Representation theory of vertex operator algebras and orbifold conformal field theory

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages221-252
Number of pages32
DOIs
StatePublished - 2021
Externally publishedYes

Publication series

NameContemporary Mathematics
Volume768
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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