charges are well defined on any generalized Kahler manifold. This allows one to consider the half-twisted model defining thus the chiral de Rham complex of a generalized Kahler manifold. The classical limit of this result allows one to recover the celebrated generalized Kahler identities as the degree zero part of an infinite dimensional Lie superalgebra attached to any generalized Kahler manifold. As a byproduct of our study we investigate the properties of generalized Calabi-Yau metric manifolds in the Lie algebroid setting.

30 pp

References in corpus (9)

• Chiral de Rham complex
• Elliptic Genera and Applications to Mirror Symmetry
• Generalized complex manifolds and supersymmetry
• Supersymmetric vertex algebras
• Generalized Kahler Geometry from supersymmetric sigma models
• Poisson sigma model on the sphere
• Courant-Dorfman algebras and their cohomology
• Generalized Calabi-Yau manifolds and the chiral de Rham complex
• Lagrangian approach to sheaves of vertex algebras

Cited by in corpus (5)

• The Hitchin--Kobayashi Correspondence for Quiver Bundles over Generalized Kähler Manifolds
• Recent advances and open questions on the susy structure of the chiral de Rham Complex
• Generalized K$\ddot{a}$hler Geometry and current algebras in classical N=2 superconformal WZW model
• Generalized Kähler Geometry and current algebras in $SU(2)\times U(1)$ N=2 superconformal WZW model
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models