Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT

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.

51 pages, 12 figures

References in corpus (12)

• Twenty Years of the Weyl Anomaly
• Conformal Symmetry and Central Charges in 4 Dimensions
• Physical States of the Quantum Conformal Factor
• Resummation and Higher Order Renormalization in 4D Quantum Gravity
• Conformal Algebra and Physical States in Non-critical 3-brane on R*S^3
• Quantum Diffeomorphisms and Conformal Symmetry
• Space-time Evolution and CMB Anisotropies from Quantum Gravity
• CMB Anisotropies Reveal Quantized Gravity
• Background-metric Independent Formulation of 4D Quantum Gravity
• Baryogenesis by Quantum Gravity
• Building Blocks of Physical States in a Non-Critical 3-Brane on R*S^3
• Analyzing WMAP Observation by Quantum Gravity

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• From CFT Spectra to CMB Multipoles in Quantum Gravity Cosmology
• Gravitational Coleman-Weinberg Mechanism
• BRST Analysis of Physical Fields and States for 4D Quantum Gravity on R x S^3
• Two-Loop Quantum Gravity Corrections to Cosmological Constant in Landau Gauge
• BRST Invariant Higher Derivative Operators in 4D Quantum Gravity based on CFT
• RG Analysis for Quantum Gravity with A Single Dimensionless Coupling
• Vertex Operators in 4D Quantum Gravity Formulated as CFT