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arxiv: 2606.13098 · v2 · pith:ZDA6R7F7new · submitted 2026-06-11 · ✦ hep-th

The Graviton Propagator in Asymptotically Safe Gravity with Non-Local Form Factors

Emiliano Maria Glaviano This is my paper

Pith reviewed 2026-06-27 06:11 UTC · model grok-4.3

classification ✦ hep-th
keywords asymptotically safe gravitygraviton propagatornon-local form factorsfunctional renormalization groupNewtonian potentialghost polesquantum gravity
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The pith

The graviton propagator constructed from running non-local form factors in asymptotically safe gravity has a single pole at zero momentum with positive residue and no ghost poles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper follows the renormalization group flow of non-local form factors in a quadratic curvature truncation of four-dimensional quantum gravity and uses those form factors to build the background graviton propagator at vanishing renormalization scale. After analytic continuation to Minkowski space the propagator is examined for its pole structure and the associated Newtonian potential is extracted. The calculation yields only the expected massless graviton pole with positive residue and produces a potential that stays finite at the origin. A reader would care because the result indicates that, at this level of approximation, the theory avoids unphysical degrees of freedom while softening short-distance gravitational interactions.

Core claim

The background graviton propagator, obtained by flowing the non-local form factors to k=0 and continuing to Minkowski space, exhibits a single pole at q²=0 with positive residue and no additional ghost poles at this level of approximation. The corresponding Newtonian potential is found to be regular at r=0.

What carries the argument

The running non-local form factors obtained from the functional renormalization group flow at quadratic curvature order, which set the momentum dependence of the propagator.

If this is right

  • Only the physical massless graviton mode appears in the propagator.
  • No ghost poles are generated by the running form factors at this truncation.
  • The Newtonian potential between point masses remains finite as their separation approaches zero.
  • The result holds after analytic continuation from the Euclidean to the Minkowski signature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same form-factor structure survives in truncations with additional curvature terms, the absence of ghosts may be a robust feature of the theory.
  • The finite short-distance potential suggests that classical curvature singularities could be resolved once the full quantum dynamics are taken into account.
  • Extending the same construction to include matter fields would show whether the regular potential alters particle scattering or bound-state formation.

Load-bearing premise

The quadratic curvature truncation and the specific running of the non-local form factors from the functional renormalization group flow must remain valid; if higher-order curvature terms change the form-factor running, the pole structure could change.

What would settle it

Recomputing the propagator after enlarging the truncation to include cubic or quartic curvature invariants and checking whether new poles with negative residue appear would directly test the claim.

Figures

Figures reproduced from arXiv: 2606.13098 by Emiliano Maria Glaviano.

Figure 1
Figure 1. Figure 1: FIG. 1. Flow of the asymptotically safe solution in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Reference AS form factors at [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. AS Euclidean propagators in the mixed (blue) and B (beige) schemes. Dashed lines indicate the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Euclidean propagators obtained from shifted AS form factors for different values of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effective anomalous dimensions as function of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) shows Geff k=0(q 2 ) in log-log scale, together with its IR and UV asymptotic regimes. A transition region starting around q 2 ∼ m2 p/16π separates the two asymptotic regimes, with UV scaling setting in at q 2 ∼ m2 p . This behavior is consistent with the results of [61] [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Plots of the perturbations of [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Plots of the perturbations of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Plot of [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Plot of [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Reference analytically continued numerical form factors at [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Real part of the reference asymptotically safe form factors in the B scheme, compared with [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Imaginary part of the reference asymptotically safe form factors in the B scheme, compared [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Analytically continued [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Analytically continued [PITH_FULL_IMAGE:figures/full_fig_p026_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Analytically continued shifted [PITH_FULL_IMAGE:figures/full_fig_p028_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Analytically continued shifted [PITH_FULL_IMAGE:figures/full_fig_p028_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Analytically continued [PITH_FULL_IMAGE:figures/full_fig_p030_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. In (a) values of [PITH_FULL_IMAGE:figures/full_fig_p033_19.png] view at source ↗
read the original abstract

We analyze the flow of the background graviton propagator driven by the running of asymptotically safe form factors in four-dimensional quantum gravity at quadratic order in the curvature expansion. We construct the propagator in the $k=0$ limit and investigate its momentum dependence. The non-local form factors are then analytically continued to Minkowski spacetime, from which the corresponding Minkowskian propagator is obtained. We find a single pole at $q^2=0$ with positive residue and no additional ghost poles at this level of approximation. The corresponding Newtonian potential is found to be regular at $r=0$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript analyzes the flow of the background graviton propagator in four-dimensional asymptotically safe quantum gravity, driven by running non-local form factors obtained from the functional renormalization group within a quadratic curvature truncation. The k=0 propagator is constructed in Euclidean signature, the form factors are analytically continued to Minkowski space, and the resulting propagator is examined for its pole structure. The authors report a single pole at q²=0 with positive residue, the absence of additional ghost poles at this level of approximation, and a Newtonian potential that remains regular at r=0.

Significance. If the reported pole structure and regularity hold under further scrutiny, the work would constitute a concrete advance for the asymptotically safe gravity program by exhibiting an explicit, ghost-free graviton propagator derived from FRG flow equations and a regular low-energy potential. The technical step of analytically continuing the non-local form factors supplies a direct link between the renormalization-group running and observable quantities.

major comments (1)
  1. [Abstract] Abstract: the central claim of a single pole at q²=0 with positive residue and no additional ghosts is explicitly restricted to the quadratic curvature truncation. No quantitative estimate or stability analysis is supplied for the effect of higher-order curvature invariants on the form-factor beta functions and the subsequent analytic continuation; because the form factors are truncation-dependent, this omission directly affects the robustness of the no-ghost conclusion.
minor comments (2)
  1. The manuscript would benefit from an explicit statement, early in the text, of the precise truncation ansatz (including the number of independent form factors retained) to allow readers to assess the scope of the approximation without consulting the methods section.
  2. Notation for the non-local form factors and their momentum arguments should be introduced with a compact table or equation block to improve readability for readers outside the immediate FRG community.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: Abstract: the central claim of a single pole at q²=0 with positive residue and no additional ghosts is explicitly restricted to the quadratic curvature truncation. No quantitative estimate or stability analysis is supplied for the effect of higher-order curvature invariants on the form-factor beta functions and the subsequent analytic continuation; because the form factors are truncation-dependent, this omission directly affects the robustness of the no-ghost conclusion.

    Authors: We agree that the results are obtained within the quadratic curvature truncation, which is already stated explicitly in the abstract ('at quadratic order in the curvature expansion' and 'at this level of approximation'). A quantitative stability analysis under inclusion of higher-order curvature invariants would require a substantially extended truncation and new FRG computations, which are computationally demanding and lie outside the scope of the present work. The manuscript therefore reports the pole structure and regularity properties at the current level of approximation, consistent with standard practice in the field when presenting truncation-dependent results. revision: no

Circularity Check

0 steps flagged

No circularity; propagator poles are direct output of FRG flow in quadratic truncation

full rationale

The paper computes the k=0 graviton propagator by inserting non-local form factors obtained from the FRG beta functions inside an explicit quadratic-curvature truncation, then performs the analytic continuation to Minkowski space. The single-pole result with positive residue is stated as the outcome of that calculation, qualified by 'at this level of approximation.' No equation redefines a quantity in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing uniqueness claim rests on a self-citation chain. The derivation is therefore self-contained against the truncation's own flow equations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the quadratic truncation of the effective action and the analytic properties of the running form factors; without the full text these cannot be enumerated exhaustively.

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discussion (0)

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Spectral Functions of Lorentzian Quantum Gravity

    hep-th 2026-06 unverdicted novelty 6.0

    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.

  2. The pole truth: an analytical graviton propagator from Asymptotic Safety

    hep-th 2026-06 unverdicted novelty 5.0

    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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