Grav. + GUT (Gravity from a Particle Physicist's perspective)

[MTd2]

And it's up to you whether or not to take seriously or not the observation that this whole structure fits in E8. Personally, I take it seriously. Slides are up for a talk I gave at Yale:

http://www.liegroups.org/zuckerman/slides.html


Garrett

Would you mind clarifying on some of the ways to find 3 generations? There are weird things there, and those are completely alien to me!

On Page 30:

What do you mean by "E8 appears to come with a nice Axion model building kit"? Can you explain this?

I really don't understand any of this:
"E9. Possible relation to QFT.
Leech lattice. Three E8's as inner shell"

Alright, the E8 lattice is an interesting object in 8 dimensions. It offers the solution to the densest sphere packing in that dimension. Or that if you transform the elements of the reciprocity vector and map each of them into a 2-spheres in 4 dimensions, linking each of them according the the dynkin diagram prescription, (that is a 1d object in 8d into a 2d objects in 4d) you get a every where non differential manifold. Probably a fractal in 4D.

But I cannot see what it has anything to do with finding 3 generations for the standard model. At best, I could you see you arguing for the emergence of a dimensional transition in the shape of a fractal because in the case of the transition of EQG in 4D to 2D, or in the embarrassingly vague idea above, you have the theme of a non integer Hausdorff dimension.

And what's up with the Leech lattice and those inner shells? What are those inner shells?

 

[apeiron]

And the IMO most obvious connection to energy scale here is the complexity of the inference system. Clearly a more complex inference system (read higher energy scale) can do a more detailed resolution. /Fredrik

But is this not a moderately standard approach? At least this seems generally the case to me as well.

So in say the language of QM decoherence, the world as a whole is the information, an inference system at some kind of general equilibrium (ie: classical), and then QM scale is what gets resolved. So as effectively the scale of classical coherence is run down (either by cutting the distances or turning up the temperatures), the ability to resolve anything crisply runs.

I mean it take a certain weight of information to constrain things and as you shrink the scale, that weight also shrinks to the point where it starts to fail to do the job. There is an exponential approach to a failure of resolving power.

 

[Fra]

And the IMO most obvious connection to energy scale here is the complexity of the inference system. Clearly a more complex inference system (read higher energy scale) can do a more detailed resolution.

But is this not a moderately standard approach? At least this seems generally the case to me as well.

Yes, the common parts is the connection between observational resolution and energy of course.

There is also of course the holographic principle and the holographic bounds, but that principle is still not yet properly understood as far as I know. I expect this to eventually be better understood.

But what is not standard is exactly how this energy connects to the observing system, and to the complexity in particular and how that can be quantified into constraining information capacity. The notion of inference system is certainly not standard.

This is exactly the problem with QM. One considers "measurements" but without considering what measurements that are possible, and how the measurement process implies an interaction that acts not ONLY on the observed system but ALSO produces a REaction back onto the observer, that forces the measurement machinery to evolve and run, since the observer is changed. This is the missing link to a intrinsic measurement theory as I see it.

But note that this can still be described in two ways. The decoherence view is to view the observer + observer system from the outside, and then just apply the same QM. This is not solving the problem, in fact it doesn't respect the information bound of the new observer, it gets larger and larger until you have some external birds view.

It's when you insist on the internal view, that the evolution of law seems like the natural way, but it is what you in fact SEE.

The reason why I think in terms of inference system, is that it can be reconstructed from discrete information structures where evidence is simply properly counted from the inside. Then the total distinguishable event counts are then corresponding (in some way) to inertia, and mass.

This also connects inertial complexity (defined as a measure of resistance to change) and gravitational complexity (defined as a measure of how intensly it competes for degrees of freedom with other complexity systems). The "resistance to change" means that if two systems are interacting, the more complex one will generally cause larger change in the smaller system that vice versa, and in terms of space distance as a measure of difference in information, there will be a mutual effect of shrinking space in between them (ie making them attract) because their interaction brings them into general agreement since they exchange information.

/Fredrik

 

[MTd2]

Hmm, I see another reason why Garrett is so interested in this article. Basically, this paper shows a 4th way to correct the radiative divergences of the Standard Model. The other 2 are supersymmetry, little higgs and little strings. The one for Percacci uses the global symmetry of little higgs, which basically predicts extra particles for every generation of the SM.

One of the things Jacques Distler has shown to Garrett it is the appearance of spurious particles in the extra generation. So, I guess Garrett is seen that this extra particles are actually sinks to the Fixed point for every generation.

 

[marcus]

MTd2, it's encouraging to see you pursue the possibility of a connection with E8 theory, which Garrett hinted at earlier. All we can do is keep our eyes open and persist in asking questions.

Today we got some help, in seeing the overall picture (the "GraviGUT" idea of putting QFT on an asymsafe basis, from a new Percacci posting. I will excerpt the conclusions:
==quote today's Percacci paper, conclusions==

Another direction for research is the inclusion of other matter fields. As discussed in the introduction, if asymptotic safety is indeed the answer to the UV issues of quantum field theory, then it will not be enough to establish asymptotic safety of gravity: one will have to establish asymptotic safety for a theory including gravity as well as all the fields that occur in the standard model, and perhaps even other ones that have not yet been discovered. Ideally one would like to have a unified theory of all interactions including gravity, perhaps a GraviGUT along the lines of [45]. More humbly one could start by studying the effect of gravity on the interactions of the standard model or GUTs.

Fortunately, for some important parts of the standard model it is already known that an UV Gaussian FP exists, so the question is whether the coupling to gravity, or some other mechanism, can cure the bad behavior of QED and of the Higgs sector. That this might happen had been speculated long ago [33]; see also [46] for some detailed calculations.

It seems that the existence of a GMFP for all matter interactions would be the simplest solution to this issue. In this picture of asymptotic safety, gravity would be the only effective interaction at sufficiently high scale. The possibility of asymptotic safety in a nonlinearly realized scalar sector has been discussed in [47]. Aside from scalar tensor theories, the effect of gravity has been studied in [48] for gauge couplings and [49] for Yukawa couplings.

==endquote==

http://arxiv.org/abs/0911.0386
Renormalization Group Flow in Scalar-Tensor Theories. I
Gaurav Narain, Roberto Percacci
18 pages, 10 figures

 

[MTd2]

Not only Garrett's E8 theory. E8 gauge theory is also the core of string theory, in fact, of a non supersymmetric theory in 12 dimensions which becomes superstring at low energies. And also, it is a core in the concept of exotic smoothness. Maybe if superstring are complicated epicycles, the picture should become really easier by a shift of frame to something in which fields or particle content are related by E8, like changing the frame of reference to the Sun.

Coincidentally, there is a paper today showing the relation between 4 and 12 dimensions due E8. It is not explicit, but you can see that this is the case because he cites Moore a several times, which is the one responsible for that E8 gauge theory.

http://arxiv.org/abs/0911.0271

Gerbes on orbifolds and exotic smooth R^4

Torsten Asselmeyer-Maluga, Jerzy Król
(Submitted on 2 Nov 2009)
By using the relation between foliations and exotic R^4, orbifold $K$-theory deformed by a gerbe can be interpreted as coming from the change in the smoothness of R^4. We give various interpretations of integral 3-rd cohomology classes on S^3 and discuss the difference between large and small exotic R^4. Then we show that $K$-theories deformed by gerbes of the Leray orbifold of S^3 are in one-to-one correspondence with some exotic smooth R^4's. The equivalence can be understood in the sense that stable isomorphisms classes of bundle gerbes on S^3, the boundary of the Akbulut cork, correspond uniquely to these exotic R^4's. Given the orbifold $SU(2)\times SU(2)\rightrightarrows SU(2)$ where SU(2) acts on itself by conjugation, the deformations of the equivariant $K$-theory on this orbifold by the elements of $H_{SU(2)}^{3}(SU(2),\mathbb{Z})$, correspond to the changes of suitable exotic smooth structures on R^4.

Read this article with attention, because I bet this is what will make all different approaches join.

I don't know. Sounds like E8 is something that is linked or is the core of all geometry.

 

[marcus]

In the Steven Weinberg asymptotic safety thread the question came up
https://www.physicsforums.com/showthread.php?p=2452268#post2452268
what is the relation of this to Percacci's recent asymptotic safety papers that include matter?

It boils down to the truism that making predictions is what counts, and is the ultimate test of the asymsafe approach to QG+matter. In this case the predictions are likely to be in the area of cosmology: to be checked by astronomical observation. (That's why Weinberg seems so on target. He is going right at the cosmology application of the approach, where the predictions are most likely to be found, without bothering with anything else.)

I should get some Percacci links handy for the Weinberg thread, so we can look at both and see what if any connection.

http://arxiv.org/abs/0910.5167
Gravity from a Particle Physicist's perspective
R. Percacci
Lectures given at the Fifth International School on Field Theory and Gravitation, Cuiaba, Brazil April 20-24 2009. To appear in Proceedings of Science
(Submitted on 27 Oct 2009)

http://arxiv.org/abs/0911.0386
Renormalization Group Flow in Scalar-Tensor Theories. I
Gaurav Narain, Roberto Percacci
18 pages, 10 figures

 

[marcus]

So where are we in terms of the renormalization of gravity+matter?

We have two threads:
one aimed at discussing Weinberg's recent paper explaining inflation by the running of G and Lambda, back from the UV fixed point. An important feature here is to place renormalization gravity into a cosmology context, where one has observations of the early universe to use for testing predictions.

and the other, this thread, is about Percacci's effort to work gauge theory of matter (e.g. standard model ingredients) in together with renormalization gravity. I suppose this could also lead to predictions that could be tested---for instance at LHC---but is still in early stages.

We just had that Asymptotic Safety conference in early November 2009. Percacci was the organizer. Weinberg was the lead speaker. We can learn a lot just by focusing on what those two have to say, as representative of the whole asymsafe gravity+matter crowd.
However, everybody's conference talk is available as video online.

I'd be happy if anyone here wants to summarize the state of things, as you see it. I'll try to do so myself later on today.
The links to Percacci's recent papers are in the preceding post.
He also has a "Asymptotic Safety FAQ" at his website, and a bibliography.
http://www.percacci.it/roberto/physics/as/faq.html

Here is Garrett's comment on Percacci's gravity+matter unification idea, the topic we started with:

Hello PF folk.

If you believe the Dirac equation in curved spacetime, and you believe Spin(10) grand unification, then a Spin(3,11) GraviGUT, acting on one generation of fermions as a 64 spinor, seems... inevitable.

Also, it's pretty.

And it's up to you whether or not to take seriously or not the observation that this whole structure fits in E8. Personally, I take it seriously. Slides are up for a talk I gave at Yale:

http://www.liegroups.org/zuckerman/slides.htmlGarrett

What I get from reading Percacci's two latest papers is not so clear, nor so technically specific. I see Percacci building on the quantum spacetime geometry he gets from asymsafe QG. Trying to build a version of standard model matter on it.

It means that not only do the geometric constants (G and Lambda) run---so do (at least a subset of) the matter couplings.

See what you think of this excerpt from the Narain-Percacci paper I gave link to a couple of posts back:

==quote Narain Percacci 0911.0386==
The original motivation for this work comes from the progress that has been made in recent years towards understanding the UV behaviour 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. non self-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 'GaussianMatter FP' or GMFP.
==endquote==

 

[marcus]

Here is how Weinberg sums up the present situation in the Asymptotic Safe QG program and its application to cosmology, as a way to explain inflation.
==quote Weinberg==
Decades ago it was suggested that the effective quantum field theory of gravitation and matter might be be asymptotically safe¹, and hence ultraviolet-complete. That is, the renormalization group flows might have a fixed point, with a finite dimensional ultraviolet critical surface of trajectories attracted to the fixed point at short distances.

Evidence for a fixed point in the quantum theory of gravitation with or without matter has gradually accumulated through the use of dimensional continuation², the large N approximation³ (where N is the number of matter fields), lattice methods⁴, the truncated exact renormalization group⁵, and a version of perturbation theory⁶.

Recently there has also been evidence that the ultraviolet critical surface is finite-dimensional; it has been found that even in truncations of the exact renormalization group equations with more than three (and up to nine) independent coupling parameters, the ultraviolet critical surface is just three-dimensional⁷. The condition that physical parameters lie on the ultraviolet critical surface is analogous to the condition of renormalizability in the Standard Model, and like that condition yields a theory with a finite number of free parameters.

The natural arena for applications of the idea of asymptotic safety is the physics of very short distances, and in particular the early universe. In Section II we show how to formulate the differential equations for the scale factor in a Robertson–Walker solution of the classical field equations in a completely general generally covariant theory of gravitation. ...Section IV...explores the circumstances under which it is possible to have an exponential expansion that persists for a long time but eventually comes to an end.

We will work with a completely general generally covariant theory of gravitation. (For simplicity matter will be ignored here, but its inclusion would make no important difference.)
==endquote==
Weinberg's references are to publications by the following authors:
1. Weinberg
2. Weinberg; Kawai Kitazawa Ninomiya; Aida Kitazawa; Niedermaier
3. Smolin; Percacci
4. Ambjorn Jurkiewicz Loll
5. Reuter; Reuter; Dou Percacci; Souma; Lauscher Reuter; Reuter Saueressig; Lauscher Reuter; Reuter Saueressig; Percacci Perini; Perini; Litim; Codello Percacci; Codello Percacci Rahmede; Reuter Saueressig; Machado Saueressig; Codello Percacci, Rahmede; Codello Percacci; Litim; Gies Scherer; Benedetti Machado Saueressig; Reuter Weyer; Reuter Saueressig.
6. Niedermaier
7. Codello Percacci Rahmede; Benedetti Machado Saueressig.

http://arxiv.org/abs/0911.3165
Asymptotically Safe Inflation
Steven Weinberg
13 pages
(Submitted on 16 Nov 2009)
"Inflation is studied in the context of asymptotically safe theories of gravitation. It is found to be possible under several circumstances to have a long period of nearly exponential expansion that eventually comes to an end."

 

[marcus]

Jacques Distler has posted an attack on Percacci's GraviGUT idea (the original topic of this thread).
http://golem.ph.utexas.edu/~distler/blog/archives/002140.html

In the blog post, rational content is mixed in with some emotive rhetoric---contemptuous dismissal.
But the objective content could be useful. I hope someone can check it out and comment on what Distler actually says (not merely what he "sounds like" he's saying.)

I see Percacci's proposal as a work in progress that is part of a broad movement---towards minimalist no-frills predictive attempts at unification. Part of the stimulus for the movement is recent appearance of encouraging asymptotic safety results. Part is a reaction against overly elaborate Baroque fantasies involving novel degrees of freedom. What several bunches of researchers are trying to do is see if the standard particles plus gravity can be combined without introducing new entities (new degrees of freedom) and without imagining new structure (or with very few new descriptors and very little new structure) to give a theory that is finite and predictive out to Planck scale.

Renate Loll, Steven Weinberg, and Hermann Nicolai have all spoken out on the theme of this minimalist unification movement. Percacci's work is part of this. I think it is usually a positive sign when Distler gets worked up enough to attack something---showing that he recognizes some type of threat---if only a threat to what remains of string prestige. But sometimes his criticisms can also be useful at the level of detail and hopefully that will turn out to be the case here.

 

[Haelfix]

Umm, an Spin(3,11) * 3 theory is about as nonminimal as you can get, by any definition of the word used by particle physicists. This is a very large, noncompact gauge group! Anyway, their is a preponderance of new degrees of freedom at high energies, and the fields are not by construction in the same representation as usually insisted upon by model builders..

Anyway this theory is in such an early form, that its hard to really know what to think. About a million things could go wrong phenomenologically, including but far from limited to the ghost modes that Jacques and Percacci mentioned. But again a the very basic level, many of the same criticisms that applied to Lisi's theory, also apply here. Coleman-Mandula violation, completely unspecified Higgs sector (in general in GUT theories, they often carry very large and cumbersome representations.. In this case here they are somewhat adhoc and inserted by hand and will likely need to be multiple breaking steps. Further a bosonic sector that is a complete mess).

 

[marcus]

I have to agree that Percacci's proposal doesn't look lean and mean enough. It doesn't quite fit the pattern AFAICS.
I guess I would pick Steven Weinberg, Hermann Nicolai, and Mikhail Shaposhnikov as the three most representative
minimalists.

Maybe in time Percacci will come out with some more Spartan unification scheme.
This is not to say that in the long run more austere approaches will prove to be on the right track, just that right now there seems to be a strong drive to get simple, and to get predictive. Wrong or right, make it tight---so that it says something testable.

 

[Haelfix]

The point is its extremely hard. The paper was designed to satisfy the chirality bounds that Lisi's proposal crashed into, as well as gauging gravity. He lists about 3 or 4 other large groups that don't suffer from this issue, but there are others, that are even larger.

Already at the level of GUT theories, the simplest models don't work. SU(5) and SO(10) *where by that we mean a single breaking stage* miss various proton decay bounds, and we need SuSY to help us there. But then if you make your group too big you start running into the aforementioned chirality problems, as well as hideously large representations, flavor changing neutral currents all over the place, doublet triplet splitting, possible cosmological issues (domain wall and monopole abundances) and so forth.

Generically the feeling is that while a simple GUT (say SuSY SO(10) or E6) probably works as an effective theory at some scale, gravity is a whole other bag of potatoes and something else is necessary to describe the physics there.

 

[MTd2]

Asymptotic Safety displays fractional dimensions, which is characteristic of theories that uses quantum groups. See Dario Benedetti:

http://arxiv.org/abs/0811.1396

Notice that the symmetries of quantum group allows bypass the limitation of Coleman Mandula:

"Quantum group symmetry, present in some two-dimensional integrable quantum field theories like the sine-Gordon model, exploits a similar loophole."

http://en.wikipedia.org/wiki/Coleman–Mandula_theorem

Maybe this is also the case here.

 

[MTd2]

Does guess Weinberg has a better trackback than Distler? I mean, I guess I can trust him.

 

[marcus]

Does guess Weinberg has a better trackback than Distler? I mean, I guess I can trust him.

In my opinion you can't trust anyone's guess about the future. But people have "track records". We remember how their guesses have turned out in the past. Did they choose fruitful problems to work on? Did they eventually see the right approach? Did they give good overviews and good advice?

I think "trackback" means something else and I could be misunderstanding your question.
But it certainly makes sense to ask about Weinberg's track record.

He was one of the first to envision the Standard Model. Then he wrote the book about Quantum Field theory. And then he had the insight to realize that in some sense the future of physics was as much in early-universe cosmology as in colliders. That astrophysical observation was as potentially important as particle experiments on the ground. So after his QFT book he wrote his Cosmology book.
Other people think he has a pretty good track record because they ask him to give the keynote opening talk at their conferences---and stuff like that. The guy has real stature.

People rely on him for vision. He combines remarkable insight with long experience.

I don't know anything especially good about Distler. Don't know any particular reason to trust his hunches. He attacks things. And some of the things he attacks continue growing and go on gaining interest and attention in the community. While other things that he attacks decline or change. It's hard to know if Distler's attack had anything to do with it, either way. Some people may think of him as an oracle Could be differences of opinion about this.

 

[atyy]

Meissner and Nicolai are not about unification per se. Their work is inspired by string theory as a unification ansatz.

 

[atyy]

I do not believe in vision. Smolin believes in vision, and it's a theme in his popular books. So the topic is fun! Let us recall that Weinberg was a very early supporter of string theory.

 

[atyy]

And while we're on the topic, let us note how wrong Smolin and Rovelli are - string theory and asymptotic safety are both particle physicist approaches. Yaay!

 

[marcus]

Meissner and Nicolai are not about unification per se...

I suppose that depends on what one means by unification, Atyy. I'm thinking of how Nicolai presented their work around July 1 in that video lecture. He talked about why QFT and gravity needed to be joined in a single framework. He said their approach was the opposite of two stringy approaches. Once he contrasted it with string phenomenology (which he said was becoming "increasingly Baroque") and later in the talk he said their approach was the antithesis of "F-theory". He listed these significant characteristics:

no GUT (no GUT scale prior to Planck scale)
no low energy SUSY
no extra dimensions.

Several times he emphasized the assumption of "no new physics between the electroweak scale and Planck scale", which I guess goes along with those three listed characteristics.

So what can we make of this? Maybe you are right and the word unification should not be used! What would you suggest as an alternative terminology?

Would you like to call M&N's a "string-inspired effective TOE"?

To me that doesn't describe it well. The theme that Nicolai repeated most often, and in the most variety is that the intent is minimalist. He referred to it as "Spartan" and "economical" and "austere" as well as "minimal".

If we accept his view of his own work and call it "minimalist" then the question is a minimalist what?

You don't like calling it minimalist unification. What about a minimalist Theory of Nature?

I guess we all realize that particle theory and gravity are closely interlocked in Meissner Nicolai Theory of Nature. But the interdependence between matter fields and geometry may not be what is conventionally imagined to be unification, in which case we should avoid calling it that. (I'm not sure about this but I'd like to know your suggestions and I'll think some about it on my own.)

 

[atyy]

Ha, ha, I don't know what to call it. Minimalist seems fine with me. I guess Meissner and Nicolai are really saying, well, we don't need a theory of gravity until the Planck scale. At that scale, maybe it's string theory or something. So we present a theory which is consistent with those (hopefully), but which is as minimalist as possible until then.

My grouping:

1) UV gravity requires new degrees of freedom

- string theory, which subdivides based on low energy proposals
--- GUT inspired F-theory (Vafa et al, Wijnholt et al)
--- No GUT (Meissner and Nicolai)

- others which don't work (yet?) but are terribly cute (Volovik, Wen, Horava; also it's too early to say, but I hope GFT will fall here)

2) UV gravity does not require new degrees of freedom, ie. Asymptotic Safety. Here to make predictions, maybe we need a definite theory of matter, so the subclassification depends on the theory of matter

- matter is asymptotically free, and matter degrees of freedom beyond the SM are needed (Percacci)

- matter is asymptotically safe, but not necessarily asymptotically free, and matter degrees of freedom beyond the SM ar not needed (not sure about this, but I think I'd put Shaposhnikov and Wetterich here, also Scherer et al)

- matter is asymptotically free, and matter degrees of freedom beyond the SM are not needed (ruled out by Landau poles)

- matter is asymptotically safe, but not necessarily asymptotically free, and matter degress of freedom beyond the SM are needed (Percacci's Asymptotic Safety landscape nightmare)

- no definite theory of matter needed, generic (universal?) asymptotic safety of gravity effects (again not sure about this, but I think I'd put Weinberg here, also Niedermaier and Reuter's Living Reviews perspective)