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
Famous quotes containing the words specific, cases and/or details:
“The permanence of all books is fixed by no effort friendly or hostile, but by their own specific gravity, or the intrinsic importance of their contents to the constant mind of man.”
—Ralph Waldo Emerson (1803–1882)
“Medication alone is not to be relied on. In one half the cases medicine is not needed, or is worse than useless. Obedience to spiritual and physical laws—hygeine [sic] of the body, and hygeine of the spirit—is the surest warrant for health and happiness.”
—Harriot K. Hunt (1805–1875)
“Different persons growing up in the same language are like different bushes trimmed and trained to take the shape of identical elephants. The anatomical details of twigs and branches will fulfill the elephantine form differently from bush to bush, but the overall outward results are alike.”
—Willard Van Orman Quine (b. 1908)