A fixed point for truncated quantum Einstein gravity

TL;DR

This paper develops a perturbative quantum theory for a reduced model of Einstein gravity with two Killing vectors, demonstrating a fixed point where the trace anomaly vanishes and supporting the asymptotic safety scenario.

Contribution

It introduces a novel approach to achieve cutoff independence in a truncated quantum gravity model and derives a closed-form beta functional for the conformal factor.

Findings

Existence of a fixed point with zero trace anomaly

Cutoff independence achieved to all loop orders

Flow compatible with asymptotic safety scenario

Abstract

A perturbative quantum theory of the two Killing vector reduction of Einstein gravity is constructed. Although the reduced theory inherits from the full one the lack of standard perturbative renormalizability, we show that strict cutoff independence can be regained to all loop orders in a space of Lagrangians differing only by a field dependent conformal factor. A closed formula is obtained for the beta functional governing the flow of this conformal factor. The flow possesses a unique fixed point at which the trace anomaly is shown to vanish. The approach to the fixed point is compatible with Weinberg's ``asymptotic safety'' scenario.