Garrett's article in SciAm December issue

[marcus]

Does anyone have a link to an online version?

I only get a couple of paragraphs from the SciAm link at Woit's blog:
http://www.math.columbia.edu/~woit/wordpress/?p=3292

Anyone seen it? Know what it covers (besides latest model E8 unification)? It's called *A Geometric Theory of Everything*.

The article is co-authored with someone at UC Irvine. It most likely has merit because pitiful moaning was heard in the comments at Woit's blog: "Oh dear lord, not again!"

The moaner recently bailed out of string theory (after 6 years postdoctoral) and took an attractive science-policy internship in government.
http://www.science.tamu.edu/articles/681

 

[sbrothy]

Dont know if the link was added later but it's there on Woit's page:

http://www.scientificamerican.com/article.cfm?id=a-geometric-theory-of-everything

EDIT: Oops. never mind. You have to pay for it as usual.

 

[MTd2]

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...

 

[negru]

I know people here get really excited about anything non stringy, but SciAm, Lisi and Weatherall, seriously? Look, many young students come to this forum to learn about physics, and to get an idea of what goes on in research. They are very easily influenced by what they read. I'm fine with the general anti-string bias, but SciAm, Lisi and Weatherall?

I have no problem with those guys working on whatever they want, but seriously Marcus, think of the children!

 

[atyy]

I know people here get really excited about anything non stringy, but SciAm, Lisi and Weatherall, seriously? Look, many young students come to this forum to learn about physics, and to get an idea of what goes on in research. They are very easily influenced by what they read. I'm fine with the general anti-string bias, but SciAm, Lisi and Weatherall?

I have no problem with those guys working on whatever they want, but seriously Marcus, think of the children!

Yeah, unfortunately it's ptrobably not anti-string enough. If it were more anti-string like Smolin's book, more people would see how stupid the anti-string stuff is.

 

[MTd2]

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

 

[negru]

It just makes me wonder why these people associate (smolin, lisi and now this Weatherall). I've heard that the enemy of my enemy is my friend, but shouldn't bad physics be everyone's enemy?

 

[MTd2]

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!

 

[negru]

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?

 

[suprised]

This is as amazing as depressing.

 

[MTd2]

So he has finally learned of the difference between fermions and bosons?

Saying he doesn't know the difference between fermions and bosons is being too dismissive. He always knew. And this is why it looks like being dishonest. He knows that the problem is to implement that within E8 as he wants. To make that work he had always to use an extra group structure, SO(8), which is the only simple lie group with triality, to rotate fermions to mirror fermions to bosons and at the same time rotate between the 3 generations.

There isn't simply enough structure in E8, any kinds, to keep track of all labels of both SO(8). Lately, he has been looking for a geometric set up such that E8 could live, in 4d, and somehow make those trialities appear naturally. But he still didn't say what structure.

The renomalization is supposed to be asymptotic safe, but non renormalizable.

 

[marcus]

Lots of talk about "enemy" and "anti-string" in this thread. I don't recall Garrett ever expressing hostility to string. Always seems modest, undefensive, and diplomatic in references to other people's work. Can anyone point to some exceptions?

To me it seems to have been the other way round. Garrett's work has been attacked by Distler (a string theorist).

To what kind of person is a rival automatically an enemy?

 

[negru]

Garret's work wasn't "attacked" by Distler, it was dismantled by him

 

[marcus]

Whatever: attack, criticize, dismantle.

I haven't commented on Garrett's SciAm article because I haven't seen it. I ASKED about it: does anyone have a link, can anyone say what-all it covers.

(Personally I think it would have great educational value if the SciAm article introduced Garrett's computer-graphic "elementary particle explorer". Call it an educational game or toy. You set up multidimensional visualizations of symmetries and find particles as points in the visualization. There may be other aspects to note: maximal tori in Lie groups, or just a better understanding of Lie groups for wide audience. I'm not a fan or regular reader of SciAm but it does have really good articles on occasion---stuff with long-term usefulness.)

We will just have to see what the ultimate value/usefulness of Garrett's work is, just as with any other unproven physical theory. You can't always tell what will come out of something or what the utility will be. Maybe you mostly can't tell.

One reason I asked about Garrett's SciAm article is that I've recently sensed a slight veering or change of editorial focus at SciAm. The big thing for me was that now, in November 2010, they posted last year's STEVEN WEINBERG VIDEO, which gives his overview of particle physics (with some interesting remarks about string theory at the end, in response to a question.)

It is a wonderful survey of particle physics, by a master, to a conference of SCIENCE WRITERS. The annual conference of the people who do the communicating---the national science writers guild. I remember watching it at the time (October 2009!)--he was feeding them real clarity, with excellent slides, right at the intelligent layman level.

What impressed me is that now, after over a year (!), SciAm is finally making a news item about this Nobelist's superb overview of particle physics. Does anyone else find this interesting. I think it goes along with their publishing Garrett's piece, but you wouldn't know that unless you had watched the Weinberg video all the way through to the end.

 

[negru]

Right, I forgot, criticizing string theory is noble and desirable, but criticizing crackpots is just string theory picking on the little guys.

 

[marcus]

I guess my basic interest is in reporting/analyzing. Current developments in basic physics.
Part of the "news" is what Steven Weinberg says. I think he is fair and gentle in how he puts things---often takes great care to be kind---and has built up wisdom and perspective over the years. You can learn by paying close attention to nuances etc.
Part is also a shift in focus or editorial policy at SciAm, which I'm not sure about, just straws in the wind.
Here is the video at SciAm.

http://www.scientificamerican.com/p...=physics-nobel-laureate-steven-weinb-10-11-15

That science writers' conference happened in October 2009, why is their report dated 15 Nov 2010? Maybe means nothing.

Anyway, if you have read my posts you will realize I have nothing against string theory itself. I don't criticize it. (Last comment I made on the mathematical theory itself was to praise it as mathematics, call it beautiful intriguing whatever. Tom's thread.)
String theory is not an interesting issue for me. However the behavior of string practitioners and their hangers-on is an issue.

Also the historical shift that has been happening since around 2003 or 2005. That is something that I think should be reported as accurately as possible. If it sounds like a criticism, that's tough.

 

[negru]

Yes, there has indeed been a slight veering or change of editorial focus at SciAm, for at least a couple of years now. It is now focusing exclusively on truly retarded physics and science policy articles.

 

[flatcp]

Anyway, if you have read my posts you will realize I have nothing against string theory itself. I don't criticize it.

Dude... You should have been a politician!

 

[marcus]

Dude... You should have been a politician!

Thanks for the compliment, but you quoted me out of context...Dude.

I guess my basic interest is in reporting/analyzing. Current developments in basic physics.
Part of the "news" is what Steven Weinberg says. I think he is fair and gentle in how he puts things---often takes great care to be kind---and has built up wisdom and perspective over the years. You can learn by paying close attention to nuances etc.
Part is also a shift in focus or editorial policy at SciAm, which I'm not sure about, just straws in the wind.
Here is the video at SciAm.

http://www.scientificamerican.com/p...=physics-nobel-laureate-steven-weinb-10-11-15

That science writers' conference happened in October 2009, why is their report dated 15 Nov 2010? Maybe means nothing.

Anyway, if you have read my posts you will realize I have nothing against string theory itself. I don't criticize it. (Last comment I made on the mathematical theory itself was to praise it as mathematics, call it beautiful intriguing whatever. Tom's thread.)
String theory is not an interesting issue for me. However the behavior of string practitioners and their hangers-on is an issue.

Also the historical shift that has been happening since around 2003 or 2005. That is something that I think should be reported as accurately as possible. If it sounds like a criticism, that's tough.

I rarely comment on string theory itself, but my last several comments have been positive. You mustn't confuse the theory with the theorists, and the historical decline of the program.

The decline of the string research program (real people, publications, jobs, careers) is a serious objective fact. Personally I'm interested in other things and rarely mention it, but I think it should be reported. It would be interesting, I guess, to understand better why it's happening. Steven Weinberg's talk to the science-writer's conference actually shed some light on that.

Weinberg BTW is obviously not an "enemy" or "critic" of the theory. He had some very nice appreciative things to say about it. And he has been a major supporter of the program in the past. Used to do string research himself. You should listen to the last 5 or 10 minutes of the video, if you haven't already.

 

[marcus]

I think it's silly that string should enter into the discussion in this thread. It's about Garrett's article in the December 2010 SciAm.
Whoever dragged string into this discussion must have a polarized "for-or-against" mentality. Interpreting everything on a simple level of for or against their pet idea.

Not what science, or mathematics, is about. Garrett's approach to particle symmetries and classification must be interesting to mathematicians and must be seen as having potential for further exploration. I can't think of any other way to interpret the fact of the Banff workshop.

It was organized by some of the world's top mathematicians. Joe Wolf, David Vogan, and others. For people working in the unitary representation of Lie Groups. I don't recall any physicists being invited besides Percacci and Garrett. If anybody remembers others, please correct me on this. I think to a large extent they were taking stock of a recent advance in understanding the structure of E₈.

Banff is the North America version of Oberwolfach. If some development in mathematical physics is seen to have interest and major growth potential they hold a workshop on it. Also significant new developments in other fields of mathematics. Oberwolfach is the number one venue, and Banff comes in second.

 

[atyy]

The article is co-authored with someone at UC Irvine. It most likely has merit because pitiful moaning was heard in the comments at Woit's blog: "Oh dear lord, not again!"

The moaner recently bailed out of string theory (after 6 years postdoctoral) and took an attractive science-policy internship in government.
http://www.science.tamu.edu/articles/681

I think it's silly that string should enter into the discussion in this thread. It's about Garrett's article in the December 2010 SciAm.
Whoever dragged string into this discussion must have a polarized "for-or-against" mentality.

...

 

[suprised]

Look, the mathematicians are interested because E8 is sweet and has been of interest since ever. This does not imply that Lisi's model makes any sense at all physically. Actually everyone in the field knows that this model is wrong on several counts and beyond repair, conceptually and technically. This is not a matter of modifying it a bit here and there until it works. Obviously there hasn't been any progress on this since it came up, and there are good reasons for that (or did the "assigning of particles" exercise discussed here in the past lead to anywhere? A status report would perhaps be useful...)

It is sad if not scandalous that despite of better knowledge, this article has been published in SA. As if things haven't been bad enough, eg when Smolin advertized Lisi as a potential successor of Einstein, next to Hawking and Witten and his own (Ex?-)wife:
http://discovermagazine.com/2008/mar/13-e-nste-n

 

[marcus]

Look, the mathematicians are interested because E8 is sweet and has been of interest since ever...

That's certainly true! Doesn't it go without saying? And their interest certainly does not prove that Lisi's model is physically right. As for "making no sense at all" or putatively leading nowhere, contributing nothing to our understanding, I don't think anyone can say at this point (present company included.)

I doubt the work should be dismissed out of hand. Same way with Roberto Percacci's work, which I think was in part stimulated and motivated by Lisi's.

It is sad if not scandalous that despite of better knowledge, this article has been published in SA.

I see. You are saddened that Lisi got an article in SciAm. I don't know what to say in response. I haven't seen the article and I'm not a regular reader of the magazine. It is hard for me to think of it as doing any harm. It is not as if Lisi was attacking anyone, or that his publishing an article is against anyone's interest, is it? Apparently the editors of the magazine thought the readers would like the article. It's not as if SA were a peer-review journal. I don't see how it can be "sad, if not scandalous". I look on it more as a sign of changes which I want to understand.

However I respect your different point of view and sympathize with your sadness.

 

[Fra]

Look, the mathematicians are interested because E8 is sweet and has been of interest since ever. This does not imply that Lisi's model makes any sense at all physically.

I think string theory is also pretty sweet ;-)

/Fredrik

 

[suprised]

I think string theory is also pretty sweet ;-)

Indeed, as it contains E8 and a million of other things as well. But the relevant difference is that is makes sense physically.

 

[MTd2]

his own (Ex?-)wife

Huh? I didn't see Dina Graser there...

 

[Fra]

Indeed, as it contains E8 and a million of other things as well. But the relevant difference is that is makes sense physically.

I think your last scentence got scambled, but otherwise I think we can agree ;)

/Fredrik

 

[S.Daedalus]

Indeed, as it contains E8 and a million of other things as well. But the relevant difference is that is makes sense physically.

Well, or it can be made to make sense, at least. As you well know, there are any number of difficulties with what one might call 'bare-bones' string theory that have to be gotten rid off using various means -- the introduction of supersymmetry, compactification of extra dimensions and so on -- in order to get the theory to apply to the physical world in any sensible way. This often includes positing new phenomena and then pushing them out of the range of current observation; one could follow a strict philosophy in which such 'trickery' would be frowned upon, a viewpoint from which one would have to discard string theory on the basis on not making any sense physically. Of course, from another viewpoint, these are just the theory's predictions.

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.

 

[grosquet]

I stopped subscribing to Scientific American because of the plethora of articles describing multiple universes, clashing branes, extra dimensions & other fantastic notions.

 

[marcus]

I stopped subscribing to Scientific American because of the plethora of articles describing multiple universes, clashing branes, extra dimensions & other fantastic notions.

exactly! Who knows, maybe as the string program loses prestige the editors will reduce SciAm's speculative physics content and move back towards firmer ground.

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.

But over the past ten years there has been rather a glut of articles along the lines you indicated.

 

[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/" .)