Asymptotically Safe Lorentzian Gravity

TL;DR

This paper explores the asymptotic safety scenario for Lorentzian quantum gravity using a novel RG approach that incorporates causal structure, finding consistent ultraviolet fixed points for both Euclidean and Lorentzian signatures.

Contribution

It introduces a new functional renormalization group equation linking Euclidean and Lorentzian signatures, demonstrating similar UV fixed points in both cases within the Einstein-Hilbert approximation.

Findings

Ultraviolet fixed points found for both signatures.

Euclidean and Lorentzian gravity share universality class.

Fixed points exhibit similar characteristics.

Abstract

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $\beta$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.