Renormalization and asymptotic safety in truncated quantum Einstein gravity

TL;DR

This paper develops a perturbative quantum theory for a reduced model of general relativity, demonstrating that despite non-renormalizability, a form of asymptotic safety can be achieved through a specific renormalization flow.

Contribution

It introduces a novel approach to achieve cut-off independence in a truncated quantum gravity model via a field-dependent conformal factor and identifies a fixed point consistent with asymptotic safety.

Findings

Achieves cut-off independence through a conformal factor in the Lagrangian.

Identifies a fixed point where the trace anomaly vanishes.

Supports Weinberg's asymptotic safety scenario in quantum gravity.

Abstract

A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be achieved in a space of Lagrangians differing only by a field dependent conformal factor. In particular the Noether currents and the quantum constraints can be defined as finite composite operators. The form of the field dependence in the conformal factor changes with the renormalization scale and a closed formula is obtained for the beta functional governing its flow. The flow possesses a unique fixed point at which the trace anomaly is shown to vanish. The approach to the fixed point adheres to Weinberg's ``asymptotic safety'' scenario, both in the gravitational wave/cosmological sector and in the stationary sector.