# Contents

## Idea

A sheaf of vertex operator algebras (in fact a vertex operator algebroid) which is naturally associated with a complex manifold whose first and second Chern class vanishes.

## Properties

### Fine resolution

The chiral de Rham complex sheaf of vertex operator algebras as a resolution to a fine sheaf by the chiral Dolbeault complex (Cheung 10).

### Relation to 2d (2,0)-superconformal QFT

The chiral de Rham complex of $X$ arises as the quantum observables of the topologically twisted 2d (2,0)-superconformal QFT sigma-model with target space $X$.

Under suitable geometric conditions (a version of string structure) the local chiral de Rham complexes glue together to a sheaf of vertex operator algebras and serves to compute the Witten genus.

## References

The resolution by the chiral Dolbeault complex is due to

• Pokman Cheung, The Witten genus and vertex algebras (arXiv:0811.1418)

• Urs Schreiber at string cafe:

• Yuly Billig, Vyacheslav Futorny, Representations of Lie algebra of vector fields on a torus and chiral de Rham complex, arxiv/1108.6092

Revised on May 8, 2017 16:09:46 by Anonymous (2607:f140:400:a02a:5378:cafd:355:d146)