The Renormalization Group and Weyl-invariance

TL;DR

This paper develops a quantization and renormalization framework for matter fields coupled to a background metric and dilaton that preserves Weyl invariance, analyzing implications for trace anomalies and extending to dynamical gravity.

Contribution

It introduces a Weyl-invariant renormalization procedure for matter fields coupled to background and dynamical metrics, including dilaton interactions and graviton loops.

Findings

Weyl invariance is maintained in the effective action despite the presence of trace anomalies.

The framework applies to both free and interacting matter fields.

The approach extends to cases with dynamical metrics and gravitons.

Abstract

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.