The Running Gravitational Couplings

Djamel Dou; Roberto Percacci

REVIEW

The Running Gravitational Couplings

Djamel Dou, Roberto Percacci

High Energy Physics - Theory · Submitted 29 Jul 1997 · 21 references

Pith's verdict: A solid, honest calculation of matter contributions to the gravitational RG; the structural results hold up, but the abstract's IR claim is scheme-dependent in a way the body admits and the abstract does not.

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arXiv IDhep-th/9707239 (version 3)

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CitationDjamel Dou, Roberto Percacci. "The Running Gravitational Couplings." arXiv:hep-th/9707239 (1997). https://pith.science/paper/HQRVBVQH

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Editor's note

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Worth your time if you work on the gravitational renormalization group; skip it otherwise. It is a 1997 paper that people still cite for one specific thing, and that thing is done properly. What is actually new: Reuter's 1996 flow was graviton-only. Dou and Percacci add matter of every spin from 0 to 2 and give the coefficients in closed form, eqs. (4.3), (4.7), (4.9), with the heat kernel table in Appendix A.II and every integral in Appendix B. That is the part the asymptotic safety literature actually uses, and it has held up. The on-shell analysis in section 6 is the nicest piece: they show the gauge parameter cancels in the leading terms once you set R = 4 Lambda, and identify kappa/Lambda as the gauge-independent combination. That is a real observation, not a throwaway. Soft spots, in order of weight. The infrared claim [abstract:s2] is scheme-dependent in a binary way, not just numerically. The footnote after eq. (5.2) says it plainly: for a gaussian cutoff (b=1) the zero-mode contribution is negligible and Lambda is not driven to zero; you need b>1. The abstract does not signal that. If you cite zero modes driving Lambda to zero, attach the b>1 caveat. The many-orders-of-magnitude figure in [abstract:s1] is a truncation-level number. The k^4 scaling is structural and robust; the 10^240 is set by c1, which is a cutoff-shape integral, and the authors say so in section 7. The truncation has no error control, their words in section 3. Also acknowledged. One correction to the record: the classifier found no stated limitations. That is wrong. Sections 3 and 7 are unusually candid about exactly these points, and the paper deserves credit for it rather than a penalty. Who it is for: anyone computing matter contributions to gravitational beta functions, or working in asymptotic safety. The structural results, k^4 running, near-constant Newton constant, on-shell gauge cancellation, are what survive. Send it out; the calculation is explicit enough to check line by line.

Referee report

Major objections (2)

[§6, Eqs. (6.5) and (6.6)] As printed, Eq. (6.6) is not the integral of Eq. (6.5). Integrating ∂_tF = −(1+ñ_S)b/(48π²) with F = κ/Λ and κ ≈ κ̄ gives Λ_k = Λ̄/[1 − (1+ñ_S)bΛ̄/(48π²κ̄) ln(k/k̄)], whereas (6.6) has (2+ñ_S) in place of (1+ñ_S) and ln(k/κ̄) in place of ln(k/k̄). The latter is also dimensionally inconsistent, since κ̄ = 1/16πḠ has mass dimension two while k has dimension one. Because (6.6) is the equation supporting the abstract's third sentence, please reconcile it with (6.5) and (5.2).
[Abstract, third sentence, and §5, footnote after Eq. (5.2)] The claim that 'zero modes drive the cosmological constant to zero' holds only for cutoff shape parameter b > 1. The footnote after (5.2) states that for a Gaussian cutoff (b = 1) P_k(0) and ∂_tP_k(0) are finite, all terms in (3.22) are of order k²/R or k²/Λ_k, and the zero-mode contribution is negligible, so Λ_k is not driven to zero. This is a qualitative, not merely quantitative, dependence on the cutoff shape, and the abstract does not signal it. Please qualify the abstract (and the corresponding statement in §7) to state the b > 1 condition, or explain why b = 1 is excluded.

Minor objections (7)

[§4, sentence quoting 'a factor 10^240'] This number is dominated by (M_Pl/H₀)⁴ and is therefore robust, but the O(1) coefficient c₁ is cutoff-shape dependent as stated in §7; a forward reference there would prevent the number from being read as a scheme-independent prediction. Note also that k ~ M_Pl lies at the edge of the stated validity κ̄ ≫ k².
[Eq. (5.3)] The term with denominator P_k − 4α/(3α−1)Λ_k carries coefficient 5/2 and argument R/3, whereas the corresponding term in (3.22) is (1/2)Σ_{j=0,1} with λ⁽⁰⁾₀ = 0 and λ⁽⁰⁾₁ = R/3; please check the coefficient and the argument against (3.22) and Table A.I.
[§6, sentence introducing F_k] F_k = κ_k/Λ_k is called a 'dimensionless ratio', but κ/Λ has mass dimension −2; the dimensionless on-shell quantity is 48π²κ/Λ, as (6.2) shows.
[Eq. (3.17)] The term written '∇ν∇νσ' should presumably be '∇μ∇νσ' in the irreducible decomposition of h_μν.
[§4 and §7] It would make the result concrete to quote the numerical values of a₁ and c₁ for a realistic particle content (e.g. the Standard Model), and to state explicitly which coefficient or limit is being compared when asserting agreement with Ref. [18].
[Eq. (6.6)] The denominator vanishes at a finite k above k̄, a Landau-pole-like singularity that should be noted together with the statement that the running is very slow.
[Throughout] Typographical corrections: 'sero mode' (§6), 'keat kernel' (Appendix A), 'spontaneusly' (§7), 'rigourous' (§4), 'Vilkoviski-de Witt' should be 'Vilkovisky–de Witt', and the journal abbreviations in Refs. [9] and [19] need fixing.

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The paper

The paper claims

Treating gravity as a quantum field theory with a sliding resolution scale, the authors compute how Newton's constant and the cosmological constant change with energy, and find the vacuum energy falls or rises steeply while gravity's pull,

The reading

The paper asks a concrete question inside the Wilsonian renormalization-group programme: if you coarse-grain gravity plus matter over a resolution scale $k$, how do the two couplings in Einstein's action — Newton's constant $G$ and the cosmological constant $Λ$ — actually move? The authors write down the exact flow equation for the effective average action, truncate it to the Einstein–Hilbert form, and feed in every free field of spin 0, 1/2, 1, 3/2 and 2, so that each species' contribution to the flow is counted. In the high-energy regime they find $Λ_k$ scaling like $k^4$ while $κ_k = 1/16πG_k$ stays essentially frozen; in the extreme infrared only zero modes survive and they push $Λ_k$ to zero logarithmically. What makes this worth attention is the size of the effect: on one admissible trajectory the vacuum energy changes by a factor of $10^{240}$ between Planck-scale and Hubble-scale resolution, which is the kind of leverage any account of the cosmological constant problem needs to explain or exploit.

What carries the argument

The engine is the exact renormalization-group equation for the effective average action, $∂_tΓ_k = ½Tr(δ^2Γ_k/δφδφ + R_k)^{-1}∂_tR_k$, with an infrared cutoff $R_k(z) = z f_k^2/(1-f_k^2)$ built from a smeared step $f_k(z) = exp(-a(z/k^2)^b)$. The cutoff makes the trace finite with no separate regularization, and the equation has the shape of a one-loop flow with the classical action replaced by $Γ_k$. To extract the coefficients of the identity and the curvature, the authors evaluate the traces on a constant-curvature background, decompose each higher-spin field into irreducible parts under $SO(5)$ (transverse vector, transverse-traceless tensor, and the various longitudinal scalars), and arrange the field redefinitions so that the functional Jacobians cancel. In the high-energy regime the traces are done with heat-kernel coefficients; in the low-energy regime they are done mode by mode with the known spectrum of $-∇^2$ on the sphere. The combination whose $\beta$ function comes out free of the gauge parameter $α$ is the dimensionless ratio $F_k = κ_k/Λ_k$, which the authors argue is also the physically meaningful one since $Λ$ and $κ$ are separately unmeasurable in pure gravity.

Extended reading notes

Core claim

The central claim is that the two gravitational couplings run very differently. Working with the exact renormalization-group equation for a coarse-grained effective action, truncated to $Γ_k = κ_k∫d^4x√g(2Λ_k - R)$ plus gauge-fixing and ghost terms, and including the one-loop contributions of $n_S$ scalars, $n_D$ Dirac fields, $n_M$ Maxwell fields, $n_P$ Proca fields and $n_{RS}$ Rarita–Schwinger fields, the authors derive off-shell $\beta$ functions for $κ_k$ and $Λ_k$ (eqs. 4.6–4.9). In the small-curvature, high-energy limit $k^2 ≫ R$ the solution is $κ_k ≈ κ̄ + ½a_1(k^2- k̄^2)$ with $a_1k^2/κ̄ ≪ 1$, so Newton's constant barely moves, while $Λ_k ≈ Λ̄ + ¼c_1κ̄(k^4- k̄^4)$: the cosmological constant scales as the fourth power of the cutoff even though it has dimensions of mass squared, because the coefficient of the identity operator in the Lagrangian is the product $κ_kΛ_k$ and $κ_k$ is nearly constant. The sign of $c_1$ is fixed by the excess of bosonic over fermionic degrees of freedom, matching the Casimir intuition that raising an infrared cutoff removes positive vacuum energy. In the opposite limit $k^2 ≪ R$, on a four-sphere where the spectrum is discrete, only zero modes still respond to $k$; the on-shell flow of the ratio $F_k = κ_k/Λ_k$ becomes $∂_tF_k = -(1+ñ_S)b/48π^2$, giving $Λ_k → 0$ as $k → 0$ (eq. 6.6), a running the authors themselves call very slow.

Load-bearing premise

The load-bearing premise is that truncating the effective action to the Einstein–Hilbert form with a single cutoff shape captures the qualitative flow, so that neglected higher-curvature operators cannot change the $k^4$ scaling or the sign of the cosmological-constant running; the authors state plainly that there is no control over this approximation and that the numerical coefficients depend on the cutoff parameters $a$ and $b$, making the running non-universal.

Editorial extensions

If this is right

The cosmological constant is not a constant: its value at laboratory or particle-physics resolution differs from its value at cosmological resolution by a factor set by $(k_{high}/k_{low})^4$ times the coefficient $c_1$, which counts the net bosonic minus fermionic degrees of freedom.
Newton's constant is effectively stable across the same range, so any experiment probing $G$ at different scales should find a variation suppressed by $a_1k^2/κ̄$ — the authors estimate $ΔG/G ∼ 10^{-66}a_1$ between planetary and centimetre scales.
Whether the vacuum energy runs up or down with resolution is decided by the sign of the particle content: a boson-dominated spectrum raises $Λ_k$ with $k$, a fermion-dominated one lowers it.
In the extreme infrared the zero-mode contribution drives $Λ_k$ to zero, so an exactly empty low-energy theory has a vanishing cosmological constant as a limit, approached logarithmically in $k$.
Because the ratio $F_k = κ_k/Λ_k$ is the gauge-independent on-shell quantity, any statement about the running of the cosmological constant alone is scheme-dependent in a way that statements about $F_k$ are not.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The factor-of-$10^{240}$ span quoted for $Λ_k$ is a statement about a single trajectory chosen with $k̄ = 0$ and $Λ̄ = 0$; a reader should treat it as an illustration of the leverage available in the flow rather than a prediction for the observed vacuum energy, which the paper does not claim to make.
The paper's remark that the Wilsonian $k → ∞$ limit corresponds to the metric-scaling $ω → 0$ limit (and vice versa) suggests that the 'ultraviolet' and 'infrared' labels attached to fixed points in gravitational flows are convention-dependent, which is a useful warning for anyone comparing fixed-point claims across the literature.
Since the coefficient $c_1$ is a Mellin transform of the cutoff shape and therefore depends on $a$ and $b$, a natural test is whether the sign of $c_1$ — the only part tied to physical degree-of-freedom counting — survives while its magnitude shifts; that split between universal sign and non-universal size is the sharpest handle the paper offers.
The appearance of $R^{-1}$-type terms in the infrared limit hints that a local truncation is straining, and that a non-local effective action of the $V\ln V$ kind could reproduce the same zero-mode-driven vanishing of $Λ$ from a different starting point.

Original abstract

We compute the running of the cosmological constant and Newton's constant taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive the cosmological constant to zero.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,912 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.26 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We compute the running of the cosmological constant and Newton's constant taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive the cosmological constant to zero.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the running of the cosmological constant and Newton's constant taking into account the effect of quantum fields with any spin between 0 and 2.	contribution 0.97	0.95	0.09	asserted 0.99
s1	We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales.	result 1.00	0.96	0.78	asserted 0.98
s2	In the extreme infrared, zero modes drive the cosmological constant to zero.	result 1.00	0.81	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.51.

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References

Works cited (21)

[1]

J. Donoghue, Phys.Rev. D 50 3874 (1994); ibid.D54 4963 (1996); Helv.Phys.Acta 69 269 (1996)

View on Pith 1994
[2]

S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)

View on Pith 1989
[3]

S. Coleman, Nucl. Phys. B 310 , 643 (1988)

View on Pith 1988
[4]

T.R. Taylor and G. Veneziano, Nucl. Phys. B 345 , 210 (1991)

View on Pith 1991
[5]

N.C. Tsamis and R.P. Woodard, Ann. of Phys. (NY) 238, 1 (1995)

View on Pith 1995
[6]

C. Wetterich, Phys.Lett B 301 , 90 (1993)

View on Pith 1993
[7]

M. Reuter, hep-th/9605030

View on Pith Pith review arXiv
[8]

C. Wetterich, hep-th/9501119

View on Pith Pith review arXiv
[9]

C. Wetterich and M. Reuter, Nucl.Phy B 417 , 181 (1994)

View on Pith 1994
[10]

G.W. Gibbons and M.J. Perry, Nucl. Phys. B 146 , 90 (1978)

View on Pith 1978
[11]

E.S. Fradkin and A.A. Tseytlin, Nucl. Phys. B 234 , 472, (1984)

View on Pith 1984
[12]

B. Allen, Phys. Rev. D 34 3670 (1986)

View on Pith 1986
[13]

V. Periwal, Mod. Phys. Lett. A10, 1543 (1995)

View on Pith 1995
[14]

R.Floreanini and R.Percacci, Phys.Lett. B 356 205 (1995)

View on Pith 1995
[15]

H. Kawai and M. Ninomiya, Nucl.Phys. B 336 , 115 (1990)

View on Pith 1990
[16]

Nelson et al., Phy.Rev D 25 , 1019 (1982); ibid. D 29 , 2750 (1984); I.L. Buchbinder et al. “Eﬀective Action in Quantum Gravity”

View on Pith 1982
[17]

R. Percacci, Nucl. Phys. B 353 271 (1991); 18

View on Pith 1991
[18]

R.Floreanini,R.Percacci, Phys.Rev. D 52 , 896 (1995)

View on Pith 1995
[19]

L.Griguolo,R.Percacci, Pys.Rev D 52 ,(1995) 5787

View on Pith 1995
[20]

C. Wetterich, gr-qc/9704052

View on Pith Pith review arXiv
[21]

B. de Witt, Dynamical theory of groups and ﬁelds , in “Relativity, Groups and Topology”, ed C.M. de Witt and B. de Witt, Gordon and Breach, NY (1964). 19

View on Pith 1964

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The Gross-Neveu model in 2<d<4 is asymptotically safe at a non-Gaussian fixed point in both fermionic and partially bosonized functional-RG formulations, with critical exponents computed analytically at large Nf and n...
Ghost anomalous dimension in asymptotically safe quantum gravity
hep-th 2010-01 accept novelty 4.0 of 10

The ghost anomalous dimension in asymptotically safe quantum gravity is negative (about -0.78 in the Landau-deWitt gauge), and its backreaction preserves the non-Gaussian UV fixed point.
Quantum gravity: a fluctuating point of view
hep-th 2020-07 accept novelty 3.0 of 10

A vertex expansion in graviton fluctuation correlation functions, truncated at the four-point level, reproduces the Reuter ultraviolet fixed point with three attractive directions and shows signs of apparent convergence.
Critical reflections on asymptotically safe gravity
gr-qc 2020-04 accept novelty 3.0 of 10

A field-internal critical review that enumerates the unresolved technical and conceptual problems of asymptotically safe gravity and clarifies frequent misunderstandings of the program.
Black holes within Asymptotic Safety
hep-th 2014-01 conditional novelty 3.0 of 10

Applying the same scale-dependent-coupling improvement to empty space produces a conical singularity, indicating that the singularity in improved black hole models is a scheme artifact rather than a black hole prediction.
Quantum Einstein Gravity
hep-th 2012-02 accept novelty 3.0 of 10

A review of the evidence that gravity is asymptotically safe, plus a two-parameter fit showing that the predicted scale-dependent spectral dimension of the effective space-time tracks 3D Causal Dynamical Triangulation...
The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
gr-qc 2006-10 accept novelty 3.0 of 10

A survey arguing that quantum gravity can be a genuine rather than merely effective field theory if its couplings approach a non-Gaussian ultraviolet fixed point, with the extreme ultraviolet behaving as a two-dimensi...
Quantum scale symmetry
hep-th 2019-01 conditional novelty 2.5 of 10

Scale symmetry in quantum field theory arises at fixed points, and its approximate breaking near those fixed points may link the Higgs hierarchy, quantum gravity, and cosmic acceleration.
Quantum Spacetime Phenomenology
gr-qc 2008-06 accept novelty 2.0 of 10

A comprehensive review argues that gamma-ray, cosmic-ray, and interferometric data analyses have reached genuine Planck-scale sensitivity to candidate quantum-spacetime effects, while acknowledging that most resulting...
Asymptotically safe quantum gravity and its phenomenology -- a review
hep-th 2026-06 unverdicted novelty 1.0 of 10

Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
An asymptotically safe guide to quantum gravity and matter
hep-th 2018-10 accept novelty 1.0 of 10

Asymptotic safety may provide a UV completion for gravity and matter through an interacting fixed point, and this review organizes the evidence and open questions.

How later papers used it

83 later papers cite it

Evidence: some. 71 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 3 of the 131 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 10 papers with this label · 1 by the same authors

By the same authors

Employed a redefinition of the form that cancels part of the Jacobian from the York decomposition given in this paper.

Asymptotic safety in an interacting system of gravity and scalar matter (2015) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

75 arXiv papers cite this in 121 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 76 sentences without a confident label

Builds on it 2 papers

Such a scaling solution is the generalization of the Reuter fixed point [ref] in the presence of matter [ref] .

Fermi scale from quantum gravity scaling solution · Introduction · 0.97
For vanishing gauge and Yukawa couplings we recover the constant scaling solution which corresponds to the extension of the Reuter fixed point [ref] of pure gravity to the presence of matter [ref] .

Effective scalar potential in asymptotically safe quantum gravity · Scaling solution with field-dependent Planck mass · 0.96

Uses its method or tool 9 papers

As the first option, we implement the Faddeev-Popov gauge fixing procedure, and choose the background field gauge (BFG) [ref] [equation] adding a gauge fixing term to the action [equation] and the Faddeev-Popov determinant in the usual form as an action for the ghosts $^μ$ and $C^μ$ [equation] Similarly to the fluctuation, the ghost field is also decomposed into its transverse and longitudinal components [ref] : [equation] with a trivial jacobian associated with ${C_μ}→{Ĉ_μ,η}$.

Gauge and parametrization dependence of Quantum Einstein Gravity within the Proper Time flow · Flow equation with different gauges and parametrizations · 0.95
We specialise to a maximally symmetric background, [equation] We decompose the fluctuation field according to the TT split [ref] , [equation] The quadratic part of the gauge-fixed action then takes the form \begin{dmath} δ^2(Γ_k+S_gf) = 1/32πG_N ∫d^d x √(g) { h^T_μν(Δ_2+2Ω)h^T μν +ξ_μ(2/α(Δ_1)^2+4ΩΔ_1)ξ^μ-σΔΔ̃2/d^2 [ ( d-2/2+1-d/α )Δ+R/α -dΩ]σ-2σα(d-2)-2β/αd^2 ΔΔ̃ h +h[ Δ̃^αβ -d-2/dΩ]h }, \end{dmath} where [equation] [equation]

Towards gauge independence in asymptotically safe quantum gravity · Explicit gauge independence at one loop · 0.99
For this reason we decompose the quantum fluctuations, according to the transverse-traceless decomposition [ref] which was first used for RG computations in [ref] [equation] Here $h=g^μνh_μν$ is the trace of the fluctuation, $h_μν^T$ denotes the transverse-traceless part of $h_μν$, $ξ_μ$ is a transverse vector that together with the scalar $σ$ makes up the longitudinal-traceless part of $h_μν$ according to [ref].

Further evidence for asymptotic safety of quantum gravity · Gravitational renormalisation group · 0.99

Compares with it 3 papers

In the case of the type Ib cutoff the results agree with the ones obtained earlier in the literature [ref] .

Functional renormalization with fermions and tetrads · Discussion · 0.99
It agrees with Refs. [ref] .

Variable Planck mass from the gauge invariant flow equation · Gauge bosons · 0.98
One can check that rewriting these equations for the variables $Λ̃=Λ/k^2=6λZ/u^2$ and $G̃=Gk^2=3u^2/4πZ$ one recovers the familiar beta functions of the Einstein–Hilbert truncation [ref] and, in the presence of matter [ref] .

The Renormalization Group and Weyl-invariance · Example: one loop beta functions of Einstein gravity · 0.86

Cites it as background 22 papers

Quantum gravity formulated in terms of the metric can be either asymptotically safe [ref] or asymptotically free [ref] .

Scaling solution for field-dependent gauge couplings in quantum gravity · Scaling solution in quantum gravity · 0.87
This type of calculation was first described in [ref] for pure gravity, and in [ref] for the non-linear sigma model.

Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization · Functional RG · 0.80
There are works in the background-field approximation [ref] , in the hybrid approach [ref] , and in a full fluctuation computation [ref] .

Quantum gravity: a fluctuating point of view · Gravity-matter systems · 0.87

Discussion

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[1] [1]

J. Donoghue, Phys.Rev. D 50 3874 (1994); ibid.D54 4963 (1996); Helv.Phys.Acta 69 269 (1996)

View on Pith 1994

[2] [2]

S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)

View on Pith 1989

[3] [3]

S. Coleman, Nucl. Phys. B 310 , 643 (1988)

View on Pith 1988

[4] [4]

T.R. Taylor and G. Veneziano, Nucl. Phys. B 345 , 210 (1991)

View on Pith 1991

[5] [5]

N.C. Tsamis and R.P. Woodard, Ann. of Phys. (NY) 238, 1 (1995)

View on Pith 1995

[6] [6]

C. Wetterich, Phys.Lett B 301 , 90 (1993)

View on Pith 1993

[7] [7]

M. Reuter, hep-th/9605030

View on Pith Pith review arXiv

[8] [8]

C. Wetterich, hep-th/9501119

View on Pith Pith review arXiv

[9] [9]

C. Wetterich and M. Reuter, Nucl.Phy B 417 , 181 (1994)

View on Pith 1994

[10] [10]

G.W. Gibbons and M.J. Perry, Nucl. Phys. B 146 , 90 (1978)

View on Pith 1978

[11] [11]

E.S. Fradkin and A.A. Tseytlin, Nucl. Phys. B 234 , 472, (1984)

View on Pith 1984

[12] [12]

B. Allen, Phys. Rev. D 34 3670 (1986)

View on Pith 1986

[13] [13]

V. Periwal, Mod. Phys. Lett. A10, 1543 (1995)

View on Pith 1995

[14] [14]

R.Floreanini and R.Percacci, Phys.Lett. B 356 205 (1995)

View on Pith 1995

[15] [15]

H. Kawai and M. Ninomiya, Nucl.Phys. B 336 , 115 (1990)

View on Pith 1990

[16] [16]

Nelson et al., Phy.Rev D 25 , 1019 (1982); ibid. D 29 , 2750 (1984); I.L. Buchbinder et al. “Eﬀective Action in Quantum Gravity”

View on Pith 1982

[17] [17]

R. Percacci, Nucl. Phys. B 353 271 (1991); 18

View on Pith 1991

[18] [18]

R.Floreanini,R.Percacci, Phys.Rev. D 52 , 896 (1995)

View on Pith 1995

[19] [19]

L.Griguolo,R.Percacci, Pys.Rev D 52 ,(1995) 5787

View on Pith 1995

[20] [20]

C. Wetterich, gr-qc/9704052

View on Pith Pith review arXiv

[21] [21]

B. de Witt, Dynamical theory of groups and ﬁelds , in “Relativity, Groups and Topology”, ed C.M. de Witt and B. de Witt, Gordon and Breach, NY (1964). 19

View on Pith 1964