Predicting the outcome of scattering processes of elementary particles in colliders is the central achievement of relativistic quantum field theory applied to the fundamental (non-gravitational) interactions of nature. While the gravitational interactions are too minuscule to be observed in the microcosm, they dominate the interactions at large scales. As such the inspiral and merger of black holes and neutron stars in our universe are now routinely observed by gravitational wave detectors. The need for high precision theory predictions of the emitted gravitational waveforms has opened a new window for the application of perturbative quantum field theory techniques to the domain of gravity. In this talk I will show how observables in the classical scattering of black holes and neutron stars can be efficiently computed in a perturbative expansion using a world-line quantum field theory; thereby combining state-of-the-art Feynman integration technology with perturbative quantum gravity. Here, the black holes or neutron stars are modelled as point particles in an effective field theory sense. Fascinatingly, the intrinsic spin of the black holes may be captured by a supersymmetric extension of the world-line theory, enabling the computation of the far field wave-form including spin and tidal effects to highest precision. I will review our most recent results at the fifth order in the post-Minkowskian expansion amounting to the computations of tens of thousands of four loop Feynman integrals.

A central outcome of the recent Higgs discovery is that the Standard Model (SM) appears to be a selfconsistent quantum field theory all the way up to the Planck scale. Moreover, the measured values for the Higgs and top masses have an intriguing consequence for the question of stability of the Higgs vacuum: The SM lies close to the border of absolute electroweak vacuum stability and metastability. However, these celebrated results extrapolate the SM into a region where quantum gravity effects become important. We have therefore computed the quantum gravitational contributions to the standard model effective potential and analyzed their effects on the Higgs vacuum stability in the framework of effective field theory. Non-renormalizability of Einstein gravity induces higher dimension φ6 and φ8 operators at the one- loop level with novel couplings η1/2. We find that the true minimum of the standard model effective potential now lies below the Planck scale for almost the entire parameter space (η1/2(mt) > 0.01). In addition quantum gravity is shown to contribute to the minimal value of the standard model NLO effective potential at the percent level. The quantum gravity induced contributions yield a metastable vacuum for a large fraction of the parameter space in the flowing couplings η1/2.

In this talk we will review the appearance of an infinite dimensional symmetry algebra of tree level scattering amplitudes of N=4 super Yang-Mills theory, known as the Yangian of psu(2,2 4). It arises through the commutation of standard superconformal and the recently discovered dual superconformal symmetries of scattering amplitudes. At the loop level the conformal and dual conformal symmetry is destroyed by infrared divergencies. The present challenge is whether it may be repaired. We point out a novel IR regularization based on a suitable Higgsing of the theory, which is natural from the dual string perspective. It turns out that in this regularization an extended conformal symmetry of the loop amplitudes arises, which remains free of anomalies.

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this talk we present an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one-loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. This settles the previously open question of a potential regularization scheme dependence of the one-loop beta-function traditionally computed in the background field approach. Furthermore, we show that the remaining logarithmic divergencies give rise to an effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six.