CFTs in the phase space of QFTs

Question

In the cases I have encountered a CFT is often realised as a RG fixed POINT of the RG flow. Is it also possible to have a whole family/mine/manifold of CFTs instead?

This post is imported from Physics StackExchange at 2016-06-02 04:57 (UTC) posted by SE User Anne O' Nyme. SE users associated with first four comments below are Gennaro Tedesco, ACuriousMind, user2309840 and Edward Hughes respectively.

Comments

"a CFT is often realised as a RG fixed POINT of the RG flow": what cases thereof have you encountered? Simple families of CFT arise from chiral theories in low dimensions as well.

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It's not exactly clear to me what you're asking. Fixed points are points. It sounds as if you're asking if a point can be a manifold instead, which doesn't make much sense to me.

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Maximally supersymmetric Yang-Mills theory in 3+1 dimensions is an example of a conformal field theory. It is conformal for all values of the Yang-Mills coupling. Thus, one could think of the Yang-Mills coupling as parametrizing a line of CFTs. More generally, a manifold of CFTs can be parametrized by the space of exactly marginal couplings.

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You should clarify your question. If you are asking for examples of CFTs which are valid at any value of the coupling(s) then user2309840 has given a good answer above.