nLab
chiral de Rham complex

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 resolutuion

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 XX arises as the quantum observables of the topologically twisted 2d (2,0)-superconformal QFT sigma-model with target space XX.

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

Revised on March 21, 2014 09:05:17 by Urs Schreiber (89.204.138.115)