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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 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 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

Last revised on May 8, 2017 at 16:09:46. See the history of this page for a list of all contributions to it.