Field Parametrization Dependence in Asymptotically Safe Quantum Gravity

Understand

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.