Renate Loll - Quantum Gravity: Getting There

New observational windows on strongly gravitating systems raise the exciting prospect to yield new insights into the quantum foundations of general relativity. This puts pressure on us theorists to deliver predictions, and in turn directs the focus on two properties any successful quantum gravity theory must have: uniqueness (no or few free parameters) and the ability to produce “numbers”, by using effective computational tools beyond perturbation theory. Our current best bet are no-frills quantum field theoretic approaches, which emulate the nonperturbative toolbox and successes of a theory like QCD. However, the symmetry structure of gravity is completely different from that of a gauge field theory, and it has taken many years to adapt lattice and renormalization group methods to a situation where geometry is dynamical and there is no pre-existing background metric or notion of scale. The good news is that sufficient progress has been made in some of these approaches to produce numbers, in the form of quantitative results on the spectrum of certain invariant quantum observables at or near the Planck scale. Most results on observables have been obtained in Causal Dynamical Triangulations or CDT quantum gravity, which uses a simplicial lattice regularization based on Regge’s idea of “General relativity without coordinates” and builds on the rich, exact mathematics of models of random geometry in two dimensions. The biggest breakthrough of CDT quantum gravity in four dimensions is the emergence, from first principles, of a nonperturbative ground state with properties of a de Sitter universe. I will summarize these results and explain what nonperturbative quantum gravity can and cannot do for you, highlighting the nonlocal character of observables and the structural challenges of relating Planckian and (semi-)classical gravity.