Classicalization and unitarity

We point out that the scenario for UV completion by " classicalization", pro- posed 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 dimen- sional operator. Provided the kinetic term is a relevant operator around this point the theory will flow in the IR to the free scalar theory. Physically, " classicalization", if it can be 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 unitarity on a quantum field theory, making the existence of classicalizing unitary theories questionable.