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Spin Foams with Matter: section 8 of Marcolli's paper, LQG/NCG roadmap, comments?

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marcus
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Jul26-10, 10:40 AM
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Quote Quote by francesca View Post
I've added it to my list, cheers! F
http://maps.google.com/maps/ms?ie=UT...e6c50e&t=h&z=0
That map is a really nice information resource, Francesca! I just updated the list of selected Lqg links here:
http://physicsforums.com/showthread....96#post2812996
and included your map.

There is also a list of LQG researchers worldwide in Wikipedia which I think may be in part your doing. Potential advisors for someone who wants to do a PhD thesis in the field.
Orbb
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Jul27-10, 11:37 AM
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What's the status in NCG concerning the Higgs mass? The last model I've seen predicted a mass around 170 GeV, which is excluded by the Tevatron. How rigid is the Higgs mass prediction in Connes' model?
marcus
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Jul27-10, 12:00 PM
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Quote Quote by Orbb View Post
What's the status in NCG concerning the Higgs mass? The last model I've seen predicted a mass around 170 GeV, which is excluded by the Tevatron. How rigid is the Higgs mass prediction in Connes' model?
This bad prediction (and some mitigating rationale) is discussed in Connes Chamseddine latest paper, that came out this year. I will get the abstract and see if I can find where they mention it.
http://arxiv.org/abs/1004.0464
Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
Ali H. Chamseddine, Alain Connes
(Submitted on 3 Apr 2010)
"We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this notation is used to determine the spectral data of the standard model. The particle spectrum with all of its symmetries is derived, almost uniquely, under the assumption of irreducibility and of dimension 6 modulo 8 for the finite space. The reduction from the natural symmetry group SU(2)xSU(2)xSU(4) to U(1)xSU(2)xSU(3) is a consequence of the hypothesis that the two layers of space-time are finite distance apart but is non-dynamical. The square of the Dirac operator, and all geometrical invariants that appear in the calculation of the heat kernel expansion are evaluated. We re-derive the leading order terms in the spectral action. The geometrical action yields unification of all fundamental interactions including gravity at very high energies. We make the following predictions: (i) The number of fermions per family is 16. (ii) The symmetry group is U(1)xSU(2)xSU(3). (iii) There are quarks and leptons in the correct representations. (iv) There is a doublet Higgs that breaks the electroweak symmetry to U(1). (v) Top quark mass of 170-175 Gev. (v) There is a right-handed neutrino with a see-saw mechanism. Moreover, the zeroth order spectral action obtained with a cut-off function is consistent with experimental data up to few percent. We discuss a number of open issues. We prepare the ground for computing higher order corrections since the predicted mass of the Higgs field is quite sensitive to the higher order corrections. We speculate on the nature of the noncommutative space at Planckian energies and the possible role of the fundamental group for the problem of generations."

The mass of the Higgs is discussed on page 33.
I think you will want to see for yourself what they say.
Orbb
#22
Jul28-10, 06:06 AM
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Thank you, marcus. I wonder why they didn't mention the sensitivity to higher-order corrections in the paper http://arxiv.org/PS_cache/hep-th/pdf/0610/0610241v1.pdf, where they first mentionned a prediction for the Higgs mass. Anyways, it will be interesting to see what Connes et al have to say and what will show up at the LHC.
sbrothy
#23
Jul28-10, 07:59 PM
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Although it is way over my little head, I think the calculation (That's their Standard Model Lagrangian right?) they perform on page 36 is the meanest looking piece of mathematics I've ever seen. :)
marcus
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Aug3-10, 10:18 PM
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This thread is about Marcolli's May paper, and I see now that I never actually copied in the abstract, to provide focus for discussion. Thanks to everyone who responded so far!

http://arxiv.org/abs/1005.1057
Spin Foams and Noncommutative Geometry
Domenic Denicola (Caltech), Matilde Marcolli (Caltech), Ahmad Zainy al-Yasry (ICTP)
48 pages, 30 figures
(Submitted on 6 May 2010)
"We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry."
marcus
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Aug3-10, 11:10 PM
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I was reminded of this paper by a post from Haelfix in the thread about what REALLY disappoints one about string theorizing.

Quote Quote by Haelfix View Post
... the landscape problem of quantum gravity (really high energy physics) is not going to go away and will be a generic problem for any approach, even if they havent studied or appreciated it yet.

String theory does better than any other current alternative on the market in this regard since it restricts what can come out of the low energy physics (the swampland).

Whereas a high energy theory of gravity that can arbitrarily couple any matter without constraints, will automatically have an (infinitely) worse landscape problem.
My question about this is can one really say with confidence that a landscape problem similar to having no selection principle amongst the 10500 string vacua MUST inevitably arise in any approach whatever?

In this particular approach, Marcolli's, can someone explain specifically how such a severe landscape problem must arise?
marcus
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Aug4-10, 09:30 AM
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Happily enough, Haelfix elaborated. And Atyy concurred. We also have an arxiv link to check out. I think the claim is interesting (any QG+matter theory would suffer from a landscape predicament), but it doesn't really fit into the "REAL string disappointment" thread, so I will copy the posts here:


Quote Quote by Haelfix View Post
I would hope that a reader would realize that what I am saying is that in fact it DOES apply broadly to any tentative theory of matter.

What we now know, which wasn't necessarily appreciated a few years ago, is that a landscape of meta stable vacua is not just a truism about KKLT in string theory, but also a *generic* property of quantum field theory (and not just supersymmetric ones) including the standard model.

That is to say, any theory (under a reasonable set of conditions like having a reasonable scalar spectrum) that wishes to include gravity, and that contains a small cosmological constant and that possesses the standard model as an effective field theory at low energies also necessarily has a large landscape of metastable vacua.

Nima, Michael Dine and a few others have convincingly shown this, and I emphasize again that it is completely independant of the nature or properties of any tentative UV completion at high energies.

See for instance arXiv:hep-th/0703067
Quote Quote by atyy View Post
In fact, Haelfix's claim is self-evidently correct.
I'm hoping someone will explain. Let's have a look at http://arxiv.org/abs/hep-th/0703067

It is possible that Haelfix has already waffled or retracted what he said, since what he now seems to be saying has been much qualified by new conditions.
The new conditions may, if examined closely, presuppose that the QG+matter theory is to be imagined in some straitjacket format not mentioned in the original claim.
marcus
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Aug4-10, 10:21 AM
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Quote Quote by tom.stoer View Post
Quote Quote by atyy View Post
In fact, Haelfix's claim is self-evidently correct.
which one? regarding the landscape issue?
Quote Quote by atyy View Post
Yes, the one about a theory of gravity which can couple to any form of matter.
I'd like to shift discussion of Haelfix generic landscape claim over to this thread so as not to distract from the original thread's focus on string.

The claim as originally stated is:
The landscape problem of quantum gravity (really high energy physics) is not going to go away and will be a generic problem for any approach, even if they havent studied or appreciated it yet.
...
[Any] high energy theory of gravity that can arbitrarily couple any matter without constraints, will automatically have an (infinitely) worse landscape problem.



BTW it should be pointed out that the string landscape problem, really I think better termed a predicament, is the absence of a selection principle and despair of finding one. It is not simply that there are a range of solutions. It is quite possible for a theory to have adjustable parameters and to come in an infinity of versions---but not to run afoul on that account, given a clear route to selecting the right version.


Haelfix offered an arxiv link---but the article does not address the main issue. It is an article from back in 2007 by Arkani-Hamed and others. It shows that the Standard Model+gravity has a range of versions (in lower dimensions than 4D) which can be easily excluded. There is no landscape problem/predicament. The article itself points out that (effective) SM+gravity has a unique 4D vacuum.
marcus
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Aug4-10, 12:45 PM
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So the question is, here is an approach to QG+M and does it necessarily face a severe landscape problem (worse than string). I'm not sure you can prove that it faces any landscape problem at all, but anyway that's the issue.

AFAIK here is the latest word on the string landscape predicament:
http://pcts.princeton.edu/pcts/bigba...m-11-21-08.pdf

There was a November 2008 mini-symposium at Princeton with a panel discussion on the landscape (Tom Banks, Nathan Seiberg, Nima Arkani-Hamed...) Peter Woit attended and we have his notes on what each of the participants said. I will quote excerpts. The different views expressed were, I think, illuminating.

==portions from http://www.math.columbia.edu/~woit/wordpress/?p=1285 ==
The Landscape at Princeton
The Princeton Center for Theoretical Science has been having a mini-symposium on the string theory Landscape, and as part of this today hosted a “panel discussion” on the topic. It turns out that there’s not a lot of support for the Landscape in Princeton.

Michael Douglas was the only real Landscape proponent in evidence. He gave a presentation on the state of Landscape studies, beginning by noting that landscapeologists keep finding more possible string vacua. Evidently the 10^500 number always quoted for the number of semi-realistic vacua is no longer operative, with latest estimates more like 10^(10^5) or higher. Douglas acknowledged that this pretty much removes any hope of making predictions by using experiment to fix this freedom and end up with non-trivial constraints...

Tom Banks began by claiming that the effective field theory picture used in the landscape is just not valid. He also pointed out that if the landscape arguments were valid, the landscape would be disconfirmed by experiment, since 10-20 of the Standard Model parameters are unconstrained by anthropics, but take unusually small values, not the random distribution one would expect. Banks takes the attitude that the CC probably has an anthropic explanation, but not particle physics or the SM parameters. He also attacked the usual claims that different vacua are all states of the same theory, arguing that they instead correspond to different theories. Finally, he pointed out that the one prediction that landscapeologists had claimed they would be able to make, the scale of SSYM breaking, hadn’t worked out at all (Douglas now acknowledges that this can’t be done).

Nati Seiberg then argued that, as one gets to deeper and deeper levels of understanding of particle physics, one might reach a level where the only explanations are environmental and have to give up. He sees no reason for that to be the case now, with the main problem that of EWSB, and nothing to indicate that anthropics has anything to do with the problem. Rather, the problem is there because we haven’t had high enough energy accelerators (the LHC should change that), and the problem is hard. He ended by saying that the appropriate response at the present time to anthropic arguments like the Landscape is to just ignore them.

The last speaker was Nima Arkani-Hamed, who I suppose was chosen as a proponent of anthropics. He didn’t live up to this, saying that he pretty much agreed with Seiberg... About the cosmological issues brought up by Douglas, his opinion is that there’s probably no point to thinking about these questions now, doing so might be like trying to come up with a theory of superconductivity in 1903. As far as EWSB goes, he believes the LHC will show us a non-anthropic explanation for its scale.

He explicitly attacked the discussion of measures that Douglas had engaged in as “not fruitful”, saying that he didn’t see any “endgame”, that it was wildly improbably that these could predict anything about particle physics... He went on to argue for the currently fashionable enterprise of studying S-matrix amplitudes, arguing that looking at the local physics embodied in Lagrangians was no longer so interesting, that instead one should be trying to understand questions where locality is not manifest.

Finally, Arkani-Hamed ended with the statement that string theory is useful as a way to study questions about quantum gravity, but “unlikely to tell us anything about particle physics”. This is an opinion that has become quite widespread among theorists, but news of this has not gotten out to the popular media, where the idea that string theory has something to do with the LHC keeps coming up.

So, all in all, I found myself in agreement with most of the speakers...
==endquote==
atyy
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Aug4-10, 01:01 PM
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Quote Quote by tom.stoer View Post
My guess is that what we call landscape problem is due to the fact that we have one great achievement in string theory, namely that it turned theories into solutions / vacua. That is nice, but it does not make all the theories go away. There seems to be not so much difference whether there is a landscape of theories or a landscape of vacua :-)
I had in mind the landscape of theories in any theory of pure gravity that can couple arbitrarily to matter. This is the "bewildering number of possibilities" Percacci mentions in http://arxiv.org/abs/0911.0386"Let us assume for a moment that this ambitious goal can be achieved, and that pure gravity can be shown to be asymptotically safe. Still, from the point of view of phenomenology, we could not be satisfied because the real world contains also dozens of matter fields ... More generally the asymptotic safety program requires that the fully interacting theory of gravity and matter has a FP with the right properties. Given the bewildering number of possibilities, in the search for such a theory one needs some guiding principle."

From a condensed matter point of view, the landscape is not a problem - since condensed matter is all about studying the landscape!
MTd2
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Aug4-10, 02:09 PM
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Quote Quote by atyy View Post
From a condensed matter point of view, the landscape is not a problem - since condensed matter is all about studying the landscape!
We, just have 1 universe to test!
marcus
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Aug4-10, 05:08 PM
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Quote Quote by atyy View Post
I had in mind the landscape of theories in any theory of pure gravity that can couple arbitrarily to matter. This is the "bewildering number of possibilities" Percacci mentions in http://arxiv.org/abs/0911.0386
"Let us assume for a moment that this ambitious goal can be achieved, and that pure gravity can be shown to be asymptotically safe. Still, from the point of view of phenomenology, we could not be satisfied because the real world contains also dozens of matter fields ... More generally the asymptotic safety program requires that the fully interacting theory of gravity and matter has a FP with the right properties. Given the bewildering number of possibilities, in the search for such a theory one needs some guiding principle."
...
But Atyy, you have not offered any evidence of a landscape problem! Your paper shows Percacci immediately applying a readily available selection principle to narrow down the (comparatively modest) range of possibilities.

He may have used the word "bewildering" at the start of the paper to highlight the challenge he is undertaking, but he does not act in any way bewildered. Nor does he desperately invoke "anthropics" as Susskind did for string in 2003. He forges right ahead and applies the Wetterich method of "effective average action" ---see the blue highlight in the quote below.

At least wait until the AsymSafe people cry "Help!" before you conclude they are in trouble. Or until you see them thrashing aimlessly around.

Many seem prone to an unfortunate tendency, whenever one hears of some snag or drawback in the string program, to project it on all the other approaches and believe (or pretend) they have it worse. Either it's not a problem, or string doesn't really have the problem, or all the other approaches have it worse.

You have probably picked up on this. I recall a couple of years back a discussion of the "no background geometry" feature where I was told seriously that LQG was not background independent and that string was much more independent than everybody else (LQG, CDT).
There is a kind of compulsion to bend the words so that it always comes out like that.

Here's the context of the Percacci passage quoted above, in case anyone is interested:

==quote Percacci 0911. ==
The original motivation for this work comes fromthe progress that has been made in recent years towards understanding the UVbehaviour of gravity. It seems that pure gravity possesses a Fixed Point (FP) with the right properties to make it asymptotically safe, or in other words nonperturbatively renormalizable [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 39] (see also [20] for reviews). Let us assume for a moment that this ambitious goal can be achieved, and that pure gravity can be shown to be asymptotically safe. Still, from the point of view of phenomenology, we could not be satisfied because the real world contains also dozens of matter fields that interact in other ways than gravitationally, and their presence affects also the quantum properties of the gravitational field, as is known since long[21].

Indeed, in a first investigation along these lines, it was shown in [22] that the presence of minimally coupled (i.e. nonself-interacting) matter fields shifts the position of the gravitational FP and the corresponding critical exponents. In some cases the FP ceases to exist, so it was suggested that this could be used to put bounds on the number of matter fields of each spin.

More generally the asymptotic safety program requires that the fully interacting theory of gravity and matter has a FP with the right properties. Given the bewildering number of possibilities, in the search for such a theory one needs some guiding principle. One possibility that naturally suggests itself is that all matter self-interactions are asymptotically free[33]. Then, asymptotic safety requires the existence of a FP where the matter couplings approach zero in the UV, while the gravitational sector remains interacting.

We will call such a FP a “Gaussian Matter FP” or GMFP. Following a time honored tradition,as a first step in this direction, scalar self interactions have been studied in [34, 35]. Here we pursue that study further. The tool that we use is the Wetterich equation, an exact renormalization group (RG) flow equation for a type of Wilsonian effective action Γk , called the “effective average action”. This functional, depending on an external energy scale k, can be formally defined by...
==endquote==
marcus
#32
Aug4-10, 06:01 PM
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So I guess there are three approaches to QG+matter that stand out, where one could ask "do they necessarily lead to intractable landscapes?"

Atyy recently posted about one, citing papers by Livine.
Essentially the approach is combined spinfoam+Feynman diagram:
http://www.physicsforums.com/showthr...99#post2809599

Approaches to QG+matter that don't seem to suffer landscape pains.

1. Spinfoam+Feynman single unified package---papers Atyy pointed to.

2. Spinfoam+NCG---this thread, there was a whole workshop devoted to this organized by Marcolli, so it is lots of people. Jesper Grimstrup was one of the early ones e.g. 2007.

3. AsymSafe QG+matter---Atyy also pointed me to this, citing a paper by Percacci, where he first acknowledges the complexity of coupling matter to QG, and then proceeds to attack it with the tools at hand. No sense that the range of variation is intractable or that one lacks principles of selection in this case.
Haelfix
#33
Aug4-10, 07:19 PM
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Marcus, I think I have wasted enough of my time on this topic for now, and will not continue the discussion.

The reason I won't continue the discussion is because it is glaringly obvious that you have no idea what we are talking about and clearly lack the correct background to even begin to have a sensible conversation about the specifics.

Unfortunately, there are a lot of specifics regarding eg moduli stabilization and AdS/CFT, and I don't expect a layman to understand everything, however I do expect some amount of civility and some intellectual integrity to admit when you are way out of your depth.

I post on these boards to try to help people learn something about physics, including bits and pieces of the cutting edge material found in modern research. I don't post on these boards to get into arguments with amateurs who obfuscate facts with a wall of text and a bunch of utter nonsense. I'll leave viewers with the following quote by the authors of the paper.

"The phenomenon that a unique action may give rise to an infinite number of vacua is not a special feature of Superstring/SUSY theories, it is also a feature of the minimal Standard Model!"
marcus
#34
Aug4-10, 07:35 PM
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Quote Quote by Haelfix View Post
"The phenomenon that a unique action may give rise to an infinite number of vacua is not a special feature of Superstring/SUSY theories, it is also a feature of the minimal Standard Model!"
However one does not see field theorists concerned with the Standard Model resorting to appeals to the Anthropic Principle.

By itself a large range or landscape does not constitute a problem. In some circumstances you can get an infinite number of solutions just by varying one parameter. String, however, has encountered a severe landscape predicament, which to many appears intractable. Your claim that any other treatment of QG+matter would necessarily meet with the same or worse predicament is unsupported by logic or evidence. I've explained this already and won't repeat here.

The 2007 paper Haelfix mentioned (I think pointlessly) is:
http://arxiv.org/abs/hep-th/0703067
in case anyone wants to check it out.
The passage quoted is on page 3, at the start of section 2:
==quote==
2. The Standard Model Landscape
We will now show that the action of the minimal Standard Model (SM) plus General Relativity (GR) has more than one distinct vacuum, actually a true landscape of vacua.
==endquote==

However, so what? the existence of extra vacua does not cause us trouble since we know how to use the SM predictively. It is a somewhat contrived "landscape" but it does not represent a landscape problem. One shouldn't have to say this.
atyy
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Aug4-10, 10:05 PM
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Quote Quote by marcus View Post
But Atyy, you have not offered any evidence of a landscape problem! Your paper shows Percacci immediately applying a readily available selection principle to narrow down the (comparatively modest) range of possibilities.

He may have used the word "bewildering" at the start of the paper to highlight the challenge he is undertaking, but he does not act in any way bewildered. Nor does he desperately invoke "anthropics" as Susskind did for string in 2003. He forges right ahead and applies the Wetterich method of "effective average action" ---see the blue highlight in the quote below.

At least wait until the AsymSafe people cry "Help!" before you conclude they are in trouble. Or until you see them thrashing aimlessly around.
I didn't say AS was in trouble. But I do imply that similarly, string theory is not in trouble.
marcus
#36
Aug5-10, 11:40 AM
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Atyy, I really like the recent post by "Surprised"! I imagine you have seen it. It is a modest frank account of string limitations which conveys a sense of integrity and leaves room for other approaches.

Too often we get misleading half-truths, obfuscation, defensiveness. There's a kind of kneejerk reaction that whatever could be wrong with the string program must be twice as wrong with the other approaches. It would be unthinkable to acknowledge a strong point in a rival program, or a weakness on one's side which doesn't equally afflict the others.

Maybe I'll copy some of "Surprised" post here so we can reflect on it conveniently without distracting from the "What I REALLY don't like..." thread. At this point it seems to me that criticising the string program is becoming more and more irrelevant. What interests me is to see how it leaves room for other approaches, and what new stuff the others bring.

Especially where there seems to be some handle on both QG and matter. It is the background independent QG+matter potential (and the cosmology potential) that seem so interesting.


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