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Asymptotic Safety Scenario in QG vs LQG

  1. Dec 3, 2015 #1
    the paper
    Asymptotic safety of gravity and the Higgs boson mass
    predicts the Higgs mass. it also forms the framework of the neutrino minimal standard model.

    any research papers comparing Asymptotic Safety Scenario in QG vs LQG? does anyone here have opinions on Asymptotic Safety Scenario in QG vs LQG?

    could both Asymptotic Safety Scenario in QG & LQG be correct or does one being correct mean the other theory is incorrect? are there any papers that attempt to combine the two programs?

    is it possible for researcher to swap Asymptotic Safety Scenario in QG with LQG to predict Higgs mass?

  2. jcsd
  3. Dec 7, 2015 #2


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    That prediction by Shaposhnikov and Wetterich was impressive. IIRC we had some discussion of it at the time. arivero (Alejandro Rivero) discussed it some in a thread of his, as I recall.
    There were other assumptions weren't there (like no new physics between here and planck scale?)
    I haven't had time to review the S&W paper.
    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.
    8 pages
    155 citations
    What you ask is really interesting. Could AsymSafe QG and LQG (or more specifically LQC) be consistent at some level, in what they predict? if you add to LQG the same assumptions about Standard Model being valid up to planck scale, could you get some comparable result?
    I'll try to get back to this--right now am swamped with real world duties and can't think about it.
    Could LQC be used to show that basic physical constants like G and cosmological constant Λ run?
    Last edited: Dec 7, 2015
  4. Dec 7, 2015 #3
    i'm asking about every variation of questions regarding AsymSafe QG and LQG on a fundamental level (LQC is derived).

    Variations of the issue AsymSafe QG and LQG/spinfoam

    Are there any AsymSafe QG and LQG/spinfoam research papers published by AsymSafe QG and LQG/spinfoam researchers ? i.e Lee Smolin?

    Are AsymSafe QG and LQG/spinfoam two different aspects of the same theory? Do they contradict one another? Can AsymSafe QG and LQG/spinfoam be combined in a single QG theory?

    Is LQG/spinfoam AsymSafe ?

    If in the paper mentioned above if you replace
    The Asymptotic Safety Scenario in QG
    with LQG/spinfoam, would you also get a prediction of 126 GeV higgs?

    The Asymptotic Safety Scenario in QG is consistent with the neutrino minimal SM.

    Is LQG/spinfoam also consistent with neutrino minimal SM

    What would happen if you attempt to combine LQG/spinfoam with Asm Safe?
    i.e start with Asymptotic Safety Scenario in QG and perform Loop quantization, or use Ashkertar-loop gravity and determine if it is Asm Safe?

    or propose a new QG that has aspects and features of loop/spinfoam with Asm Safe.

    in 4D no-SUSY ofc. theres Sugra and if you want higher dimentional gravity there's strings.

    Neutrino minimal standard model + Asymptotic Safety Scenario in QG in 4D, no SUSY no GUT as final theory of nature

    any LQG researcher proposing Neutrino minimal standard model + LQG in 4D, no SUSY no GUT

  5. Dec 7, 2015 #4


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    There is a paper by Martin Reuter (one of the main AsymSafe QG authors) which explores possible connections with LQG. I have only a slight familiarity with it, not enough to recommend, or give any useful advice. But I'll give the link, a bit of the abstract and some excerpts
    Einstein–Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
    J.-E. Daum and M. Reuter
    Institute of Physics, University of Mainz Staudingerweg 7, D-55099 Mainz, Germany

    In this paper we analyze the functional renormalization group flow of quantum gravity on the Einstein-Cartan theory space. ...
    ... Nevertheless, we do find evidence for the existence of at least one non-Gaussian renormalization group fixed point which seems suitable for the Asymptotic Safety construction in a setting where the spin connection and the vielbein are the fundamental field variables.

    ==quote page 6 and following==
    In the literature many generalizations of classical Einstein-Cartan theory with ac- tions more complicated than SHP[e,ω] have been considered [43,46]. In particular in the context of Loop Quantum Gravity (LQG) the so-called Holst action SHo[e,ω] plays an important role [47,48]. It contains an additional term that exists only in 4 dimensions; its prefactor is the dimensionless Immirzi parameter γ. This term is typical of Einstein- Cartan theory; it vanishes for vanishing torsion and, as a result, does not exist in metric gravity. Remarkably, the vacuum field equations implied by SHo[e, ω] do not depend on γ, even though the part of the action it multiplies is not a surface term. Indeed, in presence of fermions coupled to gravity in a non-minimal way, the Immirzi term induces a CP violating four-fermion interaction that might be interesting for phenomenological reasons, in the cosmology of the early universe, for instance [49–51].

    The Holst action is of central importance for several modern approaches to the quantization of gravity [52]. This includes canonical quantum gravity on the basis of Ashtekar’s variables [53], Loop Quantum Gravity [54], spin foam models [55], and group field theory [56]. In LQG, for instance, γ makes its appearance in the spectrum of area and volume operators. It was also believed to determine the entropy of black holes since the standard semiclassical result (S = A/4G) obtained for a single value of γ only. This picture was questioned recently, however [57]. At least the kinematical level of LQG suggests that γ constitutes a fixed parameter which labels physically distinct quantum theories. In this respect γ might be comparable to the Θ-parameter of QCD which, too, is absent from the classical equations of motion, but nevertheless leads to observable quan- tum effects. Contrary to the Immirzi parameter, Θ does however multiply a topological invariant which spoils the analogy to some extent.

    There is an obvious tension between this picture of a universal, constant value of γ, fixing for instance the absolute size of quantized areas of volumes, on the one hand, and the framework of RG flow equations and Asymptotic Safety on the other. Setting up a FRGE for the theory space TEC, one of the infinitely many couplings parametrizing a generic action is the Immirzi parameter. A priori it must be treated as a “running”, i. e. scale-dependent quantity γ ≡ γk; there is no obvious general principle (nonrenormalization theorem) that would forbid such a scale dependence. For this reason the renormalization behavior of the Immirzi parameter will be one of the main themes in the following.

    The purpose of the present paper is twofold: First, we are going to construct a general framework which allows the nonperturbative calculation of coarse graining flows in Einstein-Cartan gravity; ...

    1. [53] A. Ashtekar, Lectures on non-perturbative canonical gravity, World Scientific, Singapore (1991);

      A. Ashtekar and J. Lewandowski, Class. Quant. Grav. 21 (2004) R53.

    2. [54] Th. Thiemann, Modern Canonical Quantum General Relativity, Cambridge University Press, Cambridge (2007).

    3. [55] A. Perez, Class. Quant. Grav. 20 (2003) R43.

    4. [56] D. Oriti, in: Approaches to Quantum Gravity, D. Oriti (Ed.), CUP, 2009; L. Freidel, Int. J. Theor. Phys. 44 (2005) 1769.

    5. [57] E. Bianchi, arXiv:1204.5122.
  6. Dec 7, 2015 #5
    sounds interesting :) Martin Reuter should get together with Smolin, Ashketar and Rovelli to address those issues, esp immirizi parameter y=i, and how imaginary y=i might change results.
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