Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories

TL;DR

This paper investigates the beta functions in four-dimensional conformal gravity and general quadratic theories, revealing universal behaviors and fixed points across different parametrizations and theories.

Contribution

It demonstrates the universality of beta functions in conformal gravity across parametrizations and explores fixed points in quadratic theories with Einstein and cosmological terms.

Findings

Beta functions are the same in four dimensions regardless of parametrization.

Fixed points exist consistently across different parametrizations and theories.

Different parametrizations lead to different beta functions for dimensionful couplings.

Abstract

We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful couplings different from linear split, though the fact that there exists nontrivial fixed point remains the same and the fixed points also remain the same.