Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity

TL;DR

This paper constructs a functional integral representation for asymptotically safe quantum gravity, linking effective average actions to underlying bare actions with UV and IR cutoffs, and analyzes the Einstein-Hilbert truncation.

Contribution

It provides a method to derive the bare action from the effective average action in asymptotically safe quantum gravity, clarifying the microscopic structure.

Findings

Reconstructed the bare action from effective average actions.

Analyzed the flow of the Einstein-Hilbert truncation.

Discussed conceptual issues in the asymptotic safety program.

Abstract

Investigations of Quantum Einstein Gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a non-Gaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR cutoff only, induces an associated trajectory of bare actions which depend on a UV cutoff. Together with the regularized measure these bare actions give rise to a functional integral which reproduces the prescribed effective action when the UV cutoff is removed. In this way we are able to reconstruct the underlying microscopic ("classical") system and identify its fundamental degrees of freedom and interactions. The bare action of the Einstein-Hilbert truncation is computed and its flow is analyzed as an example. Various conceptual issues related to the completion of the asymptotic safety program are discussed.