Chiral vector bundles

Abstract

Given a smooth $G$-vector bundle $E\to M$ with a connection $\nabla$, we propose the construction of a sheaf of vertex algebras ${\mathcal{E}}^{ch(E,\nabla )}$, which we call a \textit{chiral vector bundle}. ${\mathcal{E}}^{ch(E,\nabla )}$ contains as subsheaves the sheaf of superalgebras $\Omega \otimes \Gamma (SE\otimes \Lambda E)$ and the sheaf of Lie algebras generated by certain endomorphisms of these superalgebras: $\nabla$, the infinitesimal gauge transformations of $E$, and the contraction operators ${\iota }_X$ on differential forms $\Omega$. Another subsheaf of primary importance is the chiral vector bundle $\mathcal{E}^{ch(M\times \C,d)}$, which is closely related to the chiral de Rham sheaf of Malikov et alii.

References in corpus (3)

• Chiral Equivariant Cohomology I
• Formal loops IV: Chiral differential operators
• $K$-theory associated to vertex operator algebras