nLab
sheaf of vertex operator algebras

Contents

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Algebra

AQFT

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

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

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.