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. The recent results on the construction 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.
This is an introductory course on orbifold conformal field theory.
In this course I will cover the following topics:
1. Vertex operator algebras and examples.
2. Modules for vertex operator algebras and examples.
3. Twisted modules for vertex operator algebras and examples.
4. Intertwining operators and twisted intertwining operators.
5. The orbifold theory conjecture and the existing results.
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.