Reconstructing the graviton

TL;DR

This paper reconstructs the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data, revealing spectral properties that suggest potential unitarity of the theory.

Contribution

It provides a novel reconstruction of the Lorentzian graviton propagator and analyzes its spectral function, highlighting differences between dynamical and background gravitons.

Findings

Spectral function of background graviton has negative parts similar to gluons.

Spectral function of dynamical graviton is positive.

Positivity of dynamical graviton spectral function may indicate unitarity.

Abstract

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.