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https://arxiv.org/abs/1701.02311

Hypercuboidal renormalization in spin foam quantum gravity

Benjamin Bahr, Sebastian Steinhaus

(Submitted on 9 Jan 2017)

In this article we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion letter, in which the existence of a fixed point in the truncated RG flow for the model was reported. Here we repeat the analysis with various modifications, and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

with some truncations, shows that spinfoam loop quantum gravity admits a UV fixed point in its renormalization group flow. the authors are quite explicit that their intention is to show LQG can be merged with Asymptotic safety.

Since Asymptotic safety scenario predicts

Asymptotic safety of gravity and the Higgs boson mass

Mikhail Shaposhnikov, Christof Wetterich

(Submitted on 1 Dec 2009 (v1), last revised 12 Jan 2010 (this version, v2))

There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson mH can be predicted. For a positive gravity induced anomalous dimension Aλ>0 the running of the quartic scalar self interaction λ at scales beyond the Planck mass is determined by a fixed point at zero. This results in mH=mmin=126 GeV, with only a few GeV uncertainty. This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For Aλ<0 one finds mH in the interval mmin<mH<mmax≃174 GeV, now sensitive to Aλ and other properties of the short distance running. The case Aλ>0 is favored by explicit computations existing in the literature.

Comments: 8 pages, typos corrected, references added. Journal version

Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)

Journal reference: Phys.Lett.B683:196-200,2010

DOI: https://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1016%2Fj%252Ephysletb%252E2009%252E12%252E022&v=69d96e2f [Broken]

Cite as: arXiv:0912.0208 [hep-th]

and

Consistency of matter models with asymptotically safe quantum gravity

P. Donà, Astrid Eichhorn, Roberto Percacci

(Submitted on 16 Oct 2014)

We discuss the compatibility of quantum gravity with dynamical matter degrees of freedom. Specifically, we present bounds we obtained in [1] on the allowed number and type of matter fields within asymptotically safe quantum gravity. As a novel result, we show bounds on the allowed number of spin-3/2 (Rarita-Schwinger) fields, e.g., the gravitino. These bounds, obtained within truncated Renormalization Group flows, indicate the compatibility of asymptotic safety with the matter fields of the standard model. Further, they suggest that extensions of the matter content of the standard model are severely restricted in asymptotic safety. This means that searches for new particles at colliders could provide experimental tests for this particular approach to quantum gravity.

Comments: prepared for the proceedings of Theory Canada 9; new results on the gravitino, 8 pages, 1 figure, 1 table

Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)

Cite as: arXiv:1410.4411 [gr-qc]

conclusions in the above paper

We conclude that, within the truncation specified above, and for a fixed number of vectors, there is an upper bound on the number of fermions and scalars that are compatible with asymptotic safety. The standard model has 12 vectors (1 photon, 8 gluons and 3 weak bosons), 4 scalars (one Higgs and three Goldstone modes that are “eaten up” by the weak bosons and become their longitudinal degrees of freedom) and 45/2 Dirac fermions. The non-integer number of fermions arises, since the standard model is chiral, i.e., it is constructed from Weyl fermions. In the gravitational β functions, a Dirac fermion essentially equals two Weyl fermions. As the standard model does not include right-handed neutrinos, it contains 45 Weyl fermions. . . . Generally, the allowed region in the NS, ND-plane for fixed NV shrinks rapidly, as the number of extra dimension is increased. We conclude that an experimental discovery of universal extra dimension could pose a challenge for the asymptotic safety scenario. Note that scenarios in which only gravity can propagate into the extra dimensions are not restricted by these results.

and also

We now turn to supersymmetric models, which must contain a gravitino.As it contributes to the beta function for G with the same sign as the graviton, it allows to extend the number of matter fields slightly in comparison to the gravitino-less case. In particular, simple SUGRA still admits a viable gravitational fixed point.The MSSM+SUGRA, however, contains too many fermions and lies in the excluded region. . . . In this work, we have added the contribution of spin- 3/2 gravitinos. We find that a model of pure supergravity admits an asymptotically safe gravitational fixed point. If we add matter, bounds on the number of allowed matter fields persists. In particular, the matter content of the MSSM is not compatible with a viable fixed point within a model with one graviton and one gravitino.

Gauge hierarchy problem in asymptotically safe gravity--the resurgence mechanism

Christof Wetterich, Masatoshi Yamada

(Submitted on 9 Dec 2016)

The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a "resurgence mechanism" where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomalous dimension plays a crucial role for the required "self-tuned criticality" in the ultraviolet regime beyond the Planck scale.

Comments: 5 pages, 1 figure

Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)

Cite as: arXiv:1612.03069 [hep-th]

results

also apply if LQG admits Asymptotic safety scenario?

Asymptotic safety scenario in gravity only admits the SM plus a small minimal extension of it, in 4D or 5D, no SUSY, no GUT particle content.

if loop quantum gravity is Asymptotic safety, does this mean the 126 Gev prediction is also a prediction of LQG?

if loop quantum gravity is Asymptotic safety, does this mean LQG also only admits the SM plus a small minimal extension of it, in 4D or 5D, no SUSY, no GUT particle content.

if loop quantum gravity is Asymptotic safety, does this mean Asymptotic safety "resurgence mechanism" to explain the higgs stability also applies in LQG.

is Asymptotic safety compatible with a hard bottom at the planck scale, as spinfoam shares with lattice gauge theories?

i.e its spinfoam admits a RG flow towards an UV fixed point in 4D

asymptotic safe loop quantum gravity:

what would mean to fundamental QG research for such a theory

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# I Asymptotic safety and loop quantum gravity

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