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:
“Most parents aren’t even aware of how often they compare their children. . . . Comparisons carry the suggestion that specific conditions exist for parental love and acceptance. Thus, even when one child comes out on top in a comparison she is left feeling uneasy about the tenuousness of her position and the possibility of faring less well in the next comparison.”
—Marianne E. Neifert (20th century)
“Only by being guilty of Folly does mortal man in many cases arrive at the perception of Sense. A thought which should forever free us from hasty imprecations upon our ever-recurring intervals of Folly; since though Folly be our teacher, Sense is the lesson she teaches; since, if Folly wholly depart from us, Further Sense will be her companion in the flight, and we will be left standing midway in wisdom.”
—Herman Melville (1819–1891)
“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)