The Renormalization Group and Weyl-invariance

Understand

We consider matter fields conformally coupled to a background metric and dilaton and describe in detail a quantization procedure and related renormalization group flow that preserve Weyl invariance.

• Even though the resulting effective action is Weyl-invariant, the trace anomaly is still present, with all its physical consequences.
• We discuss first the case of free matter and then extend the result to interacting matter.
• We also consider the case when the metric and dilaton are dynamical and gravitons enter in the loops.