An Exceptionally Technical Discussion of AESToE

[arivero]

Is there some news about Konstant's E8? I was kept thinking about the product of two copies of SU(5)... after all, remember that I suspect that the content of this E8 group (and its cousin SU(32) ) in string theory is to hold the quantum gauge version of flavour.

CarlB could perhaps relate it to mesons, because mesons do actually have global SU(5) as an approximate symmetry.

 

[garrett]

Hey PF folk,

Things are indeed going very well. The most recent gauntlet for this E8 theory was subjection to formal peer review by the FQXi scientific panel, which was passed with flying colors:

http://www.fqxi.org/

I'm officially taking one hour away from email to celebrate.

I'm also very happy to see many grants awarded to quantum gravity research, and even two others awarded for investigation into exceptional structures in particle physics.

Also, FQXi has announced an essay contest on "The Nature of Time," open to all.

 

[arivero]

When one glances the comments of Dixmier, it seems as if the limit of "two generations at most" were coming because E8 containts only two copies of SU(5)... but when one decomposes the infamous 248 into SU(5)xSU(5) one gets a pair of 24, being (24,1) or (1,24) in each group, plus four of 50, combined as (5, \bar 10) and so on.

My bet should be that at least one sum 24+50+50 is the standard model content plus 28 extra degrees of freedom, so that in reality it is 24+(36+9+5)+(36+9+5) and the content of the standard model comes from 24+36+36=96. Does it coincide with Lisi's scheme? I have not looked at it in detail.

 

[Kea]

The most recent gauntlet for this E8 theory was subjection to formal peer review by the FQXi scientific panel, which was passed with flying colors...

To be honest, I am REALLY not at all impressed. Obviously, it's who you know that counts. Two token women, only one of them a physicist, working on a theory that no longer agrees with observational data. Paolo Bertozzini was also rejected, probably for the crime of living in Thailand. There are only three names on the list that I haven't come across before. These people are already very comfortable. It must be nice to be a happy, smiling, well fed North American male.

 

[marcus]

... passed with flying colors:

http://www.fqxi.org/

I'm officially taking one hour away from email to celebrate.
...

Wonderful news! Very very glad to hear this!

 

[MTd2]

Hey PF folk,

Things are indeed going very well. The most recent gauntlet for this E8 theory was subjection to formal peer review by the FQXi scientific panel, which was passed with flying colors.

Congratulations! :) Is there any restrictions on how to use the money? Can you buy 20,000 Big Macs with it?

Also, in how much in %, aproximately, is your new paper with Simone and Lee away from completion?

 

[garrett]

Hi MTd2,
I've budgeted for 1 Big iMac. And I'm afraid I can't talk about the paper yet, since it's not just my work.

Kea,
I'm also disappointed there aren't more "outsiders" being funded. But I'm a pretty good counterexample to your "who you know" comment, since a few years ago I knew approximately no one, and wasn't particularly comfortable or well fed. Heck, I'm still technically homeless.

arivero,
Your analysis is correct. The trick is how gravity and generations may or may not work with the "other" su(5). If it can work, it's certainly not obvious how, since the 5's and 10's don't appear to match up desirably. Fun to play with though.

 

[arivero]

Your analysis is correct. The trick is how gravity and generations may or may not work with the "other" su(5). If it can work, it's certainly not obvious how, since the 5's and 10's don't appear to match up desirably. Fun to play with though.

Yep, it is not obvius. Witten himself has been thinking a lot on SU(5)xSU(5), with a couple of papers four or five years ago.

I think the problem is in the 10. As I told elsewhere, it is pretty easy to get generations from the 5 of SU(5) only, via
$$(\bar 5 \otimes 5)_s = 24$$ for all the leptons and
$$3* ((\bar 5 \otimes \bar 5) \oplus ( 5 \otimes 5))_s = 3*(15 + \bar {15})$$ for quarks
but in this case, the representations (10,5) &c., which we need to reach E8, do not appear. A disturbing point is that stringers have really E8xE8, so even not a 248 irrep but a 496 one. For two years now, I have been wondering if the SU(5) could be more straightly related to the SO(32) of the 496 irrep, via $$2^5=32$$.

 

[Kea]

Heck, I'm still technically homeless.

Garrett, you can no longer claim to be an outsider. And I would happily be homeless with such a fortune, which could sustain me for years.

 

[garrett]

Elementary Particle Explorer

http://deferentialgeometry.org/epe/

 

[MTd2]

Garrett, would mind putting a different representation instead of colors. I am color blind, and sometimes I can't tell apart heads and tails.

Also, what is your "my standard model"?

 

[arivero]

related some grouping of 6 and the projections having sort of hexagonal symmetry in your gadget: I was reading now a series of lectures on Duality Symmetries, by A. Sen in Les Houches in the 2001 session, and for the 4 dimensional duality of SO(32) heterotic, compacted with T^6, some groups of 6 appear:
- a symmetric 6x6 matrix, giving 21 scalars
- an antisymmetric 6x6, giving 15 scalars
- a 6x16 object giving 96 scalars, related to "the gauge fields in the Cartan subalgebra of the gauge group".
Sen refers to his fundational paper http://arxiv.org/abs/hep-th/9402002" for more info. It is a dense paper, but one can search for the number 16 :-)

I can not bet for an interpretation of the 21 and 15. An interesting observation is that if one reduces the standard model to SU(3)xU(1) then both the neutrinos and the top are lost (assume the mass of the top is related to the W and Z), and then the number of degrees of freedom of the fermionic sector is 2*36.

 

[MTd2]

Also, what is your "my standard model"?

Sorry, I just noticed that it is the default name for any moviment I can make.

 

[yoyoq]

so...how was lunch with distler?
what did you guys eat?
who paid?
how much of a tip did you leave?

 

[MTd2]

Garrett,

Yoyoq,

I posted your question here!:http://golem.ph.utexas.edu/category/2008/05/e8_quillen_superconnection.html#c018769

 

[rntsai]

a year later...any progress on finding a way to fit three generations into e8?

 

[Berlin]

Maybe the best strategy for E8 fans would be to accept the fact that only one generation fits into the full E8! That is, I think, not as strange as it looks. In fact, the three generations are only distinguishable in mass (and could so, be identical in the mass to zero limit). Having three doublets of Higgs could cause three different mass levels only after breakdown of some of the E8 symmetries. See it like the only true generation is stuck in three different potential wells (maybe even combined with a Pauli principle). I am trying to use a kind of trinification model based on SU(2)^3, breaking down to three left SU(2)xSU(2)xU(1) groups with a left-right symmetry breaking a la Senjanovic. One of these left SU(2) groups should be part of gravity, the rest is EW. Only the 128 spinor "1/2" states of E8 seems to be required for the fermions. Whether this means that even gravity only exists in its current form after a symmetry breaking I do not know (or that the very notion of left-right comes along at that moment). All crazy ideas and the maths turns out too difficult for me anyway. Fun though.

berlin

 

[CarlB]

On the generation structure, Marni Sheppeard and I have been working on a method of describing it based on (my view of things may differ from hers) the discrete Fourier transform. Partly to justify this, I've applied the same theory to the hadrons and have found 39 equations relating their masses.

This is similar to Regge trajectories (which were used as the basis for string theory). Regge trajectories are equations that relate the masses of the same hadrons but with different angular momenta. The equations I've got relate the same hadrons but with different radial excitations. But it attributes the different radial excitations to color phase effects.

I'm submitting this to Phys Math Central next week and would appreciate comments on it:
http://www.brannenworks.com/koidehadrons.pdf

As far as E8 theory goes, this would mean something like E8 x discrete Fourier transform for the generations.

 

[MTd2]

Hi Carl,

Have you contacted Garrett Lisi about this? He could surely help you. Also, he colaborated intesively with Lee Smolin. I would like to know what you would talk to them, if you are willing to. You should also ask Tommaso Dorigo.

 

[MTd2]

Another question,

I really really expected to see the top mass calculated with you method... I know, everything else is really awesome, but I am disapointed with this one...

 

[CarlB]

Another example of a cute theory that only gives one generation of the elementary fermions, see:

Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation

Piotr Zenczykowski.

According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.
http://arxiv.org/abs/0901.2896

So does the above have anything to do with the way Garrett packs a single generation into E8? I don't think so but others understand his theory better than me.

P.S.

MTd2, when I had done this originally, it was based on assumptions which violated special relativity. That probably put Smolin off his feed. The latest version hides all that stuff by sticking to quantum information theory (where position and momentum are ignored, hence there is no need for special relativity or a replacement for it) and so that might get by better.

I seem to have given it an attractive abstract because some important people have written to me saying that they are very busy, especially this time of year, but they are going to take the time to read the paper. I think that basically, it's an attractive way of extending Regge trajectories to radial excitations and I wonder if I should give it a title that mentions Regge trajectories instead of Koide mass formulas. Hmmm.

 

[rntsai]

I'm submitting this to Phys Math Central next week and would appreciate comments on it:
http://www.brannenworks.com/koidehadrons.pdf

I quickly read through this and I'm afraid I don't
see the main point. It looks like you take these
masses three at a time and find a data fit for them
using three real parameters. You use 3x3 circulant
matrices to inspire the form of this fit. These matrices
(and their eigenvalues) are defined by 3 parameters.
It's well known that all circulant matrices (any size)
are diagonalized by the discrete Fourier transform matrix,
so they will all have the same eigenvectors; I don't think
that adds anything. At the end, it's still just a fit of 3
numbers by three parameters. It doesn't look like there's any
relation between the different fits...each has it's own
set of 3 parameters (right?). It's also not apparent how
special these fits are. It seems there are enough degrees
of freedom to fit any randomly picked 3 numbers to this
form...

 

[CarlB]

I quickly read through this ...
At the end, it's still just a fit of 3 numbers by three
parameters.

Thanks for reading! You are right that this is the effect of the discrete Fourier transform; it takes three real variables and turns them into three real variables (or one real variable and one complex variable). Whichever, it keeps 3 real degrees of freedom. But read on.

It doesn't look like there's any relation between the different fits. Each has it's own set of 3 parameters (right?).

No, there are only two parameters for each fit, "s" and "v". You're probably confused by the $$\mu_e$$ constant that is in front of each fit. This is a constant equal to 25.054 square root MeV and is not a parameter. It's value never changes. It's taken from the electron fit.

If it still isn't obvious that there are only two degrees of freedom, note that $$\mu_e$$ multiplies s and v. So you could define
$$s_e = \mu_e s, \;\;v_e = \mu_e v$$
and get each fit down to two real parameters.

By the way, you're not the only one to make this error. When my neutrino paper came out a few years ago it used similar notation and I had a professor of physics tell me that it used 4 parameters, LOL. It must be a natural mistake on a fast read. I've got the $$\mu_e$$ factored out because it's a natural scale.

By the way, if I had 3 real parameters to play around with, I wouldn't have errors, LOL. The third parameter becomes the angle delta. The claim is that the mass spectrum can be closely approximated by quantizing delta as $$2/9$$ or $$2/9 + \pi/12$$

I wouldn't be surprised if other people make the same error, but I don't think I'm going to eliminate the scale factor. From a sociological point of view, a paper that has not passed peer review gets read by people who don't expect anything good and really don't pay very close attention to the details. So they reject things as soon as they find the first detail that disagrees with them. But after a paper is past peer review this effect should go away.

 

[MTd2]

Garrett has some new ideas. Jacques Distler couter argues:

http://golem.ph.utexas.edu/category/2009/02/the_algebra_of_grand_unified_t.html#c022012

 

[arivero]

http://www.slac.stanford.edu/spires/find/hep/www?c=ARXIV:0711.0770

 

[MTd2]

Why did you point the citations for garrett's articles?

 

[arivero]

Why did you point the citations for garrett's articles?

First because it is interesting to remark that there are some :-)

Second, because of the second one in the list, Supersymmetry and Polytopes, which is an argument independent from Garret's (and from Tony's) but touching the same theme, plus susy.

 

[MTd2]

Arivero, did you know that an attemptive version of SUSY E(8) GUT exists since the 80's?

http://arxiv.org/abs/hep-ph/0201009

And also that recently it was found that F-Theory together with M-Theory with the usual standard model as a low energy limit, which might be need to be embeded in an E(8)?

http://arxiv.org/abs/0905.0142

 

[arivero]

Arivero, did you know that an attemptive version of SUSY E(8) GUT exists since the 80's?

http://arxiv.org/abs/hep-ph/0201009

Yes, I knew It is only that the particle content seems, to me, excesive.

 

[Schreiberdk]

Does AESTOE make any new predictions, in terms of quantum gravity? Does it calculate black hole entropy?

 

[suprised]

It's not a quantum theory and not consistent anyway, as far as we know.