nLab sheaf of vertex operator algebras

Idea

A sheaf of vertex operator algebras.

This arises naturally in the descriptions of 2d CFTs such as the 2d (2,0)-superconformal QFT which patchwise on target space is a free field theory, but not globally so.

If the degree-0 part of a sheaf of vertex operator algebras is the structure sheaf of the base space, then one one may think of the whole sheaf as defining a “horizontal categorification” of a vertex operator algebra and hence one also speaks of a vertex operator algebroid.

Examples

• chiral de Rham complex

References

• Fyodor Malikov, Lagrangian approach to sheaves of vertex operator algebras, ESI preprint 1828 (2006) (pdf)

Formalization of the Witten genus in terms of sheaves of vertex operator algebras is in

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