Section 5
Defining conformal field theories

This section finally contains the definition of CFTs: We only need to put together the basic structures introduced so far. I discuss notions like equivalences of CFTs and Ward identities. Though full proofs would exceed the scope of this lecture course by far, I briefly explain how our two basic examples, the Ising model and the model of a free boson compactified on a circle, give full well-defined CFTs. I also give a (necessarily brief) account of axiomatic approaches to quantum field theories, explaining how CFTs, according to our definition, are "limits" of special quantum field theories. Finally I compare our definition to other similar approaches to CFT, like the works of Moore/Seiberg, Segal, Friedan/Shenker, Gaberdiel/Goddard, Kac, and others.