Conference

An increasing number of researchers are considering the possibility that the Standard Model, appropriately extended, can attain an interacting ultraviolet fixed point. Such a theory could, in the Wilsonian sense, be regarded as a fundamental theory. I will describe recent work that shows this goal is attainable in principle by adding gauged vector-like fermions to the Standard Model, in the limit of a large number of fermion fields. With this proof-of-principle demonstration, the challenge now to find realistic asymptotically safe extensions of the Standard Model with interesting and falsifiable phenomenological signatures

I will present constraints from central charges and gradient flow relations on UV and IR interacting fixed points under perturbative control. It is possible to extend this methodology beyond perturbation theory for supersymmetric theories where the central charges are calculated to all orders. In this case, these constraints draw a complex map of possible RG flows, some of them compatible with Asymptotic Safety. Examples of such SUSY theories are discussed

Including a large number of vector-like fermions can be used to generate fixed points for the RG flows of gauge theories. Recently this has been used as a foundation for constructing UV safe models. The talk will focus on the machinery behind the large N_f computations extended to generic gauge-Yukawa theories. For semi-simple gauge theories the phase diagram shows the persistence that the UV fixed point of simple gauge theories.

The nature of dark matter is one of the outstanding riddles of fundamental physics. Here, I will discuss first steps to explore dark matter in the asymptotic safety paradigm. As a first example, I will show indications for an asymptotically safe fixed point in the Higgs portal to fermionic dark matter, leading to a relation between the Higgs portal coupling and the dark matter mass. This model also serves as an example for different mechanisms that generate asymptotic safety. I will then review some properties of an extended Higgs sector under the coupling to asymptotically safe quantum gravity and discuss how quantum gravity fluctuations flatten the Higgs potential and thus lead to a decoupling of scalar singlets which are subject to experimental searches for dark matter.

We review the status of asymptotically safe gravity-matter systems. The existence of a UV fixed point in such systems is guaranteed if the matter-self couplings are weak and if higher-derivative gravity terms are neglected. We show how this can manifest itself in a functional renormalisation group computation. Such gravity-matter systems contain various avatars of the dynamical Newton's coupling, e.g. gravitational self-couplings or matter-graviton couplings. We uncover an effective universality for the dynamical Newton's coupling on the quantum level: its momentum-dependent avatars are in remarkable quantitative agreement in the scaling regime of the UV fixed point. This emergence of effective universality is a strong indication for the physical nature of the UV fixed point and it provides a guiding principle for setting up future truncations.

A field theory is fundamental if it features a UV fixed point (either trivial or interacting). Gravity may not change drastically the UV behavior if the Einstein gravitational interactions are softened above a critical sub-Planckian energy scale. A concrete implementation of this softened gravity can be obtained by adding terms quadratic in the curvature to the Einstein-Hilbert action. One way to implement this scenario consists in requiring that all matter couplings flow to zero at infinite energy (total asymptotic freedom). More generally, some of the couplings flow to zero, while others approach interacting fixed points. The requirement of having a fundamental field theory can have important implications for particle physics phenomenology.

I outline a configuration in which the Standard Model can be embedded into an asymptotically safe gauge-Yukawa theory. The model can be though of as a minimal UV completion of the SM without gravity. I also discuss the remaining issues that need to be addressed for the scheme to be phenomenologically viable, and outline the different energy scales and possible signatures.