Quantum Gravity and String Theory

    

Discrete Polynomial Regulators in the Functional Renormalization of Gravity

Authors: Holger Döring

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 and integrates all modi below a discrete scala exactly. The generated discrete RG-steps produce natural log-periodic oscillations and a fractal UV-structure, which agrees qualitative with results from Causal Dynamic Triangulations (CDT). The procedure is first applied to Einstein-Hilbert-truncation and then to elaborated truncations with and . Fixed points and critical exponents are 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 standard regulators in FRG and opens up new possibilities for the study of fractal spacetime structures.

Comments: 5 Pages.

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[v1] 2026-01-27 00:35:05

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