Interplay of quantum gravity and matter: Role of symmetries
Across different scales, symmetries shape physical systems: for example, in effective theories in condensed matter, various global symmetries are realized; at higher energy scales, the local symmetries of the Standard Model of particle physics take over. But what is the fate of symmetries at the Planck scale, where quantum gravity fluctuations kick in?
In this talk, I will focus on this question mainly from the perspective of asymptotic safety and will highlight a number of results about the role of symmetries in the interplay of asymptotically safe quantum gravity with matter. I will then mainly focus on particular discrete global symmetries, which have the attractive feature of generating mass-hierarchies without extra fine-tuning, and discuss whether or not these could be realized in quantum-gravity-matter models.