Chiral Equivariant Cohomology I

Abstract

We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham complex of Malikov-Schechtman-Vaintrob of a manifold with a group action. The main idea in this paper is to synthesize the algebraic approach to classical equivariant cohomology due to H. Cartan, with the theory of differential vertex algebras, by using an appropriate notion of invariant theory. We also construct the vertex algebra analogues of the Mathai-Quillen isomorphism, the Weil and the Cartan models for equivariant cohomology, and the Chern-Weil map. We give interesting cohomology classes in the new theory that have no classical analogues.

76 pages, final version, to appear in Advances in Mathematics

References in corpus (2)

• Supersymmetry of the Chiral de Rham Complex
• Chiral Equivariant Cohomology II

Cited by in corpus (17)

• Supersymmetry of the Chiral de Rham Complex
• Supersymmetric vertex algebras
• Howe Pairs in the Theory of Vertex Algebras
• Invariant chiral differential operators and the W_3 algebra
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• Chiral Equivariant Cohomology II
• Twisted chiral de Rham complex, generalized geometry, and T-duality
• Snapshots of Conformal Field Theory
• Hodge-elliptic genera and how they govern K3 theories
• T-duality of singular spacetime compactifications in an H-flux
• Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
• Not Doomed to Fail
• T-duality and the exotic chiral de Rham complex
• Chiral equivariant cohomology of a point: a first look
• Non-linear sigma models via the chiral de Rham complex
• Vertex Algebras and the Equivariant Lie Algebroid Cohomology
• Chiral vector bundles