Yi-Zhi Huang
Vertex operator algebras and orbifold conformal field theory
Orbifold conformal field theories play an particularly important role in conformal field theory and in the applications of conformal field theory. The moonshine module vertex operator algebra constructed by Frenkel-Lepowsky-Meurman is the first example of orbifold conformal field theories. Many results on the construction and classification of self-dual (or holomorphic) vertex operator algebras of central charge 24 and on the generalized moonshine depend heavily on abelian orbifold conformal field theory. The nonabelian orbifold conformal field theory still needs to be developed.
This is an introductory course on the representation theory of vertex operator algebras and orbifold conformal field theory. The topics covered in the course include:
1. Vertex operator algebras and examples.
2. Modules for vertex operator algebras and examples.
3. Twisted modules for vertex operator algebras and examples.
4. Construction of modules and twisted modules.
5. Intertwining operators and twisted intertwining operators.
5. The orbifold theory conjectures.
6. The moonshine module as an orbifold theory.
7. G-crossed tensor categories.
No textbook. Papers and chapters in books will be discussed in the classes.
Basic courses in algebra and analysis. I will start from the very beginning of the theory of vertex operator algebras.