Renormalization Group Approaches to Quantum Gravity Conference - Apr. 22-25th
In this talk I present recent work on complete UV-IR flows for the fully momentum-dependent propagator, RG-consistent vertices, Newtons coupling and the cosmological constant. For the first time, a global phase diagram is obtained where the non-Gaussian ultraviolet fixed point of asymptotic safety is connected via smooth trajectories to an infrared fixed point with classical scaling. Physics implications as well as the extension to gauge-matter-gravity systems are discussed.
Recently, the development of tensor network renormalization approach has provided us a powerful tool to construct new classes of topological quantum field theories(TQFTs) in discrete space-time. For example, the Turaev Viro’s states sum constructions are fixed point tensor networks representing a special class of 2+1D TQFTs. Interestingly, the Grassmann variable generalization of tensor network renormalization approach leads to new classes of TQFTs for interacting fermion systems, namely, the fermionic TQFTs.
The many-building-blocks limit of spin foam models remains to be an open question. The complexity of these models makes the analysis of their possible continuum phases a very difficult task. In the last years progress in this direction has been made by considering simplified, yet featured-rich, analog models to spin foams, the so-called spin net models. These models retain the main dynamical ingredient of spin foams, namely the simplicity constraints.
An attempt is made to define "lines of contant physics" in CDT and relate the corresponding picture to non-trivial UV fixed points as they appear in the asymptotic safety scenario.
The connection between two-dimensional Euclidean gravity and pure matrix models has lead to may fundamental insights about quantum gravity and string theory. The pure matrix model is thus a blueprint for the connection between discrete models and Euclidean quantum gravity. I will report on work with Astrid Eichhorn in which this "blueprint" model is investigated with the functional renormalization group. In this model, I will discuss the questions: "What is a possible meaning of asymptotic safety in a discrete model?" and "Is it possible to apply the FRGE to tensor models?
Two aspects of asymptotic safety are highlighted. First, I discuss how asymptotic safety can be tested with the help of a bootstrap strategy. This is then applied to high-order polynomial actions of the Ricci scalar and beyond. Second, I discuss how phenomenological signatures of asymptotic safety can be searched for at particle colliders such as the LHC, provided that the quantum gravity scale is in the TeV energy regime.
We know how to make perturbative calculations in quantum gravity using the framework of effective field theory. I will describe the basics of the effective field theory treatment and look at several calculations. There are obstacles to describing these with running coupling constants. Finally, I will do my best to try to connect these with the Asymptotic Safety program.