No "Theory of Everything" Inside E8: Jacques Distler & Skip Garibaldi

[MTd2]

THERE IS NO“THEORY OF EVERYTHING” INSIDE E8-new article from Jacques Distler on arxiv

http://arxiv.org/abs/0905.2658

There is no "Theory of Everything" inside E8

Jacques Distler, Skip Garibaldi
(Submitted on 16 May 2009)
We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any "Theory of Everything" obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras along the lines of Dynkin's classic papers and are written for mathematicians.

 

[garrett]

I'm curious to hear how people interpret this paper.

 

[Haelfix]

I don't follow it to be honest. Its written in a language that's a little hard to follow and unfamiliar (at least for one with meager abilities like yours truly) as its more geared for mathematicians or mathematical physicists. I do however understand his original posts on his blog (getting a generation and antigeneration out of the whole thing) and I think I follow and accept the argument up to details that I'd want to check for myself with reference material if I had the time.

 

[MTd2]

The situation for me is the same as for Haelfix. I know the arguments because I followed closely that thread on cafe category. So, I guess it is time for Garrett to say something. I am really lost here. The impression I have it is that if he doesn't say anything, he might not be taken seriously anymore since, even though I don't really get very well, Distler's new paper seems very clear and complete.

So, I would like to hear what Garrett has to say, mainly because he should have some answer. I mean, he is being with "hexalities" for months, but he never explained well what the hell that means, and that is seems to be his only hope for his theory. I know he is playing because I read his tweet posts sometimes.

BTW, things should be working better, wasn't Smolin and some other guy helping him with his stuff? And Garret has got that workshop, but it seems to never be announced. I thought that 70,000 grant he got last year would help him a lot here...

 

[Coin]

So it appears that the gist of Distler's paper, in plain language, comes down to:

- The e8 TOE cannot support the three known fermion generations
- The e8 TOE is nonchiral

The paper consists of proofs of these two things. Do I understand the basic content of the paper correctly?

 

[garrett]

Coin:
Your understanding looks good to me, as a summary. But it gets more interesting. "The e8 TOE" in this paper refers to the idea of starting with E8 and seeing how its elements transform as representation spaces under the gravitational and standard model gauge groups as subgroups. A generation of standard model fermions necessarily transforms as a complex (i.e. chiral) representation space of the gravitational and standard model Lie groups. So, Distler and Garibaldi have this ToE2 requirement on page 1: the relevant representation space in E8 needs to be complex. And then they go on to prove that this representation space in E8 is always non-complex, so that ToE2 fails. Well, that may be true. But here's the interesting question:

Are Distler and Garibaldi claiming that one cannot find a (necessarily complex) representation space in E8 that transforms under the gravitational and standard model subgroups as one generation of fermions?

 

[MTd2]

I posted a new message concerning the new article at n category cafe, and I quoted the comment above:

http://golem.ph.utexas.edu/category/2008/05/e8_quillen_superconnection.html#c023875

Let's see what Jacques Distler says.

 

[garrett]

MTd2:

I doubt you'll get a straight answer from him. I posed the same question about twenty times, in that same thread, and every time he danced around it -- it became quite comical.

Distler and Garibaldi say in their conclusion that "it is impossible to obtain even the one-generation Standard Model in this fashion." If by this statement they are implying that one cannot find a representation space in E8 that transforms under the gravitational and standard model subgroups as one generation of fermions, then they are being blatantly dishonest. Since they are almost but not saying that, their paper is merely misleading.

 

[benk99nenm312]

MTd2:

I doubt you'll get a straight answer from him. I posed the same question about twenty times, in that same thread, and every time he danced around it -- it became quite comical.

Distler and Garibaldi say in their conclusion that "it is impossible to obtain even the one-generation Standard Model in this fashion." If by this statement they are implying that one cannot find a representation space in E8 that transforms under the gravitational and standard model subgroups as one generation of fermions, then they are being blatantly dishonest. Since they are almost but not saying that, their paper is merely misleading.

I just have to say... nice job interpereting that. Well Done.

 

[MTd2]

Distler and Garibaldi say in their conclusion that "it is impossible to obtain even the one-generation Standard Model in this fashion." If by this statement they are implying that one cannot find a representation space in E8 that transforms under the gravitational and standard model subgroups as one generation of fermions, then they are being blatantly dishonest. Since they are almost but not saying that, their paper is merely misleading.

Can you debunk the paper then, equation by equation?

Man, BTW, what about your hexality?

 

[garrett]

Sure. Their ToE2 requirement is a straw man setup. For a generation of standard model fermions to be in E8, in a complex representation space of the gravitational and standard model gauge groups, it is not necessary for their complex conjugates not to be in E8. Distler and Garibaldi demand this, via ToE2, and then prove that it cannot be satisfied. But this ToE2 is not required in order to embed a standard model generation in E8 as I have done, so proving ToE2 can't be satisfied does not invalidate my work.

ToE2 requires that a generation of standard model fermions (in a complex representation space) not be a subspace of a non-complex representation space in E8. But this requirement is superfluous, because a complex representation space can be a subspace of a non-complex one. As an example, if you have so(6) acting on a real 6 representation space, then there is a su(3) subalgebra of the so(6) that acts on a 3 and on a bar{3} subspace in the 6. Distler would have you believe that, according to ToE2, it is impossible to obtain the complex 3 representation space "inside" the real 6 representation space because the bar{3} is their too. That is the ridiculous argument he uses to conclude that "it is impossible to obtain even the one-generation Standard Model [inside E8] in this fashion." It is extremely misleading, if not an outright lie.

 

[Coin]

Distler and Garibaldi say in their conclusion that "it is impossible to obtain even the one-generation Standard Model in this fashion."

Okay, well let's move away from Distler's charged language a bit and concentrate on the chirality claim. You say:

For a generation of standard model fermions to be in E8, in a complex representation space of the gravitational and standard model gauge groups, it is not necessary for their complex conjugates not to be in E8. Distler and Garibaldi demand this, via ToE2

However the reason they give for demanding this is given in their paper as:

Definition 2.3. A gauge theory, with gauge group G, is said to be chiral if the representation, R by which the fermions (2.1) are defined, is complex [in the sense of not possessing a self-conjugate structure, see 2.2]. By contrast, a gauge theory is said to be nonchiral if the representation R in 2.1 has a self-conjugate structure.

That is, they define self-conjugacy of the representation as equivalent to nonchirality. They then procede to two proofs, for real and complex e8 respectively, that I understand to be asserting that all potential subgroups of e8 that one might use as the standard model group will be inevitably equivalent to their own complex conjugates. They use this to assert that whatever you are using for the "standard model group for one generation of fermions", it will be nonchiral, and thus "not really" the 1-generational standard model group at all. This as I understand (in the sentence before the one you quote above) is the basis for their claim that it is impossible to obtain the 1-generation standard model from e8.

You don't appear (?), from your comments in this thread, to actually disagree with their claim that the standard model group in your e8 construction is self-conjugate. Do you then disagree with their basic premise that a self-conjugate gauge group will be necessarily nonchiral?

 

[MTd2]

Thanks Garrett, and I think you should also discuss this at least on category cafe. That is painful and annoying, but you must answer that guy in a more appropriate place. This forum is a great place, but its innovative is not popular with people with more status, that is, it influence other people who would otherwise gladly study your ideas.

BTW,

CAN YOU EXPLAIN WHAT IS THE HEXALITY AND HOW DO YOU GET THE 3 GENERATIONS!

 

[garrett]

MTd2:
Thanks for the advice. I like posting at PF because I feel I can speak more candidly here, and I like the checks and balances that are in place to keep the community polite. Hexality is just the product of duality and triality, so I'm not sure it really needs its own name. How to get three generations is still an open question.

Coin:
Distler's use of chirality is nonstandard -- it usually refers to how the weak force interacts with only left chiral fermions -- so I prefer to speak of complex and non-complex representations, which I think is what Distler is calling chiral and non-chiral. But, as I've explained above, it is possible to find a "chiral" representation space as a subspace of a "non-chiral one." The standard model algebra I'm working with is the usual algebra of the gravitational so(1,3) and standard model s(u(2)xu(3)) acting on the 64 dimensional representation space of one generation of fermions. This is the algebra that I find embedded in E8.

What I do next is look at how a triality automorphism maps this algebra into other parts of E8, and see if I can figure out how to relate this to the other two fermion generations. It is Distler's red herring to look directly at how the rest of E8 transforms under the gravitational and standard model subalgebras, as if that is what I'm doing, because I'm not. What I'm doing is to embed one generation of the standard model and gravity in E8 and then see where I can go from there. To say that there's a conjugate represenation space to the generation of fermions in E8 that makes that generation "not there" is silly in that context -- it depends on false assumptions about how E8 is being broken up and interpreted in my work.

 

[MTd2]

Garrett, I don't get one thing, why instead of trying to come up with 3 generations, why not trying to get rid of the junk other model from the 3 Standard Model with junk particles?

I have an idea, what if there is a way for you to combine the 1 generation model with the 3 junk generation yielding a low energy model that is the Standard Model? That is, since we are talking about QM, maybe you should consider summing over different decompositions. In the great scheme of things on your theory, what really matter is the quantum states of E8, so by seeing how different possible decompositions of E8 behave is like in a much smaller scale, in the SM, seeing how apparently distinct compostions of states like leptons, mesons, baryons and gluons interact, in a great family, where everyone must be taken seriously to have harmony. Maybe that one generation of a decomposition increases the cross section of just the particles (states) that are not of the so called junky part of the 3 generation. The probability of seeing in any reasonalbe experiment with these junks are almost null for several hundreds of TeV. Again, on smaller scale, Top was hard to find, but had to be there.

 

[garrett]

Yep, that's a good thing to try.

 

[MTd2]

I think you didn't like my idea or has already tried or has been trying that.

 

[Coin]

Coin:
Distler's use of chirality is nonstandard -- it usually refers to how the weak force interacts with only left chiral fermions -- so I prefer to speak of complex and non-complex representations, which I think is what Distler is calling chiral and non-chiral. But, as I've explained above, it is possible to find a "chiral" representation space as a subspace of a "non-chiral one." The standard model algebra I'm working with is the usual algebra of the gravitational so(1,3) and standard model s(u(2)xu(3)) acting on the 64 dimensional representation space of one generation of fermions. This is the algebra that I find embedded in E8.

Okay, so... let me see if I follow all this.

Assuming we're only trying for a single-gen SM, what is bothering D&G here really is that they want to be able to fit both a generation and its "antigeneration" (i.e. the antiparticles of that generation?) in. They assert the way you go from a generation to the antigeneration is to take the complex conjugate of the gauge group (for the 1-generation standard model group). This I take it is their reason for demanding the SM group not be self-conjugate, because if the conjugate is not unique then of course there are no antiparticles, and thus no "left and right handed fermions" (because the right handed fermions are supposed to be the antiparticles of the left handed ones?). This potential failure to distinguish between left and right handed fermions is what they mean by the word "nonchiral".

What you're saying however is that you can somehow take a "nonchiral" (self-conjugate?) group, and split it into a pair of "chiral" groups. So (for example) if the group you start with is SO(6) then you break SO(6) in two, you get two SO(3) and you identify one SO(3) as being the "antigeneration" of the other. (Meaning one SO(3) is the complex conjugate of the other, and also meaning one will wind up being the "left" and the other the "right"?) Am I correct so far?

So this makes sense intuitively, but I'm still not sure how you get around D&G's proof. The problem is that their proof appears to be inductive-- they talk about subgroups, so if (for example) SO(6) is a subgroup of E8 and their proposition applies to SO(6) then their propostion will also apply to SO(3) since SO(3) is a subgroup of SO(6) and so also a subgroup of the gauge group. You depict their argument as being a claim that chirality is impossible so long as "the conjugate is there too" inside of E8. But this is not how they depict their own argument. They claim they can show all of the groups self-conjugate.

Now, maybe what you're saying is this: SO(3) is self-conjugate. But you have two SO(3)s. You say one gets to be the "mirror" or conjugate or antigeneration of the other. So when you say "both the group and its conjugate are present in E8" and D&G say "the group is self-conjugate" you are really describing the same situation, it is just that D&G are unwilling to treat two "equivalent" groups as being antigenerations of one another whereas you are. Is this where the disagreement over chirality ultimately lies? If so, can you point to anything that might guide those of us without gauge theory knowledge as to how this particular problem has been handled in theory in the past? For example, you claim you can use two copies of a single self-conjugate group as the left and right handed fermions for a single generation-- is this really standard practice in gauge theory? D&G meanwhile claim that the groups for a fermion generation and its antigeneration must be inequivalent-- is this a condition that existing GUTs, like I don't know the Georgi-Glashow/SU(5) theory, actually follow?

Thanks for the patient explanations, and please excuse me if I am garbling any concepts here...

(One particular caveat that may be confusing what I write above, I notice that D&G consistently speak of subgroups of the gauge group whereas you consistently speak of subspaces of the representation. I'm mixing the two freely. Are these things actually equivalent, or are the two different terminologies in some important way masking two different sets of rules?)

 

[arivero]

So it is the old argument about GUT theories, that they can never get V-A coupled fermions without a whole mirror set of V+A coupled ones. Is this all the content of the paper? If so, they could simply to refer to Georgi or Zee papers from 20 years ago.

 

[MTd2]

So it is the old argument about GUT theories, that they can never get V-A coupled fermions without a whole mirror set of V+A coupled ones. Is this all the content of the paper? If so, they could simply to refer to Georgi or Zee papers from 20 years ago.

I don't understand anything what you are saying. Can you explain yourself better?

 

[Haelfix]

Mirror particles are not the antiparticles of the regular generation. You cannot identify them that way, the quantum numbers are wrong.

The problem with a mirror generation are numerous phenomenologically. On one hand, why don't we see them (either directly or indirectly via their coupling to the regular particles). More specifically, why should we see any fermions at all? Generically you would expect both the generation and antigeneration to become very heavy.

Phenomenologists have been trying to get them to work for a long time in various guises and utilizing various mechanisms (discrete symmetries, hidden sectors and so forth) and the result is usually not very convincing.

I don't really know if its even possible at this stage without breaking some sort of underlying symmetry that's already been imposed.

 

[MTd2]

Phenomenologists have been trying to get them to work for a long time in various guises and utilizing various mechanisms (discrete symmetries, hidden sectors and so forth) and the result is usually not very convincing.

Can you tell me more about this hidden sector approach?

 

[MTd2]

Hmm, It seems that mirror matter and mirror generations, etc, are used for very different things:

https://www.physicsforums.com/showpost.php?p=2211533&postcount=8

So, I don't think what garrett found is not of any kind of mirror matter as they wre in hidden sector because it is not a related to the question of symmetry breaking, but actualy it is closer to the kind that of mirror matter that means having heavy particles.

 

[Haelfix]

Certainly these things comes in different guises. It depends the specifics. Often phenomenologists will just write them in as an effective theory and not worry about where they come from fundamentally (alla hidden sector proposals--actually the original dealt with mirror matter). For instance you can have adhoc mirror particles (put in by hand), lattice mirror particles (which are artifacts), mirror gauge groups, or the ones that descend directly from a GUT (nonchiral matter).

Garrets model has an action though and is supposed to be fundamental, which makes them explicit and consequently harder to explain away. He needs a mechanism to explain away the nonchiral nature of his spectrum (eg how to make the lefthanded fermions massless, and the others heavy) and I don't see how he can do that. Regardless what comes out, it will be highly nonminimal and he has plenty of other constraints to deal with as well..

 

[MTd2]

Haelfix, how would you fix that? Like, suppose I give you 1million dollars to fix that, what would you propose?

I made this vague guess:

https://www.physicsforums.com/showpost.php?p=2207034&postcount=15

 

[Haelfix]

Eyeballing the problem (which is quite outside my field of expertise), its complicated to the nth degree by the fact that gravity is explicit in his model and that you can't really tinker too much with that structure without breaking the equivalence principle.

Your guess is as good as mine.

 

[MTd2]

Eyeballing the problem (which is quite outside my field of expertise), its complicated to the nth degree by the fact that gravity is explicit in his model and that you can't really tinker too much with that structure without breaking the equivalence principle.

Well, I was thinking just about mixing different modes of low energy symmetry breakings, but just on those that did not mixed with the gravity sector. At least Jacques Distler did all possible decompositions of E8 that fits the SM group, which makes the job easier.

 

[Berlin]

Hi,

I also have the same idea MTd2 has: work your way down from one generation inside E8 and work from there. The three generations are equivalent except for their mass. This is also more or less the case for the effective mass of electrons inside a semiconductor. A dynamical potential and fermi exclusion could do the trick. Personally I would incorporate the gravitation part in this breaking procedure. I mean (and I hope!) that the gravitational part of the unbroken E8 will NOT have an a priori lorentz invariance. We should explain (and not take it for granted) that our (+,+,+, -) signature will have a dynamical origine. I like to use the recent Zenczykowski ideas as a starting point for this, but do not know how yet. Only after a breaking mechanisme gravity will become the one we know.

berlin

 

[arivero]

I don't understand anything what you are saying. Can you explain yourself better?

Vector minus axial, V-A, is the old way to name chiral interactions. The old books say that any GUT theory is forced to have also V+A. I have not followed the evolution of the terms, but I would guess that "mirror matter" and "V+A interacting particles" is the same concept, is it?