We pave the way for future gravitational-wave detection experiments, such as the Big Bang Observer and DECIGO, to constrain dark sectors made of SU(N) Yang-Mills confined theories. We go beyond the state-of-the-art by combining first principle lattic
e results and effective field theory approaches to infer essential information about the non-perturbative dark deconfinement phase transition driving the generation of gravitational-waves in the early universe, such as the order, duration and energy budget of the phase transition which are essential in establishing the strength of the resulting gravitational-wave signal.
In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art in pure gr
avity and general gravity-matter systems. This includes the discussion of results on the existence and properties of the asymptotically safe ultraviolet fixed point, full ultraviolet-infrared trajectories with classical gravity in the infrared, and the curvature dependence of couplings also in gravity-matter systems. The results in gravity-matter systems concern the ultraviolet stability of the fixed point and the dominance of gravity fluctuations in minimally coupled gravity-matter systems. Furthermore, we discuss important physics properties such as locality of the theory, diffeomorphism invariance, background independence, unitarity, and access to observables, as well as open challenges.
We determine the $1/N_f^2$ and $1/N_f^3$ contributions to the QED beta function stemming from the closed set of nested diagrams. At order $1/N_f^2$ we discover a new logarithmic branch-cut closer to the origin when compared to the $1/N_f$ results. Th
e same singularity location appears at $1/N_f^3$, and these correspond to a UV renormalon singularity in the finite part of the photon two-point function.
We compute curvature-dependent graviton correlation functions and couplings as well as the full curvature potential $f(R)$ in asymptotically safe quantum gravity coupled to scalars. The setup is based on a systematic vertex expansion about metric bac
kgrounds with constant curvatures initiated in arXiv:1711.09259 for positive curvatures. We extend these results to negative curvature and investigate the influence of minimally coupled scalars. The quantum equation of motion has two solutions for all accessible numbers of scalar fields. We observe that the solution at negative curvature is a minimum, while the solution at positive curvature is a maximum. We find indications that the solution to the equation of motions for scalar-gravity systems is at large positive curvature, for which the system might be stable for all scalar flavours.
We search for an extension of the Standard Model that contains a viable dark matter candidate and that can be embedded into a fundamental, asymptotically safe, quantum field theory with quantum gravity. Demanding asymptotic safety leads to boundary c
onditions for the non-gravitational couplings at the Planck scale. For a given dark matter model these translate into constraints on the mass of the dark matter candidate. We derive constraints on the dark matter mass and couplings in two minimal dark matter models: i) scalar dark matter coupled via the Higgs-portal in the $B$-$L$ model; ii) fermionic dark matter in a $U(1)_X$ extension of the Standard Model, coupled via the new gauge boson. For scalar dark matter we find 56 GeV $ < M_text{DM} < 63$ GeV, and for fermionic dark matter $M_text{DM} leq 50$ TeV. Within our framework, we identify three benchmark scenarios with distinct phenomenological consequences.
We study the analytic properties of the t Hooft coupling expansion of the beta-function at the leading nontrivial large-$N_f$ order for QED, QCD, Super QED and Super QCD. For each theory, the t Hooft coupling expansion is convergent. We discover that
an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first singularity. We study summations of the beta-function expansion at order $1/N_f$, and identify the physical origin of the singularities in terms of iterated bubble diagrams. We find a common analytic structure across these theories, with important technical differences between supersymmetric and non-supersymmetric theories. We also discuss the expected structure at higher orders in the $1/N_f$ expansion, which will be in the future accessible with the methods presented in this work, meaning without the need for resumming the perturbative series. Understanding the structure of the large-$N_f$ expansion is an essential step towards determining the ultraviolet fate of asymptotically non-free gauge theories.
The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem and a possible explanation of an---asymptotica
lly---vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted.
The link between a modified Higgs self-coupling and the strong first-order phase transition necessary for baryogenesis is well explored for polynomial extensions of the Higgs potential. We broaden this argument beyond leading polynomial expansions of
the Higgs potential to higher polynomial terms and to non-polynomial Higgs potentials. For our quantitative analysis we resort to the functional renormalization group, which allows us to evolve the full Higgs potential to higher scales and finite temperature. In all cases we find that a strong first-order phase transition manifests itself in an enhancement of the Higgs self-coupling by at least 50%, implying that such modified Higgs potentials should be accessible at the LHC.
The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in cite{Christiansen:2015rva
} for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to $Lambda$, $R$, $R^2$ as well as $R_{mu u}^2$ and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.
We study the ultraviolet stability of gravity-matter systems for general numbers of minimally coupled scalars and fermions. This is done within the functional renormalisation group setup put forward in cite{Christiansen:2015rva} for pure gravity. It
includes full dynamical propagators and a genuine dynamical Newtons coupling, which is extracted from the graviton three-point function. We find ultraviolet stability of general gravity-fermion systems. Gravity-scalar systems are also found to be ultraviolet stable within validity bounds for the chosen generic class of regulators, based on the size of the anomalous dimension. Remarkably, the ultraviolet fixed points for the dynamical couplings are found to be significantly different from those of their associated background counterparts, once matter fields are included. In summary, the asymptotic safety scenario does not put constraints on the matter content of the theory within the validity bounds for the chosen generic class of regulators.
