Quantization and fixed points of non-integrable Weyl theory

Understand

We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations.

• We quantize the theory by suitably defining renormalization group flows that describe the integration of successive momentum shells, in such a way that Weyl--invariance is maintained in the flow.
• When the gauge fields are massless the theory has, in addition to Weyl invariance, an abelian gauge symmetry.
• According to the definition of the cutoff, the flow can break or preserve this extended symmetry.