Representation theory of vertex operator algebras and orbifold conformal field theory

Abstract

We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories. We also clarify some misunderstandings on vertex operator algebras, modular functors and intertwining operator algebras. Then we discuss some basic open problems and conjectures in mathematical orbifold conformal field theory. Generalized twisted modules and their variants, their constructions and some existence results are reviewed. Twisted intertwining operators and their basic properties are also reviewed. The conjectural properties in the basic open problems and conjectures mentioned above are then formulated precisely and explicitly. Some thoughts of the author on further developments of orbifold conformal field theory are also discussed.

36 pages

References in corpus (6)

• Braided tensor categories of admissible modules for affine Lie algebras
• On $G$--equivariant modular categories
• On the tensor structure of modules for compact orbifold vertex operator algebras
• Twisted modules and $G$-equivariantization in logarithmic conformal field theory
• On the applicability of logarithmic tensor category theory
• A construction of lower-bounded generalized twisted modules for a grading-restricted vertex (super)algebra