Does Loop quantum gravity have an effective UV fixed point?

[kodama]

loop quantum gravity and loop quantum cosmology gravity becomes weaker then repulsive instead of stronger, towards the Planck regime, due to the onset of quantum effects. gravity near Planck energies and densities, LQG/LQC becomes repulsive.

at the inflection point where LQG gravity strength is exactly balanced by repulsion, so the sum is zero, is this an effective UV fixed point?

 

[marcus]

...
at the inflection point where LQG gravity strength is exactly balanced by repulsion, so the sum is zero, is this an effective UV fixed point?

You might want to clarify. I, for one, don't understand in a concrete way what it would mean. Isn't a "UV fixed point" something defined in a Wilsonian renormalization context? There is a multidimensional space of possible values of the coupling constants, and the the couplings RUN towards a fixed point, as energy increases.

In Loop gravity there is no comparable structure. The constants do not run. When they run computer simulations of collapse they get a bounce but G and Λ do not change. The important constants do not "run" as the energy density increases. So this is not "UV fixed point" behavior at all! There is no physical connection with the Wilsonian renormalization picture you get in AsymSafe QG. No analogy.

So in Loop, you measure G and Λ in the usual way, and you stick with the standard handbook values. And you use ordinary G to calculate the critical energy density at which the bounce occurs. And it occurs by an entirely different mechanism from a "UV fixed point".

At least that is as far as I can see. this is with the present-day versions of LQG, e.g. spin foam, and LQC---to connect with AsymSafe QG you would probably have to treat ASQG as an effective theory that arises from some more fundamental theory akin to LQG. So you might be able to show how LQG causes the key coupling constants (in a Wilsonian context) to appear to "run" towards a UV fixed point.
this is something that needs explanation. It is just taken ad hoc by the AsymSafeQG researchers. So I imagine there might be a conceptual bridge joining LQG and ASQG but it would probably involve formulating a theoretical foundation for ASQG. Just my guess.

 

[kodama]

the strong force in QCD becomes weaker at shorter distances.

gravity in LQG becomes weaker at shorter distances in Planck regime then repulsive, its strength goes to zero then becomes repulsive due to quantum mechanical effects.

gravity then in LQG behaviors similarly to strong force in QCD.

 

[marcus]

But that is just a vague analogy, Kodama. Where are the coupling constants that "run" to a UV fixed point? that's my point.
AFAICS you don't yet have the quantitative machinery to begin to talk about a "UV fixed point".

So far, in LQG and LQC, Newton's G and Einstein's cosmological curvature constant Λ both do not "run". They remain constant all through the bounce.
A lot of computer simulations have been done, trying out different initial conditions and assumptions. AFAIK they all keep the two constants constant, so none of them have a "UV fixed point" and they all obtain a bounce---it is a robust feature.

 

[kodama]

what i meant by an effective UV fixed point is that gravity in LQG gets weaker at Planckian energies and densities, not stronger. specific details do not matter.

 

[Vladimir Nachev]

As mentioned gravity's weakening force are you all so sure that the gravitational forces of even planets do completely go to zero after a length of let's name it delta X (sorry for going into astrophysics) I mean that my theory is that all gravitational sources are afecting each other more or less everywhere in the Universe for example even Pluto may affect with a tiny bit Belthelgeise's axis, axial rotation speed and even its direction and linear speed :) cheers for not laughing at me at the beginning

 

[atyy]

As I understand it, the question of whether there is a "UV fixed point" in LQG is phrased in the following way: Does the limit that is assumed just before Eq 3 of http://arxiv.org/abs/1010.5437 exist?

There is a bit more discussion of this and the relationship to the "UV fixed point" in http://arxiv.org/abs/1205.2019, section 14.10 about discertization dependence, where Perez says "It has been often emphasized that such refinement limit may be studied from the Wilsonian renormalization view point."

 

[kodama]

As I understand it, the question of whether there is a "UV fixed point" in LQG is phrased in the following way: Does the limit that is assumed just before Eq 3 of http://arxiv.org/abs/1010.5437 exist?

There is a bit more discussion of this and the relationship to the "UV fixed point" in http://arxiv.org/abs/1205.2019, section 14.10 about discertization dependence, where Perez says "It has been often emphasized that such refinement limit may be studied from the Wilsonian renormalization view point."

I guess the way i should phrase it is that QCD becomes weaker at shorter distances due to asymtoptic safety. Gravity in LQG gets weaker then repulsive in the shorter distances of the Planck scale, so could this also be described as asymptotic safe? the exact details may differ from what is usually meant by the term

 

[marcus]

I guess the way i should phrase it is that QCD becomes weaker at shorter distances due to asymtoptic safety. Gravity in LQG gets weaker then repulsive in the shorter distances of the Planck scale, so could this also be described as asymptotic safe? the exact details may differ from what is usually meant by the term

asymptotic freedom ≠ asymptotic safety

Asymptotic freedom is the essential property of QCD.

 

[kodama]

asymptotic freedom ≠ asymptotic safety

Asymptotic freedom is the essential property of QCD.

thanks.
Asymptotic freedom is the essential property of of LQC - correct?

 

[marcus]

We are using words differently so there is a risk of talking at cross purposes. As you said in post#8 " the exact details may differ from what is usually meant by the term".
To me the details when you talk about "UV fixed point" are all important. You have to have a Wilsonian renormalization setup, you have to specify a definite number that e.g. goes zero , or to some non-zero limit as k→∞.
If you are talking "UV fixed point" then I think you can't just say "gravity gets weaker and then stronger" without specifying what number you are talking about and calling "gravity". That's talking intuitively OK, but too loosely for that context.

I think it might be possible to re-formulate something akin to spinfoam QG so that there is defined a number k, and some there is defined a definite quantity that goes to zero or some other limit as k→∞. But that would involve creative work that, as far as I know, has not been done.

Apparently there was talk of that back in 2002-2004 but AFAIK it never went anywhere. I don't know any currently central person in LQG research who has written any paper in the last 5 or even 10 years in which any version of LQG actually has running coupling constant or is "asymptotically safe" in the usual sense of the word, or has a "UV fixed point" in the way that AsymSafe QG does.

 

[kodama]

We are using words differently so there is a risk of talking at cross purposes. As you said in post#8 " the exact details may differ from what is usually meant by the term".
To me the details when you talk about "UV fixed point" are all important. You have to have a Wilsonian renormalization setup, you have to specify a definite number that e.g. goes zero , or to some non-zero limit as k→∞.
If you are talking "UV fixed point" then I think you can't just say "gravity gets weaker and then stronger" without specifying what number you are talking about and calling "gravity". That's talking intuitively OK, but too loosely for that context.

I think it might be possible to re-formulate something akin to spinfoam QG so that there is defined a number k, and some there is defined a definite quantity that goes to zero or some other limit as k→∞. But that would involve creative work that, as far as I know, has not been done.

Apparently there was talk of that back in 2002-2004 but AFAIK it never went anywhere. I don't know any currently central person in LQG research who has written any paper in the last 5 or even 10 years in which any version of LQG actually has running coupling constant or is "asymptotically safe" in the usual sense of the word, or has a "UV fixed point" in the way that AsymSafe QG does.

thanks for this insightful discussion.

LQC/LQG as it is currently understood has Asymptotic freedom for gravity. gravity gets weaker and then repulsive at Planckian distances. worth considering if other QG theories like strings also have Asymptotic freedom for gravity

 

[atyy]

thanks for this insightful discussion.

LQC/LQG as it is currently understood has Asymptotic freedom for gravity. gravity gets weaker and then repulsive at Planckian distances. worth considering if other QG theories like strings also have Asymptotic freedom for gravity

Strings does not have asymptotic safety for gravity. Rather, gravity is not a fundamental force in string theory.

 

[marcus]

Strings does not have asymptotic safety for gravity. Rather, gravity is not a fundamental force in string theory.

Good line of reasoning! Neither is gravity a fundamental force in the LQC/LQG context! When one says "gravity gets weaker at extreme energy densities" one is talking at a verbal intuitive level, not a quantitative mathematical level. One is intuitively describing the relation between matter and geometry in LQG and how it behaves at high energy concentrations.

Maybe this will help get us on the same page and help Kodama accept that one should not use terms unqualified like "UV fixed point" or "asymptotic safety" in connection with LQG because they are normally understood to have a technical quantitative meaning which does not apply to any version of LQG now actively researched, that I know of. You need well-defined running coupling constants. (how the fundamental "force" you mentioned can be defined : ^))

It can be misleading and confusing to people to use technical terms as vague, purely verbal, analogies--without the normally expected math/quantitative ground

 

[kodama]

if gravity is not a fundamental force in strings/ lqg what is the correct term ?

 

[marcus]

if gravity is not a fundamental force in strings/ lqg what is the correct term ?

Atyy made the point in post #13, so he has priority in answering. I'll wait for him. But to anticipate a bit: gravity is not a force in GR. It can be eliminated by a simple coordinate transformation. This is the famous "equivalence principle" Einstein made basic to General Relativity.

Since it is not a force, in GR, and GR is our currently prevailing theory of gravity, I would say, for the correct term, that "gravity is geometry". I think Atyy would agree, if not I retract since the question is really to him. A theory of gravity is therefore a mathematical description of how geometry and matter interact.

Since gravity is not a force, in GR, and LQG is a quantum theory following the conceptual lead of GR, obviously gravity would not appear as a force in LQG. There is no mathematical object representing the "force of gravity" in any version of LQG that I can remember.

what does appear in LQG is geometry (quantized) and one can speak intuitively (on a purely verbal level) about gravity attracting or repelling when what one is really talking about is how matter and geometry interact--roughly speaking *waves hands*: is the geometry expanding or contracting where matter/energy is concentrated?

I should be quiet and let Atyy respond. I'm interested to know what he had in mind in post#13.

 

[kodama]

I wonder what the implications to the Higgs hiearchy problem is with LQG view of gravity if there is no GUT

 

[kodama]

this paper seems to try to do this

On selfdual spin-connections and Asymptotic Safety
Ulrich Harst, Martin Reuter
(Submitted on 30 Sep 2015)
We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG) equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-)selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein-Cartan gravity without the selfduality condition.
Comments: 14 pages, 4 fgures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1016%2Fj%252Ephysletb%252E2015%252E12%252E016&v=4b0bf9d3
Cite as: arXiv:1509.09122 [hep-th]
(or arXiv:1509.09122v1 [hep-th] for this versio

 

[marcus]

Reference [4] of the Harst-Reuter paper is to arXiv:1408.4336.
It's a comparative review paper by Ashtekar, Reuter, Rovelli (three of the principal QG researchers) which I think is very good at sketching the possible relationships between Asymptotic Safety and LQG. AS is discussed first and then the discussion of Spin Foam LQG begins on page 23.

http://arxiv.org/abs/1408.4336
From General Relativity to Quantum Gravity
Abhay Ashtekar, Martin Reuter, Carlo Rovelli
(Submitted on 19 Aug 2014)
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades.
54 pages. To appear in General Relativity and Gravitation: A Centennial Survey, commissioned by the International Society for General Relativity and Gravitation and to be published by Cambridge University Press. Abhay Ashtekar served as the `coordinating author' and combined the three contributions.
.

 

[kodama]

Reference [4] of the Harst-Reuter paper is to arXiv:1408.4336.
It's a comparative review paper by Ashtekar, Reuter, Rovelli (three of the principal QG researchers) which I think is very good at sketching the possible relationships between Asymptotic Safety and LQG. AS is discussed first and then the discussion of Spin Foam LQG begins on page 23.

http://arxiv.org/abs/1408.4336
From General Relativity to Quantum Gravity
Abhay Ashtekar, Martin Reuter, Carlo Rovelli
(Submitted on 19 Aug 2014)
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades.
54 pages. To appear in General Relativity and Gravitation: A Centennial Survey, commissioned by the International Society for General Relativity and Gravitation and to be published by Cambridge University Press. Abhay Ashtekar served as the `coordinating author' and combined the three contributions.
.

self-dual LQG implies immiriz is i. reuters suggets it is also As Safe