Reconstructing the graviton

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.

Automated summary

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The positive spectral function of the dynamical graviton suggests the unitarity of asymptotically safe quantum gravity, while the negative parts in the spectral function of the background graviton are similar to the gluon spectral function.