Asymptotically safe quantum gravity: from higher order curvatures to unitarity

A key question of theoretical physics is the formulation of a consistent quantum theory of gravity. While quantum field theory has been very successful in describing particle physics, its application to gravity faces several challenges. A promising approach to lift these problems is the asymptotic safety scenario. It stipulates the existence of a nontrivial UV fixed point and can render quantum gravity well-defined and predictive. While significant evidence for the existence of a fixed point has been gathered, fundamental questions remain open, such as the role of higher order curvature interactions as well as unitarity of the resulting field theory.

In this thesis, we investigate how fixed points of gravity change when higher order curvatures are taken into account. For this, important tools are developed, such as the computation of relevant heat kernel coefficients in any dimension, general functional flows for gravity which are independent of the form of the gravitational action and allow for new wide-ranging applications, and the implementation of techniques to reduce reparametrisation redundancies. Several extensions of Einstein-Hilbert gravity are studied in depth, retaining Ricci, Riemann, and Weyl tensor interactions up to very high orders. The implications on the phase space of quantum gravity are analysed, also accounting for the existence of multiple and strongly interacting fixed points. Our results highlight the significance of higher order curvatures, especially regarding the possibility of generating new free parameters. On a different tack, we study spectral functions as a tool to address unitarity in quantum field theory and gravity. Using the Banks-Zaks phase of QCD as a well-controlled toy model, we find conditions for good causal behaviour of quarks and gluons at all scales, despite being gauge-variant degrees of freedom. Given the similarity with gravity, our results lay the groundwork for future studies of unitarity in the latter.