Discrete polynomial regulators in the functional renormalization of quantum gravity

Introduced is a discrete, algebraic polynom-regulator for the functional reormalization-group (FRG)in quantum gravity. The regulator bases on projections of the Laplace-Beltrami-operators andintegrates all modi below a discrete scala exactly. The generated discrete RG-steps produce naturallog-periodic oscillations and a fractal UV-structure, which agrees qualitative with results fromCausal Dynamic Triangulations (CDT). The procedure is first applied to Einstein-Hilbert-truncation and then to elaborated truncations with R 2 and R 2 μ ν . Fixed points and critical exponentsare analyzed. The iteration shows stable UV-fixed points and log-periodic patterns in all couplings.The approach offers a diffeomorphism-compatible, exact and discrete alternative to standardregulators in FRG and opens up new possibilities for the study of fractal spacetime structures.