Quantum Gravity is Renormalizable near Two Dimensions

Abstract

We prove the renormalizability of quantum gravity near two dimensions. The successful strategy is to keep the volume preserving diffeomorphism as the manifest symmetry of the theory. The general covariance is recovered by further imposing the conformal invariance. The proof utilizes BRS formalism in parallel with Yang-Mills theory. The crucial ingredient of the proof is the relation between the conformal anomaly and the $\beta$ functions.

16 pages, latex, no figures

References in corpus (4)

• Scaling Exponents in Quantum Gravity near Two Dimensions
• Ultraviolet Stable Fixed Point and Scaling Relations in 2+$\epsilon$ Dimensional Quantum Gravity
• Conformal Invariance and Renormalization Group in Quantum Gravity Near Two Dimensions
• Two-loop Renormalization in Quantum Gravity near Two Dimensions

Cited by in corpus (5)

• Renormalizability of Quantum Gravity near Two Dimensions
• Two-loop Prediction for Scaling Exponents in (2 + ε)-dimensional Quantum Gravity
• Non-Perturbative Gravity and the Spin of the Lattice Graviton
• BRST Cohomology and Renormalizability of Quantum Gravity near Two Dimensions
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric