Renormalization group analysis for quantum gravity with a single dimensionless coupling

We study the quantum conformal gravity whose dynamics is governed by a single dimensionless gravitational coupling with negative beta function. Since the Euler term is not dynamical classically, the constant in front of it is not an independent coupling. Quantum mechanically, however, it induces the Riegert conformal-factor dynamics with Becchi-Rouet-Stora-Tyutin conformal symmetry representing background free nature. In this paper, we propose how to handle the Euler term systematically, incorporating such dynamics on the basis of renormalization group analysis using dimensional regularization. As a nontrivial test of renormalization, we explicitly calculate the three-loop anomalous dimension of the cosmological constant operator and show that it agrees with the exact expression derived using the Becchi-Rouet-Stora-Tyutin conformal symmetry. The physical significance to inflation and the cosmic microwave background is also discussed.

Figure 1

Diagrams representing the background-metric independence.

Figure 2

Loop corrections to cosmological constant operator.