# nLab sheaf of vertex operator algebras

Contents

topos theory

## Theorems

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

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.

## 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

Last revised on March 21, 2014 at 08:51:29. See the history of this page for a list of all contributions to it.