Speaker
Description
One candidate for a quantum theory of gravity is the Asymptotic Safety conjecture, which postulates the existence of a non-trivial fixed point for the gravitational couplings. We investigate the search for such a fixed point within the framework of perturbation theory.
For this, we employ the Ricci flow as the central tool, pursuing a perturbative scheme analogous to the gradient flow formalism in QCD. In QCD, the gradient flow was introduced to bridge the gap between lattice simulations and perturbative calculations, allowing for a definition of a renormalization scheme that is accessible in both settings. Applied to gravity, the gradient flow is known as Ricci flow.
In this talk, I will describe the perturbative implementation of the Ricci flow: the flow equation for the graviton field and its gauge fixing, the resulting Feynman rules, the BRST symmetry of the flowed theory, and its renormalization. On this basis we define Newton's coupling in the Ricci flow scheme and investigate its renormalization group behavior.