Gauge and Cutoff Function Dependence of the Ultraviolet Fixed Point in Quantum Gravity

Abstract

The exact renormalization group equation for pure quantum gravity is derived for an arbitrary gauge parameter in the space-time dimension $d=4$. This equation is given by a non-linear functional differential equation for the effective average action. An action functional of the effective average action is approximated by the same functional space of the Einstein-Hilbert action. From this approximation, $\beta$-functions for the dimensionless Newton constant and cosmological constant are derived non-perturbatively. These are used for an analysis of the phase structure and the ultraviolet non-Gaussian fixed point of the dimensionless Newton constant. This fixed point strongly depends on the gauge parameter and the cutoff function. However, this fixed point exists without these ambiguities, except for some gauges. Hence, it is possible that pure quantum gravity in $d=4$ is an asymptotically safe theory and non-perturbatively renormalizable.

18 pages, 3 figures

References in corpus (1)

• On the construction of renormalized gauge theories using renormalization group techniques

Cited by in corpus (7)

• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• Aspects of asymptotic safety for quantum gravity
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Asymptotic safety goes on shell
• Interacting Scalar Fields in the Context of Effective Quantum Gravity
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge