UV fixed point

A theory has a UV fixed point if its renormalization group flow runs towards a fixed point in the ultraviolet (i.e. short length scale/large energy) limit. Among other things, it means that such a theory is not an effective field theory because it is well-defined at arbitrarily small distance scales. At the UV fixed point itself, the theory behaves as a conformal field theory.

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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 (according to the classical scaling dimensions).

See also

• Ultraviolet divergence