Quantum gravity with higher derivative terms

Julve, J.; Tonin, M.

doi:10.1007/bf02748637

Cited by 276 publications

(279 citation statements)

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“…The signs of the coefficients imply that α, β, γ are asymptotically free in d = 4 (for a suitable range of parameters) [6][7][8][9][10] whereasG goes in the UV to a fixed pointG = −(d −2)/B 1 . In order for this nontrivial fixed point to make sense, B 1 must be negative.…”

Section: Discussionmentioning

confidence: 99%

“…1 This theory is important because in four dimensions it is power-counting renormalizable [5] and asymptotically free [6][7][8][9][10]. In spite of these appealing 1 There has been recently some progress on theories that contain more than four, and possibly infinitely many derivatives [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

“…Then the equation for the pole mass m 2 phys = m 2 (k = m phys ) (where m(k) is the running mass) may not have a solution [6,11,12].…”

Section: Introductionmentioning

confidence: 99%

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Gauges and functional measures in quantum gravity II: higher-derivative gravity

2017

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We compute the one-loop divergences in a higher-derivative theory of gravity including Ricci tensor squared and Ricci scalar squared terms, in addition to the Hilbert and cosmological terms, on an (generally off-shell) Einstein background. We work with a two-parameter family of parametrizations of the graviton field, and a two-parameter family of gauges. We find that there are some choices of gauge or parametrization that reduce the dependence on the remaining parameters. The results are invariant under a recently discovered "duality" that involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gauges and functional measures in quantum gravity II: higher-derivative gravity

2017

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“…In the continuum limit, the action (iliz) really approaches Einstein's action (for references about the † It has been shown that in a suitable range of the couplings a and b the theory is asymptotically free with respect to them. Also, asymptotic freedom with respect to G may arise under certain circumstances [Julve and Tonin, 1978] exact meaning of this limit and the uniqueness of Regge's action, see [Menotti, 1990] and [Williams and Tuckey, 1991]). The extension of Regge's action by a cosmological term of the form λ s V s is straightforward.…”

Section: Regge Calculusmentioning

confidence: 99%

Vacuum correlations at geodesic distance in quantum gravity

Modanese

1994

Riv. Nuovo Cim.

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The vacuum correlations of the gravitational field are highly non-trivial to be defined and computed, as soon as their arguments and indices do not belong to a background but become dynamical quantities. Their knowledge is essential however in order to understand some physical properties of quantum gravity, like virtual excitations and the possibility of a continuum limit for lattice theory. In this review the most recent perturbative and non-perturbative advances in this field are presented. (To appear on Riv. Nuovo Cim.)

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“…It turns out that only two additional terms, involving fourth derivatives of the metric, need to be added to the Einstein action in order to obtain a perturbatively renormalizable theory, and cure at the same time the unbonndedness problem [7]. More remarkably, the resulting theory is asymptotically free in the new coupling constants (if they are chosen with the right sign) and is thus ultraviolet stable [8,9]. Furthermore, because of the asymptotic freedom the infrared behavior of the theory is computable and cutoff-independent.…”

Section: Introductionmentioning

confidence: 99%