Form Factors in Asymptotically Safe Quantum Gravity

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 chapter, we discuss a different facet of Asymptotic Safety, reviewing its imprint on the quantum effective action. We start with a concise introduction to form factors in gravity and gravity–matter systems, before giving an overview of gravity-mediated scattering amplitudes derived from the quantum effective action. We illustrate the use of the framework based on the 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 form factors offer a unique, unifying perspective on quantum gravity. In particular, they play a pivotal role in determining the phenomenological consequences of Asymptotic Safety at the level of observables.