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.
Highlights
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
This work is structured as follows: In Sec. 2, we give a brief overview of the setup of our approach to asymptotically safe (AS) quantum gravity as well as the functional renormalisation group (fRG) approach used for the computation of Euclidean correlation functions
It is minimal in the sense that it only relies on standard quantum field theory, and its viability has been furthered by many results in the past two decades following the seminal paper [44] within the fRG-approach, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
Summary
E Computation of the anomalous dimension E.1 Asymptotics of the anomalous dimension E.2 Symmetrisation of the anomalous dimension. E Computation of the anomalous dimension E.1. F Parameters of the spectral functions F.1. F Parameters of the spectral functions F.1 Fluctuation spectral function F.2 Background spectral function F.3 Gauge dependence of Ah and Ag
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