Benjamin Knorr: Asymptotically (un)safe scattering amplitudes from scratch: a deep dive into the IR jungle

We compute leading order quantum gravity contributions to a simple scalar scattering amplitude in Asymptotic Safety. Our model admits an analytic treatment so that several subtleties can be analysed. We find that (i) the existence of an asymptotically safe renormalisation group fixed point alone does not imply the boundedness of scattering amplitudes, (ii) gravitational logarithms can dominate the infrared regime of massless theories, (iii) a derivative expansion of the effective action fails quantitatively to predict the correct Wilson coefficients in massless theories, and (iv) standard renormalisation group improvement techniques fail qualitatively to describe the momentum dependence of correlation functions. Only momentum-dependent computations can resolve these issues. For theories that include massive fields, the derivative expansion can work effectively in most cases, but it can still fail for classically marginal couplings, and purely gravitational couplings. We also speculate about an effective realisation of the no-global-symmetries conjecture in Asymptotic Safety.