Line of Fixed Points in Gross-Neveu Theories.

In the limit of many fermion flavors it is demonstrated that the sextic Gross-Neveu theory in three dimensions displays a line of interacting UV fixed points, characterized by an exactly marginal sextic interaction. We determine the conformal window of UV-complete theories, universal scaling dimensions, and the phase diagram using renormalization group methods. Massless theories arise naturally, and the generation of mass proceeds without the breaking of a discrete symmetry. Striking similarities with critical scalar theories at large N are highlighted, and implications from the viewpoint of conformal field theory and the AdS/CFT conjecture are indicated.

Lorentzian Quantum Gravity and the Graviton Spectral Function.

We present the first direct and nonperturbative computation of the graviton spectral function in quantum gravity. This is achieved with the help of a novel Lorentzian renormalization group approach, combined with a spectral representation of correlation functions. We find a positive graviton spectral function, showing a massless one-graviton peak and a multigraviton continuum with an asymptotically safe scaling for large spectral values. We also study the impact of a cosmological constant. Further steps to investigate scattering processes and unitarity in asymptotically safe quantum gravity are indicated.

Price of Asymptotic Safety.

All known examples of four-dimensional quantum field theories with asymptotic freedom or asymptotic safety at weak coupling involve non-Abelian gauge interactions. We demonstrate that this is not a coincidence: No weakly coupled fixed points, ultraviolet or otherwise, can be reliably generated in theories lacking gauge interactions. Implications for particle physics, critical phenomena, and conformal field theory are indicated.

Asymptotic Safety Guaranteed in Supersymmetry.

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.

Renormalization group and the Planck scale.

I discuss the renormalization group approach to gravity, and its link to Weinberg's asymptotic safety scenario, and give an overview of results with applications to particle physics and cosmology.

Signatures of gravitational fixed points at the Large Hadron Collider.

We study quantum-gravitational signatures at the CERN Large Hadron Collider (LHC) in the context of theories with extra spatial dimensions and a low fundamental Planck scale in the TeV range. Implications of a gravitational fixed point at high energies are worked out using Wilson's renormalization group. We find that relevant cross sections involving virtual gravitons become finite. Based on gravitational lepton pair production we conclude that the LHC is sensitive to a fundamental Planck scale of up to 6 TeV.

Infrared behavior and fixed points in Landau-gauge QCD.

We investigate the infrared behavior of gluon and ghost propagators in Landau-gauge QCD by means of an exact renormalization group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimization procedure is devised to remove residual regulator dependences. In Landau-gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.

Fixed points of quantum gravity.

Euclidean quantum gravity is studied with renormalization group methods. Analytical results for a nontrivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameters in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.