Weyl consistency conditions from a local Wilsonian cutoff

Abstract

A local UV cutoff Λ(x) transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms for scalar fields including cutoff functions. We consider scalar fields in curved space-time with local couplings and masses. This approach allows to derive Weyl consistency conditions for the corresponding β functions and anomalous dimensions. These are obtained for β functions and anomalous dimensions with respect to a renormalization scale μ, as well as with respect to the UV cutoff, the latter for couplings to operators of arbitrary canonical dimension. In the Weyl consistency conditions the UV cutoff plays the role of an additional coupling, albeit with a trivial constant β function. Including the UV cutoff, the Weyl consistency conditions assume the form of a gradient flow for β functions and anomalous dimensions. ar X iv :2 10 1. 07 61 5v 2 [ he pth ] 2 5 Ja n 20 21