- #36
MTd2
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arivero said: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.
arivero said:If triality fails you, look for some SU(5).
garrett said: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"?
marcus said:
...
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.
...
smoit said: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."
garrett said: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.
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.Is this really the SU(3) color?
arivero said: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.
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.arivero said: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.
arivero said: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.
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.
Garrett said: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.
garrett said:The answer is that this symmetry remains unbroken within E8.
[PLAIN]http://garrettlisi.com/stuff/su(3).png
(From the http://deferentialgeometry.org/epe/" .)
Garrett Lisi said:One small part of this [tex]E_8[/tex] shape can be used to describe the curved space-time of Einstein's General Relativity explaining gravity.
Slansky pg. 123 - ref. 1 said:A major objection to [tex]E_7[/tex] and [tex]E_8[/tex] 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.
It would mean that they are wrong, and that we live in a Standard Model universe.Orion1 said: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?
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.There are many different GUT options, however, how many of those options still work with the theory?
No, spin(1,3) and su(3) sit in different parts of E8.MTd2 said:Does that mean that SU(3) is a symmetry of gravity too?
garrett said: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.
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.
Wikipedia ref. 1 and 4 said:Some GUT theories like SU(5) and SO(10) suffer from what is called the doublet-triplet problem. These theories predict that for each electroweak Higgs doublet, there is a corresponding colored Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. Such triplets have not been observed. They would also cause extremely rapid proton decay (far below current experimental limits) and prevent the gauge coupling strengths from running together in the renormalization group.
In particle physics, the doublet-triplet (splitting) problem is a problem of some Grand Unified Theories, such as SU(5), SO(10), E6. Grand unified theories predict Higgs bosons (doublets of SU(2)) arise from representations of the unified group that contain other states, in particular, states that are triplets of color. The primary problem with these color triplet Higgs, is that they can mediate proton decay in supersymmetric theories that are only suppressed by two powers of GUT scale (ie they are dimension 5 supersymmetric operators). In addition to mediating proton decay, they alter gauge coupling unification.
Garrett Lisi said:In the Georgi-Glashow Grand Unified Theory, the Standard Model Lie algebra embeds in [tex]SU(5)[/tex] and the fermions live in [tex]\overline{\text{5}}[/tex] and [tex]\text{10}[/tex] representation spaces. Unfortunately for this GUT, the new particles in [tex]SU(5)[/tex] would allow protons to decay at a rapid rate, which has been ruled out by experiment.
[tex]SU(4) \times SU(2)_L \times SU(2)_R = spin(6) \times spin(4) \subset spin(10)[/tex]Garrett Lisi said:In another Grand Unified Theory, which has not yet been ruled out by proton decay, the Standard Model Lie algebra embeds [tex]spin(10)[/tex] and fermions live in a 16 spinor rep. This [tex]spin(10)[/tex] GUT contains the [tex]SU(5)[/tex] GUT as a subalgebra and also contains a third GUT, the Pati-Salam GUT, via:
Wikipedia ref. 2 said:The renormalization group running of the three gauge couplings in the Standard Model has been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5) or SO(10) GUTs, which are precisely the GUT groups which lead to a simple fermion unification. This is a significant result, as other Lie groups lead to different normalizations.