Foliated Asymptotically Safe Gravity: Lorentzian Signature Fluctuations from the Wick Rotation

TL;DR

This paper investigates the relationship between Euclidean and Lorentzian renormalization group flows in asymptotically safe gravity, demonstrating that the UV and IR completions are consistent across spacetime signatures, supporting the robustness of the asymptotic safety mechanism.

Contribution

It introduces a method to relate Euclidean and Lorentzian RG flows in asymptotic safety using ADM decomposition and analytic continuation, confirming the consistency of the fixed points.

Findings

Euclidean and Lorentzian beta functions can be equivalent under certain conditions.

The graviton two-point function flow shows agreement between Euclidean and Lorentzian signatures.

UV and IR completions are robust under signature change in asymptotic safety.

Abstract

Asymptotic Safety constitutes a promising mechanism for a consistent and predictive high-energy completion of the gravitational interactions. To date, most results on the interacting renormalization group fixed point underlying the construction are obtained for Euclidean signature spacetimes. In this work, we use the Arnowitt-Deser-Misner (ADM) decomposition of the metric degrees of freedom and investigate the relations between the Euclidean and Lorentzian renormalization group flows resulting from the analytic continuation of the lapse function. We discuss the general conditions which guarantee the equivalence of the beta functions. These insights are illustrated based on the flow of the graviton two-point function within the Einstein-Hilbert truncation, demonstrating agreement of the Euclidean and Lorentzian settings. Hence the UV- and IR-completions identified in the Euclidean case are robust when changing spacetime signature. We take this as an important indicator that the Euclidean asymptotic safety mechanism carries over to Lorentzian signature spacetimes.