Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT

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 sy...

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Bibliographic Details
Published in:Foundations of physics 2009-12, Vol.39 (12), p.1356-1393
Main Author: Hamada, Ken-ji
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Statistical Physics and Dynamical Systems
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Summary: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. 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.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-009-9358-x