RG flow of Weyl-invariant dilaton gravity

TL;DR

This paper develops a formalism for deriving renormalization group equations in Weyl-invariant dilaton gravity, enabling a consistent treatment of scale dependence in theories with local conformal symmetry.

Contribution

It introduces a method to construct RG equations that preserve Weyl invariance in gravity theories with a dilaton, demonstrated through one-loop beta function calculations.

Findings

Weyl invariance can be maintained in RG flow equations.

Explicit one-loop beta functions for a dilaton conformally coupled to gravity are derived.

The formalism links position-dependent cutoffs to conformally related metrics.

Abstract

Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely for the one loop beta functions of a dilaton conformally coupled to a dynamical metric, but the results have wider validity. This formalism could be used to define the meaning of a theory with a position-dependent cutoff: it is equivalent to a theory with a constant cutoff, but a conformally related metric.