Weyl Consistency Conditions from a local Wilsonian Cutoff

Abstract

A local UV cutoff $\Lambda (x)$ 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 $\beta$ 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 $\beta$ functions, and we derive conditions under which it becomes the form of an exact gradient flow.

22 pages, Sections 3 and 4 re-written

References in corpus (10)

• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Weyl Connections and their Role in Holography
• Weyl Consistency Conditions and ${\gamma }_5$
• Gauge coupling beta functions to four-loop order in the Standard Model
• Limit Cycles in Four Dimensions
• General scalar renormalisation group equations at three-loop order
• General RGEs for dimensionful couplings in the $\overline{\mathrm{MS}}$ scheme
• Functional and Local Renormalization Groups
• $a$-theorem at large $N_f$
• Developing local RG: quantum RG and BFSS

Cited by in corpus (2)

• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• Gradient Flow and Holography from a Local Wilsonian Cutoff