Specific Cases and Details
Among other things, it means that a theory possessing a UV fixed point may not be an effective field theory, because it is well-defined at arbitrarily small distance scales. At the UV fixed point itself, the theory can behave as a conformal field theory.
The converse statement, that any QFT which is valid at all distance scales (i.e. isn't an effective field theory) has a UV fixed point is false. See, for example, cascading gauge theory.
Noncommutative quantum field theories have a UV cutoff even though they are not effective field theories.
If the UV fixed point is trivial (aka Gaussian), we say that we have asymptotic freedom.
If the UV fixed point is nontrivial, we say that we have "asymptotic safety". Theories with asymptotic safety may be well defined at all scales despite being nonrenormalizable in perturbative sense (according to the classical scaling dimensions).
Read more about this topic: UV Fixed Point
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