# Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT

## TL;DR

This paper develops a renormalizable 4D quantum gravity framework based on conformal field theory, managing conformal modes non-perturbatively and tensor modes perturbatively, ensuring diffeomorphism invariance and calculating key physical quantities.

## Contribution

It introduces a novel approach to quantum gravity as a perturbed CFT, handling conformal modes non-perturbatively and tensor modes perturbatively, with implications for renormalization and anomalies.

## Key findings

- Conformal symmetry remains exact at the quantum level.
- Asymptotic freedom of the tensor mode coupling constant.
- Effective cosmological constant derived in large matter field limit.

## Abstract

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. There are no massive ghosts because they are not gauge invariant in this formulation. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.