Asymptotically Safe Quantum Field Theories in Perturbative Regime and Beyond

The range of topics covered in this thesis reflects the extent to which the tree of Asymptotic Safety research has branched out in recent years. The thesis consists of two parts, one dealing with pure particle models and one adding gravity to the mix. Having roots in a 1996 paper by Reuter, Asymptotic Safety was for a long time thought of as “only” a promising approach to quantum gravity. In 2014 an impor- tant new branch was grafted to the tree when Litim and Sannino discovered first examples of asymptotically safe quantum field theories structurally similar to the Standard Model. In the first part of the thesis we work in perturbation theory and with instanton calculus to extend the work of Litim and Sannino. The extension goes in two directions. A more formal one studies the instanton effects in their model. The other, more pragmatic one, seeks asymptotically safe minimal extensions of the Standard Model. Despite being historically first, asymptotic safety in quantum grav- ity context is studied after pure particle models here. The reasons are that quantum gravity is a logical extension of “beyond the Standard Model” particle physics, and that it relies heavily on the less-known functional renormalization group. We will show that a generic matter-gravity fixed point of the renormalization group flow al- ways contains gravity-induced non-minimal matter-gravity interactions. This com- putation will also demonstrate the practical necessity of dealing with background independence in Asymptotic Safety, which is the final topic that we address.