Resummation and Higher Order Renormalization in 4D Quantum Gravity

Abstract

Higher order renormalization in 4D quantum gravity is carried out using dimensional regularization with great care concerning the conformal-mode dependence. In this regularization, resummation can be automatically carried out without making an assumption like that of David, Distler and Kawai. In this paper we consider a model of 4D quantum gravity coupled to QED. Resummation inevitably implies a four-derivative quantum gravity. The renormalizability is directly checked up to $O(e_r^6)$ and $O(t_r^2)$, where $e_r$ and $t_r$ are the running coupling constants of QED and the traceless gravitational mode. There is no other running coupling constant in our model. The conformal mode is treated exactly, which means it is unrenormalized. It is found that Hathrell's results are included in our results. As a by-product, it is found that a higher-order gravitational correction to the beta function of QED is negative. An advantage of our model is that in the very high-energy regime, it closely resembles exactly solvable 2D quantum gravity. Thus, we can study physical states of 4D quantum gravity in this regime in parallel to those of 2D quantum gravity, which can be described with diffeomorphism invariant composite fields.

39 pages, minor typo error corrected

Cited by in corpus (25)

• Quadratic Gravity
• Agravity up to infinite energy
• Dimensional Transmutation in Gravity and Cosmology
• Space-time Evolution and CMB Anisotropies from Quantum Gravity
• CMB Anisotropies Reveal Quantized Gravity
• Determination of Gravitational Counterterms Near Four Dimensions from RG Equations
• Background Free Quantum Gravity based on Conformal Gravity and Conformal Field Theory on M^4
• From CFT Spectra to CMB Multipoles in Quantum Gravity Cosmology
• Baryogenesis by Quantum Gravity
• Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT
• Gravitational Coleman-Weinberg Mechanism
• BRST Analysis of Physical Fields and States for 4D Quantum Gravity on R x S^3
• The search for the universality class of metric quantum gravity
• Building Blocks of Physical States in a Non-Critical 3-Brane on R*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
• Diffeomorphism Invariance Demands Conformal Anomalies
• Localized massive excitation of quantum gravity as a dark particle
• Physical Cosmological Constant in Asymptotically Background Free Quantum Gravity
• Conformal Field Theory on R x S^3 from Quantized Gravity
• Vertex Operators in 4D Quantum Gravity Formulated as CFT
• Making a Universe
• Birth and Growth of Two-dimensional Universe
• Quantum Gravity Effective Action Provides Entropy of The Universe