Asymptotic safety goes on shell

TL;DR

This paper introduces a new scheme for analyzing asymptotically safe gravity that isolates the on-shell effective action, resulting in gauge-independent beta functions and a fixed point with a gauge-independent cosmological constant.

Contribution

It develops a novel on-shell focused approach with technical innovations to achieve gauge-independent results in asymptotically safe gravity analysis.

Findings

Identifies a non-trivial fixed point in the Einstein-Hilbert truncation.

Demonstrates the cosmological constant at the fixed point is gauge-independent.

Introduces new decomposition, ghost sector implementation, and cut-off scheme.

Abstract

It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.