# Why can consistent QFTs only arise from CFTs?

This is claimed by Jared Kaplan in his Lectures on AdS/CFT from the Bottom Up.

He writes:

It seems that all QFTs can be viewed as points along an Renormalization Flow (or RG flow, this is the name we give to the zooming process) from a ‘UV’ CFT to another ‘IR’ CFT. Renormalization flows occur when we deform the UV CFT, breaking its conformal symmetry. [...] Well-defined QFTs can be viewed as either CFTs or as RG flows between CFTs. We can remove the UV cutoff from a QFT (send it to infinite energy or zero length) if it can be interpreted as an RG flow from the vicinity of a CFT fixed point. So studying the space of CFTs basically amounts to studying the space of all well-defined QFTs.

Why is this true?

Especially, how can we see that we can only remove the cutoff (i.e. renormalize) if the QFT "can be interpreted as an RG flow from the vicinity of a CFT fixed point"?

Another remark is that the standard $\phi^4$ theory in 4D is not well-defined if interacting, and the only such theory that is a CFT is the trivial one (no interactions), which is quite boring. However, this of course does not mean that $\phi^4$ in 4D is useless (and that's why people spent decades studying it), only that insisting on a continuum limit is meaningless.