March 3, 2026Open Access

Discrete polynomial regulators in the functional renormalization of quantum gravity

Key Points

The analysis shows stable UV-fixed points and log-periodic patterns in all couplings, reflecting natural oscillations.
Notably, this approach utilizes discrete RG-steps based on the Laplace-Beltrami operator to study quantum gravity.
The method has been applied to the Einstein-Hilbert truncation and more sophisticated truncations involving R² terms.
Through detailed investigation, the study offers a new, exact, and diffeomorphism-compatible alternative to traditional regulators.

Abstract

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.

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Cite This Study

Holger Döring (Wed,) studied this question.

synapsesocial.com/papers/69a75c4ec6e9836116a250f0 https://doi.org/https://doi.org/10.5281/zenodo.18400728

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