As I know, the fundamental concept of QFT is Renormalization Group and RG flow. It is defined by making 2 steps:

We introduce cutting-off and then integrating over "fast" fields $\widetilde{\phi}$, where $\phi=\phi_{0}+\widetilde{\phi}$.

We are doing rescaling: $x\to x/L$: $\phi_{0}(x)\to Z^{-1/2}(L)\phi(x)$.

This procedure defines RG flow on the manifold of quasi local actions: $\frac{dA_{l}}{dl}=B\{A_{l}\}$.

In this approach we have such notions as crytical points $A_{*}$, relevant and irrelevant fields, Callan–Symanzik equation etc, and we can apply it, say, to phase transitions.

Also we can introduce stress-energy tensor $T^{\mu\nu}$. And, as far as i know, if we consider scale transformations $x^{\mu} \to x^{\mu}+\epsilon x^{\mu}$ , we can obtain Callan–Symanzik equation, and if the theory have a crytical point: $\beta^{k}(\lambda^{k})=0$, then trace of stress energy tensor $\Theta(x)=T^{\mu}_{\mu}=0$, so our correlation functions have symmetry at scaling transformation.

**So the question is**: As far as I know, at this point they somehow introduce conformal transformations and Conformal Field Theory. **Can you explain, what place in Quantum Field Theory CFT takes?** (I mean connection between them, sorry if the question is a little vague or stupid). **How it relates to the RG approach exactly?** (This point is very important for me). Maybe some good books?

This post imported from StackExchange Physics at 2014-04-23 15:13 (UCT), posted by SE-user xxxxx