A non-trivial UV fixed point for the scalar matter form factor exists in asymptotically safe quantum gravity, with a discrete spectrum of critical exponents and infrared locality restored.
The functional $f(R)$ approximation
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This formulation is used as an example to give a detailed explanation for how asymptotic analysis and Sturm-Liouville analysis can be used to uncover some of its most important properties. In particular, if defined appropriately for all values $-\infty<R<\infty$, one can use these methods to establish that there are at most a discrete number of fixed points, that these support a finite number of relevant operators, and that the scaling dimension of high dimension operators is universal up to parametric dependence inherited from the single-metric approximation. Formulations using adaptive cutoffs, are also reviewed, and the main differences are highlighted.
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hep-th 5years
2026 5roles
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background 2representative citing papers
In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
Analytical approximation to the graviton propagator from Asymptotic Safety shows no extra poles and identifies a mechanism where spurious pole residues vanish at higher orders.
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
citing papers explorer
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Scaling Solutions of Matter Form Factors in Asymptotically Safe Quantum Gravity
A non-trivial UV fixed point for the scalar matter form factor exists in asymptotically safe quantum gravity, with a discrete spectrum of critical exponents and infrared locality restored.
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Towards gauge independence in asymptotically safe quantum gravity
In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
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Spectral Functions of Lorentzian Quantum Gravity
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
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The pole truth: an analytical graviton propagator from Asymptotic Safety
Analytical approximation to the graviton propagator from Asymptotic Safety shows no extra poles and identifies a mechanism where spurious pole residues vanish at higher orders.
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Asymptotically safe quantum gravity and its phenomenology -- a review
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.