Garrett's article in SciAm December issue

[garrett]

Hey Kids,
Thanks for making note of this Scientific American article here on Physics Forums. Looking through the comments...

Does anyone have a link to an online version?

Unfortunately, SciAm does not make these articles available for free -- one has to pay five dollars or so to download the pdf, or pick up the magazine. I suppose magazine editors do need to eat. However, Jim and I did negotiate to be able to put our own version of this article on the arxiv in a few months, which we will do.

Garrett Lisi gave a talk with the same title of this paper last month. The slides are available on his website. Probably, there is nothing new and this is just about his latest paper...

This is true of the technical material. But much of the popular material has been updated, especially the weight diagrams for various theories. These diagrams, such as for the electroweak model and for GUTs, are really cool, and I'm excited to see them in SciAm. Also, we've done the best we could describing the geometry of Lie groups, fiber bundles, and unification in a way that's precise but accessible.

Yeah, unfortunately it's ptrobably not anti-string enough.

I tried to avoid string theory -- the point of the article was to lay out an alternative unification effort.

Everyone loves the underdog! But I cannot understand anymore why this thing with Garrett. He is not an underdog anymore thinking proportionally to the level of attention that his theory gets

This is somewhat true. But I was an underdog.

I really don't think this is a case of bad physics but of over publicity. His model is OK with 1 generation and it is up to him to fix that and he pointed several ways to try to fix that. He hasn't published on these alternatives. But the problem it is that, despite of being an embryonic state, the theory is still being called by himself a TOE!

This is also true, and I have personally always tried to make it clear that this is just a prospective and developing ToE, not a completed one. Unfortunately, it's editors that get to choose article titles.

It works for one generation, really? So he has finally learned of the difference between fermions and bosons? And how exactly does renormalization work in his theory?

I will answer this even though it's a troll. Yes, it works for one generation, as described explicitly here: http://arxiv.org/abs/1006.4908
I expect renormalization to work similarly to how it works in Y-M QFT, including asymptotic safety for gravity. I see that MTd2 has answered as well.

Actually everyone in the field knows that this model is wrong on several counts and beyond repair, conceptually and technically.

It is true that most people in the field think this, largely thanks to the effort of Distler and Motl. The "several counts" that I recall were:
1) Impossible mixing of bosons and fermions.
This was agreed on by mathematicians to be possible, such as here: http://golem.ph.utexas.edu/category/2008/05/e8_quillen_superconnection.html
2) Violation of the Coleman-Mandula theorem.
The relevant novel loophole in the theorem was described here: http://arxiv.org/abs/0803.0303
3) Even one generation of fermions does not fit in E8.
This misconception, introduced by Distler and Garibaldi, is directly addressed and cleared up here: http://arxiv.org/abs/1006.4908
It was one of the more enjoyable experiences of my life to see Skip go down in flames over this issue in Banff. What counts remain that say the theory is wrong? That mirror fermions have almost been ruled out by experiment? Is it just me, or does that seem not the same as "E8 Theory can't work"?
4) The theory does not accommodate three generations of fermions.
This issue was identified (by me) as a problem from the beginning, with a potential solution coming from triality. I had lost hope in the theory myself a bit over this issue a year ago, but with some insights gained at Banff I now think triality will indeed work. It's tricky though, and I'm working on that now.

The question is, can Lisi's theory perhaps be 'made to make sense' in a similar way? There's a good possibility that it can't, but that doesn't necessarily mean that one should discard the whole direction of research on that possibility alone. Obviously, there are certain people willing to invest time and resources into following what to them at least seem to be promising hints of something that could be connected to physical reality within E₈, just as there once were some people willing to investigate the forbidding structures of strings on the basis of its promise despite its problems, and that's entirely their call to make -- nobody's forcing you to go along with it, or even constrain your criticism in any way.

This comment from Daedalus is insightful enough that it bares repeating, and I agree completely.
-Garrett

 

[atyy]

Hey Garrett, sorry for my comment. It wasn't aimed at you, though it did come out this way.

 

[marcus]

Congratulations on both the events at Banff and SciAm article!

 

[arivero]

4) The theory does not accommodate three generations of fermions.
This issue was identified (by me) as a problem from the beginning, with a potential solution coming from triality.

If triality fails you, look for some SU(5). It is possible to build three generations into SU(5), the 5x5bar produces a 24, and the 5 x 5 + 5bar x 5bar produces a 15 + 15bar. You fit all the leptons in the 24, and all the quarks of a given colour in the other (yep, that is a 12 + 12 bar; no idea what to do about the other three of the 15.).

 

[Kevin_Axion]

Awesome work garrett! I found it quite odd that Garibaldi and Distler would try to deform your idea since people usually do this when they find that funding isn't being used effectively. Keep on working, E8 is very beautiful and I wouldn't be surprised if your work has something deeper to say about the Universe.

 

[MTd2]

If triality fails you, look for some SU(5).

This is the method attempted by Distler. It doesn`t work since E8 is just too small when you try to put gravity together.

 

[smoit]

3) Even one generation of fermions does not fit in E8.
This misconception, introduced by Distler and Garibaldi, is directly addressed and cleared up here: http://arxiv.org/abs/1006.4908
It was one of the more enjoyable experiences of my life to see Skip go down in flames over this issue in Banff. What counts remain that say the theory is wrong? That mirror fermions have almost been ruled out by experiment? Is it just me, or does that seem not the same as "E8 Theory can't work"?

FYI, here is Garrett's "addressing and clearing up the issue" from page 12 in http://arxiv.org/abs/1006.4908:

"In their work, Distler and Garibaldi prove that, using a direct decomposition of E8,
when one embeds gravity and the Standard Model in E8, there
are also mirror fermions. They then claim this prediction of mirror fermions (the
existence of “non-chiral matter”) makes E8 Theory unviable. However, since there
is currently no good explanation for why any fermions have the masses they do, it
is overly presumptuous to proclaim the failure of E8 unification – since the detailed
mechanism behind particle masses is unknown, and mirror fermions with large
masses could exist in nature."

 

[MTd2]

"smoit" is a nickname that Susskind and more recently LM use to refer to crackpots.

http://www.math.columbia.edu/~woit/wordpress/?p=593

notice that the member above has 1 post at the moment of this message.

 

[Spinnor]

...
They still have an occasional article with real educational value, like Charley Lineweaver's Misconceptions about the Big Bang. It's absolutely essential, hard-nose, zero-fantasy, straight dope about cosmology. No Brian Greene literary analogies---just knocks off popular misconceptions one by one.

...

That article googled as a free pdf. file, thanks for pointing that out Marcus. See:

http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

 

[fzero]

FYI, here is Garrett's "addressing and clearing up the issue" from page 12 in http://arxiv.org/abs/1006.4908:

"In their work, Distler and Garibaldi prove that, using a direct decomposition of E8,
when one embeds gravity and the Standard Model in E8, there
are also mirror fermions. They then claim this prediction of mirror fermions (the
existence of “non-chiral matter”) makes E8 Theory unviable. However, since there
is currently no good explanation for why any fermions have the masses they do, it
is overly presumptuous to proclaim the failure of E8 unification – since the detailed
mechanism behind particle masses is unknown, and mirror fermions with large
masses could exist in nature."

Yet there is an excellent explanation of why the mass of a fermion is likely to be equal to that of it's "mirror." It's explained by Distler on his blog, as well as in Percacci's paper. Namely, in an effective field theory, such as the theory of light fields below a GUT-breaking scale, all possible terms that are not otherwise forbidden by symmetries will appear in the low-energy action. These terms need not be in the GUT action: they will be generated by quantum corrections with heavy particles in the loops.

In the case of any GUT that contains a "chiral" fermion \psi and its mirror \tilde{\psi}, this mass term has the form

m_\psi \psi\tilde{\psi}. ~~~(*)

Furthermore, since the coefficient of this term is set by GUT physics, we can also say that

m_\psi = \alpha \Lambda_{\text{GUT}},

where \alpha is a factor of order 1. This is the statement of naturalness. So the fermions get a mass within an order of magnitude or so of the GUT scale. Such a fermion is definitely not a candidate for even the heaviest SM fermion, the top quark.

This illustrates an important distinction of physical terminology. While we can consider a fermion by itself to be chiral by virtue of its representation under the Lorentz group, when a theory contains an antichiral fermion with exactly conjugate charges to every chiral fermion, the theory itself is not chiral. These theories are called "vector-like." A chiral theory contains at least one chiral fermion with no antichiral conjugates. Any GUT must be chiral because the electroweak theory is manifestly chiral: only left-handed fermions have non-trivial SU(2) charges.

Now one can try to explain this problem away with different arguments. Perhaps the first is ignorance. We don't know all of the features of mass generation. Certainly the Higgs mechanism hasn't been experimentally verified. And the electron mass itself is known to be unnaturally smaller than the electroweak scale. However trying to find a candidate electron within a vectorlike theory is only adding another 15 orders of magnitude of unnaturalness to the problem. Even if we allow the mass to be unnaturally small, we end up with an unwanted anti-generation in the low-energy spectrum. If there were a way to build a model with 3 generations and one anti-generation, there's a small area of parameter space where this is not ruled out by experiment. If we were to end up with 3 generations and 3 anti-generations, the resulting model could not reproduce measured physics.

The other way to evade the problem is use a symmetry to forbid the mass term (*). If the mirror antichiral fermion carries an additional charge q, then (*) is not invariant under the associate symmetry. However, the paper of Distler and Garabaldi shows that there are no such charges in E_8 GUTs or GraviGUTs. All ways of embedding SM-type symmetries into E_8 in that fashion lead to vector-like theories. So any such symmetry would have to be added by hand to an E_8 model. Furthermore, we'd need to add a mechanism, possibly using this new charge, to give a large mass to the antigeneration while leaving the generation light. At some point we have to conclude the model is no longer so exceptionally simple.

The simple point that's left to be made is that a huge amount of work was done in the 70s and 80s on GUT models. All of this work was done with the above understanding that, whatever the GUT, the resulting model had to be chiral to be worthy of consideration, in the absence of some other reasonable mechanism to explain how chiral matter was to be generated. It was just one of the first laws of model building, no doubt enforced rigorously by the editors at the Physical Review. No string theorist conspiracy was needed to explain why nonchiral theories were not pursued, the string theorists hardly existed at that point.

 

[smoit]

Thanks, fzero! Unfortunately, your message will likely be ignored by the "new Einstein" who will keep on spreading the fog.

 

[garrett]

atyy: Don't worry about it. Since I left academic physics to get away from string theory, it is odd to find myself pulled back into the fray (ba-da-bing!) a decade later. But since I am offering an alternative unification model, it makes sense that I would play a role, whether I like the contentiousness of it or not. As a result I've developed a fairly thick skin.

Marcus: Thanks! Since you enjoy keeping track of how things develop, here's a link back to when my work first hit PF in 2005: https://www.physicsforums.com/showthread.php?t=100984 Back then I had no idea that the algebraic structure I'd constructed to unify gravity and the Standard Model would happen to match E8, but it sure looked interesting. Who could have guessed...

arivero: I tried to get gravity and SM out of the SU(5)xSU(5) in E8, but couldn't figure out a way to make it work, especially with three generations. You're welcome to make a go of it.

Kevin: Thanks! I do welcome honest criticism, I just take the gloves off when that criticism is based on lies.

smoit: The issue that paper clears up is whether or not one generation of fermions embeds, as algebraic elements, in the Lie algebra of E8. Distler and Garibaldi mislead many physicists, including Sean Carroll, to think that it does not. When, in fact, it does. In that paper I was quite happy to be able to show the embedding in E8 via a direct numerical identification of the conventional gravitational and SM generators.

fzero: That was a very clear description of why mirror fermions are bad. Thank you. However, you forgot to mention that 3 anti-generations are only ruled out by experiment for the case of a single Higgs -- an important point, since there are several Higgs in E8. Also note that it is very very different to claim, as Distler and Garibaldi have done, that one has a mathematical proof that E8 Theory can't work, than it is to say, as is the case, that because of experimental constraints a particular version of E8 Theory has almost been ruled out. However, I don't actually expect there to be mirror fermions. You see, one can use an E8 gauge transformation, related to triality, to identify mirror fermion degrees of freedom with those of usual fermions. I expect this is how things are going to work, and why the mirrors won't be a problem.

smoit: From sarcasm to ad hominem attack in only two posts, congratulations.

 

[jal]

Hi!

I like your Elementary Particle Explorer because it makes it easier to understand the symmetry.
jal
http://deferentialgeometry.org/epe/

 

[fzero]

smoit: The issue that paper clears up is whether or not one generation of fermions embeds, as algebraic elements, in the Lie algebra of E8. Distler and Garibaldi mislead many physicists, including Sean Carroll, to think that it does not. When, in fact, it does. In that paper I was quite happy to be able to show the embedding in E8 via a direct numerical identification of the conventional gravitational and SM generators.

The fundamental problem with saying that one generation of fermions embeds is that while it is true mathematically, the physics of a model with a generation and conjugate antigeneration is drastically different from a chiral theory of one generation. While a browing of blog posts suggests that there might have been early confusions about embeddings, the paper with Garibaldi seems have sorted the issues out with rigor. They do not say that there is no embedding of a generation of fermions, they explain that there are no chiral theories obtained from any embedding.

fzero: That was a very clear description of why mirror fermions are bad. Thank you. However, you forgot to mention that 3 anti-generations are only ruled out by experiment for the case of a single Higgs -- an important point, since there are several Higgs in E8.

I apologize, I hadn't recently read your original paper, so wasn't familiar with the other sectors of the theory. I am puzzled by the comments about having colored Higgs fields. Is this really the SU(3) color? If so, is there some reason to expect SU(3) to remain unbroken at low energies?

Also note that it is very very different to claim, as Distler and Garibaldi have done, that one has a mathematical proof that E8 Theory can't work, than it is to say, as is the case, that because of experimental constraints a particular version of E8 Theory has almost been ruled out.

But the problem is that, just to get to a discussion of how many antigenerations would be allowed in the low-energy theory, one must demand an incredible 19 order-of-magnitude fine tuning of the GUT scale generation-antigeneration mass term. One also needs a rather large coupling of the electroweak Higgs to the antigeneration. This latter point isn't a huge objection, since, for example, the top coupling is already much larger than the electron coupling, which is itself unnaturally small. The fine-tuning remains a serious problem. This is also to say nothing of the fact that there isn't an explicit model with 3 chiral generations in the first place.

That said, I'll grant you that there is a difference between "mathematical proof" and "phenomenologically unviable." However, for all of the physical reasons explained, there's a good reason for a physicist to argue that a physically realistic GUT must be chiral.

However, I don't actually expect there to be mirror fermions. You see, one can use an E8 gauge transformation, related to triality, to identify mirror fermion degrees of freedom with those of usual fermions. I expect this is how things are going to work, and why the mirrors won't be a problem.

I look forward to seeing the details. I have to admit that I haven't intuited exactly how the different 8s transform under the SM gauge group. I'm also confused about how you might transform the antigeneration into a generation without also transforming the generation into something else at the same time.

 

[garrett]

fzero: I agree that mirror fermions are unattractive, but "unviable" is too strong, as were Distler and Garibaldi's claims, to the point of being untrue. To answer your last question: as long as the action term for the mirror fermions is independent, the mirror fermions may be transformed independently.

 

[arivero]

Actually, I don't quite understand the explanation of fzero. It amount to say that the mass term between the fermions and the mirrorfermions is not protected and then it is of the order of the GUT scale. We want it to be of the order of the GUT scale, do we? What we don't want is a term of the order of the electroweak scale, or a zero term.

I mean, there are another two possible mass term, between the fermions and themselves and between the mirrorfermions and themselves. The real problem, seems to me, is how to argue that one of these is protected (and then takes values at electroweak breaking) while the other one is not.

EDIT: I think that at the end, the problem stated by fzero is the typical of GUT: that one needs different scales for the higgses breaking GUT and for those breaking the electroweak symmetry. If gravity fails to provide the first scale (and it is near but not exactly there), there are uglyfication models, more than than unification models.

Is this really the SU(3) color?

In the literature there was another curious SU(3) which was a diagonal of color plus flavour. In my notebook I had it jointly with a reference to Ne'eman but it was probably a mistake (sometimes I write again over old notes). I think to remember that it was proposed when looking at some SU(3) appearing in compactification from 10 or 11 dimensions.

 

[smoit]

Actually, I don't quite understand the explanation of fzero. It amount to say that the mass term between the fermions and the mirrorfermions is not protected and then it is of the order of the GUT scale. We want it to be of the order of the GUT scale, do we? What we don't want is a term of the order of the electroweak scale, or a zero term.

When a theory has a non-chiral spectrum, as is clearly the case in Garrett's construction, the GUT scale bare mass term for the vector-like pairs renders both the fermions and their conjugates simultaneously massive, in which case the EW scale spectrum has no fermions as they all decouple at the GUT scale.

I mean, there are another two possible mass term, between the fermions and themselves and between the mirrorfermions and themselves. The real problem, seems to me, is how to argue that one of these is protected (and then takes values at electroweak breaking) while the other one is not.

A bare quadratic mass term containing the fermions only is not gauge invariant and is therefore forbidden. The same is true for the conjugates. That's why when a theory is chiral at the GUT scale, one naturally obtains light fermions at scales far below the unification scale, as in the SM. The masses are then generated via the Higgs mechanism due to the cubic Yukawa interactions between the Higgs field and the fermions, once the Higgs develops a non-zero vev.
Garrett's construction has a non-chiral spectrum at the GUT scale, which is what Distler and Garibaldi have demonstrated.

 

[Orion1]

symmetry breaking...



My confusion about Garrett's exceptional simple Lie group E_{8} model originates when 7 charge dimensions based upon the Pati–Salam model breaks symmetry into 6 charge dimensions based upon the Standard Model, that is when SU(4) \times SU(2)_{L} \times SU(2)_R \rightarrow U(1) \times SU(2) \times SU(3).

[PLAIN]http://home.comcast.net/~lambo1826/physics/038_0001.jpg
U(1) \times SU(2) \times SU(3)

[PLAIN]http://home.comcast.net/~lambo1826/physics/038_0003.jpg
SU(4) \times SU(2)_{L} \times SU(2)_R

For one, the Standard Model predicts only one Higgs boson, meanwhile the Pati–Salam model predicts eight new particles, (three Higgs bosons, one electroweak Higgs boson, one singlet, two mass particles, one sterile neutrino), none of which has ever been detected in any particle detector experiment.

If 7 charge dimensions can break symmetry into 6 charge dimensions and the Pati–Salam model is only one possible solution to this subset, then how many possible solutions are there?

If all the particles, charges, and forces are completely known in 6 charge dimensions based upon the Standard Model, then how can I rotate the Standard Model in 7 charge dimensions without producing any new particles?
[/Color]
Reference:
http://en.wikipedia.org/wiki/Gauge_theory"
http://en.wikipedia.org/wiki/Standard_Model"
http://en.wikipedia.org/wiki/Pati%E2%80%93Salam_model"

 

[fzero]

Actually, I don't quite understand the explanation of fzero. It amount to say that the mass term between the fermions and the mirrorfermions is not protected and then it is of the order of the GUT scale. We want it to be of the order of the GUT scale, do we? What we don't want is a term of the order of the electroweak scale, or a zero term.

I mean, there are another two possible mass term, between the fermions and themselves and between the mirrorfermions and themselves. The real problem, seems to me, is how to argue that one of these is protected (and then takes values at electroweak breaking) while the other one is not.

Just to clarify smoit's reply, the mass term I was talking about is not a bare mass in the GUT Lagrangian. The problem is that we can have a zero bare mass for the generation-antigeneration and we can even keep the direct Yukawa couplings to the GUT Higgs sector zero, but, below the GUT scale, a nonzero effective mass term will be generated by quantum corrections. The resulting low energy theory has no light fermions at all.

In a chiral theory, the the mass term between the chiral fermion and it's conjugate is forbidden by gauge invariance, since the electroweak part of the gauge group is parity-violating.

In the literature there was another curious SU(3) which was a diagonal of color plus flavour. In my notebook I had it jointly with a reference to Ne'eman but it was probably a mistake (sometimes I write again over old notes). I think to remember that it was proposed when looking at some SU(3) appearing in compactification from 10 or 11 dimensions.

Well I'm not really worried about other SU(3)'s in the literature, just what "color" means in that part of Garret's paper. It's certainly not an SU(3) due to compactification from 10 or 11 dimensions.

 

[garrett]

Orion1: It is typical that such unification models, involving embedding the 6 dimensional SM charge structure in larger models, predicts the existence of new particles. This is one of many reasons it's very exciting to see what comes out of the LHC. There are many different GUT options.

smoit+fzero+arivero: You seem to be happily talking to each other, which is good. The one question for me I see that I didn't answer was where the strong SU(3) comes from in E8 Theory. The answer is that this symmetry remains unbroken within E8.
[PLAIN]http://garrettlisi.com/stuff/su(3).png
(From the http://deferentialgeometry.org/epe/" .)

 

[arivero]

Still, if someone can help me with my dumb memory and find out where in the theory world the idea of SU(3) as diagonal was proposed, I would be really really grateful. I am speaking diagonal of SU(3) flavour plus SU(3) colour, not the usual diagonal of chiral symmetry.

 

[MTd2]

This one:

http://en.wikipedia.org/wiki/Chiral_color

 

[MTd2]

KEK preprint: http://www-lib.kek.jp/cgi-bin/img_index?8705246

Chiral Color: An Alternative to the Standard Model.
Paul H. Frampton, Sheldon L. Glashow, (Harvard U. & Boston U.) . BUHEP-87-4, HUTP-87/A007, IFP-283-UNC, Feb 1987. 12pp.
Published in Phys.Lett.B190:157,1987.http://arxiv.org/abs/0910.0307

Alternative Version of Chiral Color as Alternative to the Standard Model

Paul H. Frampton
(Submitted on 2 Oct 2009 (v1), last revised 29 Dec 2009 (this version, v3))
In a variant of chiral color with the electroweak gauge group generalized to $SU(3)_L \times U(1)$ anomaly cancellation occurs more readily than in the $SU(2)_L \times U(1)$ case. Three families are required by anomaly cancellation and the top family appears non-sequentially.

 

[Orion1]

special unitary group symmetry...


[PLAIN]http://home.comcast.net/~lambo1826/physics/038_0001.jpg
U(1) \times SU(2) \times SU(3)

Orion1: It is typical that such unification models, involving embedding the 6 dimensional SM charge structure in larger models, predicts the existence of new particles. This is one of many reasons it's very exciting to see what comes out of the LHC. There are many different GUT options.

What if all the known particles that can exist within the Standard Model have already been discovered except the Higgs boson? What if there are not any more new particles except the Higgs boson? What would that mean for the E_8 theory and other GUT theories?

There are many different GUT options, however, how many of those options still work with the E_8 theory?

With respect to the speculative chiral color model, are we discussing this?
U(1) \times SU(2)_L \times SU(3)_L \times SU(3)_R

And this?
U(1) \times SU(3)_L \times SU(3)_L \times SU(3)_R

I noticed that this model also produces massive new particles also, called axigluons, a lower bound on the axigluon mass is about 1 TeV.

Exactly how many possible special unitary group symmetry combinations are there?
[/Color]
Reference:
http://en.wikipedia.org/wiki/Chiral_color"
http://en.wikipedia.org/wiki/Special_unitary_group"
http://en.wikipedia.org/wiki/Gauge_field_theory"

 

[MTd2]

The answer is that this symmetry remains unbroken within E8.
[PLAIN]http://garrettlisi.com/stuff/su(3).png
(From the http://deferentialgeometry.org/epe/" .)

Remains unbroken? Does that mean that SU(3) is a symmetry of gravity too?

 

[Orion1]

triality symmetry...


[PLAIN]http://home.comcast.net/~lambo1826/physics/040_0001.jpg
SO(8) \; \; \; E_8
Special orthogonal group, exceptional simple Lie group
1st, 2nd and 3rd matter generations triality symmetry - 248 dimensions

One small part of this E_8 shape can be used to describe the curved space-time of Einstein's General Relativity explaining gravity.

So how exactly does this special orthogonal group SO(8) bridge over to the Einstein Field Equations?

Does Garrett Lisi's E_8 model break symmetry as this?:
SO(8) \rightarrow SU(4) \times SU(2)_{L} \times SU(2)_R \rightarrow U(1) \times SU(2) \times SU(3)

I surmise that this symmetry breaking can generate up to 26 different particles not included in the Standard Model.
[/Color]
Reference:
http://en.wikipedia.org/wiki/Triality"
http://en.wikipedia.org/wiki/E8_%28mathematics%29"
http://en.wikipedia.org/wiki/SO%288%29"
http://en.wikipedia.org/wiki/Einstein_field_equations"

 

[arivero]

Hmm Orion1, no, SO(8) does not contain the SM groups. You need SO(10).

If this is going to be about group theory, I urge everyone to look the tables in Slansky's report. There is a scanned copy at KEK, freely available.

 

[jal]

Garrett

Your chosen diagram shows 6 gluons on the outside, doing the confining, I presume.

I refreshed my memory by checking http://en.wikipedia.org/wiki/Gluon

CERN is producing a perfect liquid. What would the perfect liquid look like in the “Elementary Particle Explorer”?

jal

 

[Orion1]

Exceptional simple Lie group...


[PLAIN]http://home.comcast.net/~lambo1826/physics/040_0001.jpg
E_8
Exceptional simple Lie group
1st, 2nd and 3rd matter generations triality symmetry - 248 dimensions

A major objection to E_7 and E_8 is that they have self-conjugate irreps (irreducible representations) only. So it appears to take a detailed analysis of the symmetry breaking to determine whether the flavor-chiral character of the weak interactions is recovered in the low energy limit. (example cited)

It is not clear at this time what requirements must be satisfied for a vector-like theory to reduce to the chiral weak-interaction theory at low energies.

Does Garrett Lisi's E_8 model break symmetry as this?:
E_8 \rightarrow SU(4) \times SU(2)_{L} \times SU(2)_R \rightarrow U(1) \times SU(2) \times SU(3)

Slansky - Table 15 - pg. 181 - ref. 1
E_8 \supset SO(16)
E_8 \supset SU(5) \times SU(5)
E_8 \supset SU(3) \times E_6
E_8 \supset SU(2) \times E_7
E_8 \supset SU(9)
E_8 \supset SU(2)
E_8 \supset G_2 \times F_4
E_8 \supset SU(2) \times SU(3)
E_8 \supset Sp_4

Arivero is correct that the Pati–Salam model can break symmetry from SO(10): (Slansky - Table 15 - pg. 178, SO(10) Wikipedia)
Rank 5:
SO(10) \rightarrow SU(4) \times SU(2)_{L} \times SU(2)_R

Slansky does not have the Pati–Salam model listed in table 15 as a subset of E_8, therefore I rely upon my colleagues to determine if this is a correct subset of E_8.

The closest solution I could locate from the Slansky tables is: (Slansky - Table 15 - pg. 181)
E_8 \supset SU(2) \times E_7
E_7 \supset SU(2) \times F_4

Therefore:
E_8 \rightarrow F_4 \times SU(2)_L \times SU(2)_R

Is this interpretation correct?
[/Color]
Reference:
http://home.comcast.net/~lambo1826/physics/Slansky01.pdf"
http://en.wikipedia.org/wiki/Triality"
http://en.wikipedia.org/wiki/E8_%28mathematics%29"
http://en.wikipedia.org/wiki/SO(10)#Spontaneous_symmetry_breaking"
http://en.wikipedia.org/wiki/Einstein_field_equations"
http://en.wikipedia.org/wiki/Gauge_theory"
http://en.wikipedia.org/wiki/Standard_Model"
http://en.wikipedia.org/wiki/Pati%E2%80%93Salam_model"

 

[garrett]

Orion1:

What if all the known particles that can exist within the Standard Model have already been discovered except the Higgs boson? What if there are not any more new particles except the Higgs boson? What would that mean for the E8 theory and other GUT theories?

It would mean that they are wrong, and that we live in a Standard Model universe.

There are many different GUT options, however, how many of those options still work with the theory?

The SU(5) GUT embeds in E8, as does Pati-Salam and SO(10). You can actually see all these embeddings with the http://deferentialgeometry.org/epe/" as an introduction. Since there are several GUT embeddings, there are several symmetry breaking possibilities.

MTd2:

Does that mean that SU(3) is a symmetry of gravity too?

No, spin(1,3) and su(3) sit in different parts of E8.

jal:
The Elementary Particle Explorer allows you to select one interaction at a time, to see what interactions are possible between different kinds of particles. A quark-gluon plasma is an ensemble of many particles. The're related, but different.


Also, I'm very happy to announce that the new http://blondegeek.net/E8/" are now available, from a physics undergrad friend.