Classicalization and unitarity

We point out that the scenario for UV completion by classicalization, proposed recently is in fact Wilsonian in the classical Wilsonian sense. It corresponds to the situation when a field theory has a nontrivial UV fixed point governed by a higher dimensional operator. Provided the kinetic term is a relevant operator around this point the theory will flow in the ID to the free scalar theory. Physically, classicalization, if it can he realized, would correspond to a situation when the fluctuations of the field operator in the UV are smaller than in the IR. As a result there exists a clear tension between the classicalization scenario and constraints imposed by unitarily on a quantum field theory, making the existence of classicalizing unitary theories questionable.