Generalized Parametrization Dependence in Quantum Gravity

TL;DR

This paper investigates how gauge choices and field parametrizations affect the renormalization group flows in quantum gravity, finding stable fixed points that support the asymptotic safety scenario.

Contribution

It introduces a two-parameter class of covariant gauges and analyzes their impact on quantum gravity fixed points, demonstrating parametrization insensitivity at certain stationary points.

Findings

Identification of stationary points with minimal parametrization dependence

Existence of non-Gaussian UV stable fixed points

Analytical phase diagram with UV and IR complete trajectories

Abstract

We critically examine the gauge, and field-parametrization dependence of renormalization group flows in the vicinity of non-Gau\ss{}ian fixed points in quantum gravity. While physical observables are independent of such calculational specifications, the construction of quantum gravity field theories typically relies on off-shell quantities such as $\beta$ functions and generating functionals and thus face potential stability issues with regard to such generalized parametrizations. We analyze a two-parameter class of covariant gauge conditions, the role of momentum-dependent field rescalings and a class of field parametrizations. Using the product of Newton and cosmological constant as an indicator, the principle of minimum sensitivity identifies stationary points in this parametrization space which show a remarkable insensitivity to the parametrization. In the most insensitive cases, the quantized gravity system exhibits a non-Gau\ss{}ian UV stable fixed point, lending further support to asymptotically free quantum gravity. One of the stationary points facilitates an analytical determination of the quantum gravity phase diagram and features ultraviolet and infrared complete RG trajectories with a classical regime.