Field Parametrization Dependence in Asymptotically Safe Quantum Gravity

TL;DR

This paper explores a new exponential parametrization of the metric in Quantum Einstein Gravity, examining its effects on fixed points, RG flow structures, and background independence within the asymptotic safety framework.

Contribution

It introduces an exponential field parametrization in quantum gravity and analyzes its impact on fixed points and RG flows, advancing the understanding of background independence.

Findings

Reproduces the critical central charge in 2+ε dimensions

Identifies new structures in RG flow in 4D

Discusses background independence restoration

Abstract

Motivated by conformal field theory studies we investigate Quantum Einstein Gravity with a new field parametrization where the dynamical metric is basically given by the exponential of a matrix-valued fluctuating field, $g_{\mu\nu}=\bar{g}_{\mu\rho}(e^h)^\rho_{\nu}$. In this way, we aim to reproduce the critical value of the central charge when considering $2+\epsilon$ dimensional spacetimes. With regard to the Asymptotic Safety program, we take special care of possible fixed points and new structures of the corresponding RG flow in $d=4$ for both single- and bi-metric truncations. Finally, we discuss the issue of restoring background independence in the bi-metric setting.