Representation theory of vertex operator algebras and orbifold conformal field theory. (English) Zbl 1518.17032
Adamović, Dražen (ed.) et al., Lie groups, number theory, and vertex algebras. Representation theory XVI. Conference, Inter-University Center, Dubrovnik, Croatia, June 24–29, 2019. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 768, 221-252 (2021).
Summary: 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.
For the entire collection see [Zbl 1470.17001].
For the entire collection see [Zbl 1470.17001].
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
Keywords:
construction of general orbifold conformal field theories; representation theory of vertex operator algebras.References:
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