Speaker
Description
Over the past few decades, significant evidence for an asymptotically safe fixed point in quantum gravity has accumulated. An important direction of research relates to the inclusion of higher-curvature interactions. Stable results have been found in "vertical" extensions involving increasing powers of Ricci scalars and tensors, Riemann tensors, and specific combinations thereof, up to order 144 in curvature. Recently, RG flows have been derived by Kluth & Litim for general f(Riemann) theories on maximally symmetric backgrounds (MSB). This approach allows for systematic scans over the entire space of invariants, modulo projection redundancies due to MSBs. Here, we report on first systematic "horizontal" scans covering flows for all invariants at quadratic and cubic order in curvature.
At fourth order, the operator choice on MSBs is governed by a single parameter. The EH (Reuter) plus quadratic branch remains a non-Gaussian fixed point with three UV-attractive directions and is robust under regulator, background field and operator variations.
At sixth order, the operator choice is governed by a further two parameters. Homotopy tracks the principal continuation of this branch from fourth order. The additional, predominantly cubic eigendirection is UV-repulsive, so the UV critical surface remains three-dimensional. Continuation around the operator plane returns to the same fixed point, with no evidence of branch switching, and we again find the fixed points are robust under technical parameter choice and operator composition. Other sixth-order fixed points exist, but none is equally robust: their relevant-direction counts vary, their eigendirections become nearly collinear, or their critical exponents are near-marginal.
These results provide further support for an asymptotically safe fixed point in quantum gravity.