Is Quantum Einstein Gravity Nonperturbatively Renormalizable?

M. Reuter; O. Lauscher

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Is Quantum Einstein Gravity Nonperturbatively Renormalizable?

O. Lauscher, M. Reuter

High Energy Physics - Theory · Submitted 2 Oct 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense.	result 0.98	0.94	0.89	asserted 0.62
s1	This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales.	interpretation 1.00	0.15	0.29	hedged possibility 1.00
s2	For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit.	result 0.92	0.95	0.25	asserted 1.00
s3	The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.	method 0.98	0.73	0.02	asserted 0.99

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The paper

Original abstract

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.

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Cited by 34 Pith papers

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26 arXiv papers cite this in 31 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 2 papers

We summarize recent evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity (QEG) is nonperturbatively renormalizable along the lines of Weinberg's asymptotic safety scenario.

Towards Nonperturbative Renormalizability of Quantum Einstein Gravity · 0.99
We find strong evidence supporting the hypothesis that 4-dimensional Einstein gravity is asymptotically safe, i.e. nonperturbatively renormalizable.

Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity · 0.92

Papers citing it · 23 sentences without a confident label

Cites it as background 8 papers

Since then, a plethora of approximations and aspects were studied, including different approximations on the Einstein-Hilbert sector [ref] , higher derivatives and $f(R)$ [ref] , the two-loop counterterm [ref] , aspects of unitarity [ref] , different variables [ref] and the coupling to matter [ref] .

Infinite order quantum-gravitational correlations · Introduction · 0.97
The functional RG flow in the context of gravity [ref] has been studied in various truncations, starting with the Einstein-Hilbert truncation [ref] , including higher curvature invariants [ref] and matter fields [ref] , as well as closed flow equations for $f(R)$ gravity [ref] , and general scalar-tensor theories [ref] .

Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity · Asymptotic safety · 0.95
(4) Like in [I], also in this paper we shall illustrate the general considerations by examples taken from Asymptotic Safety, more precisely from Quantum Einstein Gravity (QEG), the nonperturbatively renormalized quantum theory whose basic degrees of freedom are carried by a bare metric field [ref] .

On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety · Introduction · 0.91

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