David Prinz - Hopf Ideals for General Relativity

This talk was part of the of the Master Class and Workshop on "Higher Structures Emerging from Renormalisation" held at the ESI November 8 - 19, 2021.

In this talk, I will present recent results on a possible renormalization of (effective) Quantum General Relativity in the Hopf algebra setup of Connes and Kreimer. It was shown by van Suijlekom (2007) that the quantum counterparts of gauge symmetries induce Hopf ideals in the respective renormalization Hopf algebra. In a recent article, I have generalized this correspondence to non-renormalizable theories with multiple coupling constants. This suggests, as I will explain in detail, a renormalization of (effective) Quantum General Relativity by properly incorporating the diffeomorphism invariance into the renormalization operation. Finally, I will close with an outline on the current state of this endeavor and comment on the related concepts of Feynman graph cohomology and the Corolla polynomial.