Conformal and non conformal dilaton gravity

Álvarez, Enrique; Herrero-Valea, Mario; Martı́n, C.P.

doi:10.1007/jhep10(2014)115

Cited by 14 publications

(32 citation statements)

References 37 publications

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“…To gauge-fix the gauge symmetries in (2.5), we shall use the BRST technique in a similar way as in [18] and introduce the following nilpotent BRST operator…”

Section: Fixing the Gauge Freedommentioning

confidence: 99%

Quantum corrections to unimodular gravity

Álvarez

González-Martín

Herrero-Valea

et al. 2015

J. High Energ. Phys.

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The problem of the comological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.

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“…To gauge-fix the gauge symmetries in (2.5), we shall use the BRST technique in a similar way as in [18] and introduce the following nilpotent BRST operator…”

Section: Fixing the Gauge Freedommentioning

confidence: 99%

Quantum corrections to unimodular gravity

Álvarez

González-Martín

Herrero-Valea

et al. 2015

J. High Energ. Phys.

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“…In a recent paper [4] (the notation of which will be followed here), we have examined an apparently quasitrivial theory, namely, what we have dubbed conformal dilaton gravity (CDG). In it, the Weyl parameter is upgraded to a Stückelberg field to compensate the Weyl transformation of the Einstein-Hilbert Lagrangian.…”

Section: Introductionmentioning

confidence: 99%

“…[4] (essentially because there is no preferred scale in them). Conformal theories are also bizarre in other aspects [5,6], notably in the absence of the usual concept of a particle.…”

Section: Introductionmentioning

confidence: 99%

Conformal dilaton gravity: Classical noninvariance gives rise to quantum invariance

2016

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When quantizing conformal dilaton gravity, there is a conformal anomaly which starts at two-loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm, which is necessary in order to insure cancellation of the Weyl anomaly to every order in perturbation theory, has been determined using only conformal invariance. Those finite counterterms do not have any inverse power of any mass scale in front of them (precisely because of conformal invariance), and then they are not negligible in the low-energy deep infrared limit. The general form of the ensuing modifications to the scalar field equation of motion has been determined, and some physical consequences have been extracted.

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“…The inclusion of conformal symmetry is the reason for the cancelations. Explicitly, the one-loop counter term of the conformal dilation gravity (S CDG ) is given by [6,7] which is proportional to the S WG (3), reflecting the conformal symmetry. We don't need any counter terms more.…”

mentioning

confidence: 99%

“…The inclusion of conformal symmetry is the reason for the cancelations. Explicitly, the one-loop counter term of the conformal dilation gravity (S CDG ) is given by [6,7] …”

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confidence: 99%

Comment on “Quantum massive conformal gravity” by F. F. Faria

Myung

2016

Eur. Phys. J. C

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In a recent paper in EPJC doi:10.1140/epjc/ s10052-016-4037-5, Faria has shown that quantum massive conformal gravity is renormalizable but has ghost states. We comment this paper on the aspect of renormalizability.Recently, a paper in EPJC [1], Faria has insisted that quantum massive conformal gravity is renormalizable but has ghost states. The proposed action for this purpose is just the massive conformal gravity action (MCG) [2,3] which is classically invariant under the conformal transformations asHere (x) is an arbitrary function of the spacetime coordinates. We note here that the MCG action (S MCG ) is composed of the conformal dilation gravity (S CDG ) and the conformal gravity (S CG ). Since the integral of the Euler densityis a topological invariant quantity, S CG reduces to the Weyl gravityIt was argued that the massive conformal gravity (1) is a renormalizable quantum theory of gravity which has two massive ghost states. However, Faria's work is far from showing that (1) is a renormalizable quantum gravity because it was based on performing the canonical quantization of the second-order bilinear action. Concerning the renormalizability, Faria has mentioned that the graviton propagator of a e-mail: ysmyung@inje.ac.krhas a good behavior of 1/ p 4 at high momenta, making (1) power-counting renormalizable in the Minkowski spacetime. Unless the massive pole is shown to be unphysical, the MCG (1) is perturbatively meaningless because the graviton propagator (4) has ghost state. We wish to point out that this was a clear observation since the seminal work of Stelle released 40 years ago [4]. It was known that the MCG (1) is a promising quantum (gravity) model because the conformal symmetry restricts the number of counter-terms arising from the perturbative quantization of the scalar (dilaton) φ, while keeping the graviton fixed [5]. The inclusion of conformal symmetry is the reason for the cancelations. Explicitly, the one-loop counter term of the conformal dilation gravity (S CDG ) is given by [6,7] which is proportional to the S WG (3), reflecting the conformal symmetry. We don't need any counter terms more. In the absence of conformally coupled term (φ 2 R), however, quantizing a purely kinetic term requires (5) as well as R 2 -term (conformally non-invariant term). Hence (1) plays the role of a proper quantization action when quantizing the dilation φ in the fixed curved background g μν . On the other hand, Stelle has proposed the conformally non-invariant Lagrangian of √ −g(R + aC 2 + bR 2 ) to improve the perturbative properties of Einstein gravity [4]. The first two terms could be derived from (1) by making use of the conformal transformation (2). Also, one includes R 2 term as a counter term of g μν . If ab = 0, the renormalizabil-123

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Conformal and non conformal dilaton gravity

Cited by 14 publications

References 37 publications

Quantum corrections to unimodular gravity

Quantum corrections to unimodular gravity

Conformal dilaton gravity: Classical noninvariance gives rise to quantum invariance

Comment on “Quantum massive conformal gravity” by F. F. Faria

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