A Critique of the Asymptotic Safety Program

TL;DR

This paper critically examines the current Asymptotic Safety approach in quantum gravity, highlighting conflicts with low-energy calculations and proposing potential solutions for a Lorentzian formulation.

Contribution

It provides a critique of the existing Asymptotic Safety program, analyzing its inconsistencies with low-energy quantum gravity and suggesting ways to develop a consistent Lorentzian theory.

Findings

Current Asymptotic Safety predictions conflict with low-energy quantum gravity calculations.

Obstacles exist in formulating a well-behaved Lorentzian version of the theory.

Proposed modifications may resolve issues in the Lorentzian approach.

Abstract

The present practice of Asymptotic Safety in gravity is in conflict with explicit calculations in low energy quantum gravity. This raises the question of whether the present practice meets the Weinberg condition for Asymptotic Safety. I argue, with examples, that the running of $\Lambda$ and $G$ found in Asymptotic Safety are not realized in the real world, with reasons which are relatively simple to understand. A comparison/contrast with quadratic gravity is also given, which suggests a few obstacles that must be overcome before the Lorentzian version of the theory is well behaved. I make a suggestion on how a Lorentzian version of Asymptotic Safety could potentially solve these problems.