https://doi.org/10.1140/epjc/s10052-021-09215-4
Regular Article - Theoretical Physics
Weyl consistency conditions from a local Wilsonian cutoff
University Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France
Received:
7
April
2021
Accepted:
3
May
2021
Published online:
15
May
2021
A local UV cutoff 
transforming under Weyl rescalings allows to construct Weyl invariant kinetic terms for scalar fields including Wilsonian cutoff functions. First we consider scalar fields in curved space-time with local bare couplings of any canonical dimension, and anomalous dimensions which describe their dependence on the UV cutoff. The local component of the UV cutoff plays the role of an additional coupling, albeit with a trivial constant 
function. This approach allows to derive Weyl consistency conditions for the corresponding anomalous dimensions which assume the form of an exact gradient flow. For renormalizable theories the Weyl consistency conditions are initially of the form of an approximate gradient flow for the functions, and we derive conditions under which it becomes the form of an exact gradient flow.
© The Author(s) 2021
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