Jonas Wessely: Self-consistent graviton spectral function in Lorentzian quantum gravity

We present the first fully self-consistent computation of the graviton spectral function in (asymptotically safe) quantum gravity, using the spectral renormalisation group within a physical mass-shell renormalisation scheme. Self-consistency here means that the full non-perturbative spectral function, including the scattering continuum, is used in all diagrams. We begin by introducing the spectral functional renormalisation group (fRG) and discussing the properties of causal Callan–Symanzik flows, which enable the direct implementation of renormalisation conditions.

Our results show a positive graviton spectral function featuring a massless one-graviton peak and a multi-graviton continuum with a near-quadratic spectral decay in the ultraviolet. Within the physical on-shell renormalisation scheme, the graviton satisfies the sum rule of an asymptotic state and exhibits unit total spectral weight. We conclude by briefly discussing the implications of this physical formulation for the computation of scattering processes and for studies of unitarity in asymptotically safe quantum gravity.