Quantum Gravity and Gravitational-Wave Astronomy

Ultraviolet-complete quantum field theories with fractional operators

“…Therefore, for γ < 1 the theory is non-renormalizable (i.e., it has divergences at all loop orders and their number grows with L), for γ = 1 it is strictly renormalizable (divergences at all loop orders and their number does do not grow with L), for 1 < γ 2 it is superrenormalizable (there are only a finite number of divergences up to some loop order L max , excluding divergent sub-diagrams), while for γ > 2 it is one-loop super-renormalizable (only In non-local quantum gravity with asymptotically polynomial operators, the presence in the action of certain higher-order local operators called killers can make the theory finite [109]. Finiteness, the absence of divergences at all perturbative orders, can lead to Weyl conformal invariance in the UV [110,111], which in turn can have momentous consequences for phenomenology [112][113][114][115][116][117][118][119][120][121][122][123][124][125][126], but it is not necessary in order to have a predictive, fully controllable QFT in the UV. The model (2.2) is finite for any γ only when it is free, that is, when λ γ−1 = 0 = λ 0 .…”