Form Factors in Asymptotically Safe Quantum Gravity

Abstract: Asymptotic Safety implies that observables including scattering amplitudes remain finite at the highest energy scales. Traditionally, this feature is connected to an interacting fixed point of the Wilsonian renormalization group that provides the high-energy completion of the theory. In this article, we discuss a different facet of Asymptotic Safety, reviewing its imprint on the quantum effective action. We start with a concise introduction to the form factor framework for gravity and gravity-matter systems, before giving an encyclopaedic overview of gravity-mediated scattering amplitudes derived from the quantum effective action. We illustrate the use of the framework based on form factors appearing in the context of quadratic gravity and Asymptotic Safety, before making the connections to positivity bounds derived for low-energy effective field theories and the computation of form factors from first principles. We conclude that the form factor framework offers a unique, unifying perspective on quantum gravity. In particular, it plays a pivotal role in determining the phenomenological consequences of Asymptotic Safety at the level of observables.