Abstract

Chiral CFTs (VOAs or conformal nets) are interesting for their representation theory. Orbifolds are a standard method for constructing new chiral CFTs from old ones. Start with a chiral theory with trivial representation theory, and orbifold it by a finite group; the result (called a holomorphic orbifold) has the representation theory given by the twisted Drinfeld double of that finite group, where the twist is a 3-cocycle. In practise it is hard to identify that twist. 

I'll begin my talk by giving some examples of orbifolds. I'll identify a well-known class of holomorphic orbifolds where we now know the twist. I'll relate holomorphic orbifolds to KK-theory as well as the PhD thesis of a certain Vaughan Jones. Then I'll explain how any choice of finite group and 3-cocycle is realized by a chiral CFT . This is joint work with David Evans.