Field Parametrization Dependence in Asymptotically Safe Quantum Gravity

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, $g_{\mu \nu }={\bar{g}}_{\mu \rho }(e^h{)}_{\nu }^{\rho }$. 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.

12 pages, 6 figures. In version 2 some comments in the introduction were added. To appear in Phys. Rev. D

References in corpus (5)

• Exact evolution equation for the effective potential
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Matter Induced Bimetric Actions for Gravity
• On the UV structure of quantum unimodular gravity

Cited by in corpus (8)

• The Renormalization Group flow of unimodular f(R) gravity
• Correlation functions on a curved background
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• The background scale Ward identity in quantum gravity
• The path integral of unimodular gravity
• Composite Operators in Asymptotic Safety
• Split Weyl transformations in quantum gravity
• Spin-base invariance of Fermions in arbitrary dimensions