Self-consistent graviton spectral function in Lorentzian quantum gravity

TL;DR

This paper computes the graviton spectral function in quantum gravity using a self-consistent, non-perturbative spectral renormalisation group approach, revealing a positive spectral function with a massless graviton peak and a continuum.

Contribution

It introduces the first fully self-consistent, non-perturbative calculation of the graviton spectral function within a physical mass-shell renormalisation scheme.

Findings

Positive graviton spectral function with a massless peak

Multi-graviton continuum with quadratic decay in UV

Graviton satisfies sum rule with unit spectral weight

Abstract

We present the first fully self-consistent computation of the graviton spectral function in quantum gravity, using the spectral renormalisation group for gravity put forward in arXiv:2111.13232v2 [hep-th] within a physical mass-shell renormalisation scheme. Here, self-consistency refers to the fact that the full non-perturbative spectral function is used in the diagrams, including the scattering continuum. We find a positive graviton spectral function with a massless one-graviton peak and a multi-graviton continuum with a close-to-quadratic spectral decay in the ultraviolet. Within the physical on-shell renormalisation scheme, the graviton satisfies the sum rule of an asymptotic state and features a unit total spectral weight. We briefly discuss the implications of the physical formulation for the computation of scattering processes and investigations of unitarity in asymptotically safe quantum gravity.