UV fixed point - Citizendia

A theory has a UV fixed point if its renormalization group flow runs towards a fixed point in the ultraviolet (i. In Theoretical physics, renormalization group (RG refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views 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. In Physics, an effective field theory is an approximate theory (usually a Quantum field theory) that includes appropriate degrees of freedom to describe At the UV fixed point itself, the theory behaves as a conformal field theory. A conformal field theory (CFT is a Quantum field theory (or Statistical mechanics model at the Critical point) that is Invariant under

The converse statement, that any QFT which is valid at all distance scales (i. In quantum field theory (QFT the forces between particles are mediated by other particles e. isn't an effective field theory) has a UV fixed point is false. See, for example, cascading gauge theory. In Theoretical physics, a cascading gauge theory is a Gauge theory whose coupling rapidly changes with the scale in such a way that Seiberg duality must

Noncommutative quantum field theories have a UV cutoff even though they are not effective field theories. In Physics, Noncommutative quantum field theory (or quantum field theory on noncommutative Space-time) is a branch of Quantum field theory in

If the UV fixed point is trivial (aka Gaussian), we say that we have asymptotic freedom. A Gaussian fixed point is a Fixed point of the Renormalization group flow which is noninteracting in the sense that it is described by a Free field theory In Physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles such as Quarks, becomes arbitrarily

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). In Quantum field theory, the Statistical mechanics of fields and the theory of self-similar geometric structures renormalization refers to a collection In Theoretical physics, namely Quantum field theory, the classical scaling dimension of an Operator O is the power of Mass of an operator

See also