Exact renormalization group and running Newtonian coupling in higher-derivative gravity

Bytsenko, A. A.; Granda, L. N.; Odintsov, Sergei D.

doi:10.1134/1.567411

Cited by 13 publications

(11 citation statements)

References 10 publications

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“…The first step to enlarge the functional space is to include the so-called R 2 -terms. [9] From another point of view, the extension of the functional space is important. This is because the RG flows that move toward the UV NGFP are governed by the higher derivative terms.…”

Section: Summary and Discussionmentioning

confidence: 99%

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Non-Trivial Ultraviolet Fixed Point in Quantum Gravity

Souma

1999

Progress of Theoretical Physics

333

370

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The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions $(2\simeq d\leq4)$. It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbatively $\epsilon$-expanded calculations in $2+\epsilon$ gravity theory remains in d=4. Hence it is possible that quantum gravity is an asymptotically safe theory and renormalizable in 2

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Section: Summary and Discussionmentioning

confidence: 99%

“…In the Landau-De Witt gauge α = 0, it is recognized that the UV NGFP remains in d = 4. [9] However, to guarantee the existence of the UV NGFP in 2 < d ≤ 4, more accurate calculations must be done. [8] In addition, there is the possibility that the physical quantities derived from this formulation depend on the gauge.…”

Section: Summary and Discussionmentioning

confidence: 99%

Non-Trivial Ultraviolet Fixed Point in Quantum Gravity

Souma

1999

Progress of Theoretical Physics

333

370

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“…The gauge fixing dependence of the original formulation [1] was investigated in [34] and [35]. An incomplete higher-derivative calculation was begun in [36] where the running of the R 2 -couplings was neglected, however, and no conclusions about the fixed point could be drawn.…”

Section: −1mentioning

confidence: 99%

Flow equation of quantum Einstein gravity in a higher-derivative truncation

2002

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Motivated by recent evidence indicating that Quantum Einstein Gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term (R 2 ). The beta-functions describing the renormalization group flow of the cosmological constant, Newton's constant, and the R 2 -coupling are computed explicitly. The fixed point properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian fixed point predicted by the latter is found to generalize to a fixed point on the enlarged theory space. In order to test the reliability of the R 2 -truncation near this fixed point we analyze the residual scheme dependence of various universal quantities; it turns out to be very weak. The two truncations are compared in detail, and their numerical predictions are found to agree with a suprisingly high precision. Due to the consistency of the results it appears increasingly unlikely that the non-Gaussian fixed point is an artifact of the truncation. If it is present in the exact theory QEG is probably nonperturbatively renormalizable and "asymptotically safe". We discuss how the conformal factor problem of Euclidean gravity manifests itself in the exact renormalization group approach and show that, in the R 2 -truncation, the investigation of the fixed point is not afflicted with this problem. Also the Gaussian fixed point of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding fixed point on the enlarged theory space.

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“…Independent evidence for a nontrivial FP also comes from Monte Carlo simulations [15,16]. However, so far only partial results are known for higherderivative terms [14,17,18].…”

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confidence: 99%