Garrett's article in SciAm December issue

[arivero]

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

 

[MTd2]

This one:

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

 

[MTd2]

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

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

Alternative Version of Chiral Color as Alternative to the Standard Model

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

 

[Orion1]

special unitary group symmetry...


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

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

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

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

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

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

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

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

 

[MTd2]

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

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

 

[Orion1]

triality symmetry...


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

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

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

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

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

 

[arivero]

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

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

 

[jal]

Garrett

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

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

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

jal

 

[Orion1]

Exceptional simple Lie group...


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

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

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

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

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

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

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

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

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

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

 

[garrett]

Orion1:

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

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

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

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

MTd2:

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

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

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


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

 

[Kevin_Axion]

Awesome looking t-shirts. I might buy one, possibly, maybe not, my friends would think of me strangely.

 

[qsa]

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.

In a paper by smolin he mentions E8 in regards to a theory that regard particles as end of lines can you elaborate on that.

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0977v2.pdf


here is a quote from that paper

I would like to close by listing a few out of many open issues facing this kind of unification.
• The kinematical quantum theory can now be developed along loop quantum gravity
lines for a general G, as well as for the particular case of E8.
• The spin foam quantization may also be explored based on the proposal discussed
here. It will be interesting to see if the ultraviolet convergence results from the
Barrett-Crane model also apply here.
• The proposal of matter as the ends of long distance links needs more development.
One needs to check whether the spin foam dynamics gives the right dynamics for
the fermions in the case of graviweak unification or a larger unification. There are
also open issues regarding spin and statistics; these may be addressed by generalized
or topological spin-statistics theorems.

 

[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.

You answer sent me to review the following info.

http://en.wikipedia.org/wiki/Quark–gluon_plasma
http://en.wikipedia.org/wiki/QCD_matter
http://en.wikipedia.org/wiki/Color–flavor_locking

I would be interested in seeing how the quark-gluon plasma looks like with the “Elementary Particle Explorer”.

jal

 

[garrett]

Kevin: I don't have that problem -- my friends already think of me strangely. A cool thing about the shirts, other than E8 being pretty, is that one can find all possible particle interactions on it by balancing charges.

qsa: I think Lee was talking about this because it connects to some ideas about spinors from LQG and spin networks.

jal: Well, in a quark-gluon plasma you have all possible strong interactions happening all over the place. So, I suppose you could use the EPE to see what all these are if you like.

 

[Kevin_Axion]

I'll think about getting one. Anyways, are you contemplating about visiting PI again Garrett?

 

[garrett]

Sure, I like PI.

 

[MTd2]

Garrett,

What about this: whenever you talk about using triality on a part of E(8), it seems you are not talking about E(8) anymore, but a semiderect product of SO(8)XE(8), SO(8) being the group that “insert” the triality. Now, what do you think of this?

 

[Orion1]

doublet-triplet problem...

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.

SO(10) \rightarrow SU(4) \times SU(2)_{L} \times SU(2)_R \rightarrow U(1) \times SU(2) \times SU(3)
E_8 \rightarrow SU(4) \times SU(2)_{L} \times SU(2)_R \rightarrow U(1) \times SU(2) \times SU(3)

Given that both SO(10) and E_8 both break symmetry into a Pati-Salam model, then how does the Garrett Lisi E_8 model resolve the doublet-triplet problem?

In the Georgi-Glashow Grand Unified Theory, the Standard Model Lie algebra embeds in SU(5) and the fermions live in \overline{\text{5}} and \text{10} representation spaces. Unfortunately for this GUT, the new particles in SU(5) would allow protons to decay at a rapid rate, which has been ruled out by experiment.

SU(5) Georgi–Glashow model proton decay lifetime:
\tau_p = \frac{\hbar m_X^4}{10^9 e m_p^5 \alpha_5^2} = 5.063 \cdot 10^{27} \; \text{years}

Super-Kamiokande X boson mass and Z boson mass proton decay lifetime:
\tau_p = \frac{\hbar m_X^4}{10^9 e m_p^5 \alpha_s^2 (m_Z)} = 7.228 \cdot 10^{36} \; \text{years}

In another Grand Unified Theory, which has not yet been ruled out by proton decay, the Standard Model Lie algebra embeds spin(10) and fermions live in a 16 spinor rep. This spin(10) GUT contains the SU(5) GUT as a subalgebra and also contains a third GUT, the Pati-Salam GUT, via:

SU(4) \times SU(2)_L \times SU(2)_R = spin(6) \times spin(4) \subset spin(10)

How does the spin(10) GUT contain the SU(5) GUT as a subalgebra without the protons experiencing a similar rapid decay rate as SU(5)?

Is the Garrett Lisi E_8 model evolved enough to predict a value for \alpha_{U}?

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.

I also noticed that the predicted mass of a Super-Kamiokande X boson exists within the same energy spectrum as the grand unification energy scale and I am inquiring if in fact they are the same. That is, the X boson is generated and exists and marks the exact energy spectrum location where grand unification begins:

GUT scale energy equals X boson mass energy:
\boxed{\Lambda_{GUT} = m_X}

\boxed{\Lambda_{GUT} = m_X = \left(\frac{10^9 e \tau_p m_p^5 \alpha_s^2 (m_Z)}{\hbar} \right)^{\frac{1}{4}} = 4.320 \cdot 10^{16} \; \text{GeV}}
[/Color]
Reference:
http://en.wikipedia.org/wiki/GUT_scale"
http://en.wikipedia.org/wiki/Grand_Unified_Theory#Proposed_theories"
http://arxiv.org/PS_cache/arxiv/pdf/1006/1006.4908v1.pdf"
http://en.wikipedia.org/wiki/Doublet-triplet_problem"
http://en.wikipedia.org/wiki/Georgi%E2%80%93Glashow_model"
http://en.wikipedia.org/wiki/Pati%E2%80%93Salam_model"
https://www.physicsforums.com/showthread.php?t=235055"
https://www.physicsforums.com/showthread.php?t=234596"

 

[MTd2]

This is a question mainly for Garrett, but anyone that can answer it.

This is just an overview idea.

In his theory, gauge bosons and fermions use same representation, while fermions use combinations of half of the same representation. So why not say they are all combinations of preons? While E8 is not a preon like theory, maybe some parts of it are. Let's see:

The some bosons would be metastable states which would give rise to fermions. But this metastable is just as stable at the fermion state. So, the field would be just have part of its volume broken.

If this symmetry is broken, it should be arranged a way in which 2 preons, with "generation color" could attach. Colors are 0 and 1. 1 repels 1. 0 is just attractive. So, (0,1);(1,0);(0,0). Since it's chiral, side matters.

Is there anyway to find this scheme on Garrett's theory?

 

[jal]

I must admit that since I cannot get pass 4 space dimensions, that I cannot use the Elementary Particle Explorer.
jal
===
I did a blog at https://www.physicsforums.com/blog.php?b=2460
the Elementary Particle Explorer and quark gluon plasma

 

[garrett]

MTd2: I answered your same question on Peter Woit's blog: "When I am talking about E8 triality I am talking about the triality outer automorphisms of the so(4,4) and so(8) subalgebras, and the corresponding inner automorphisms of E8.” Asking in two places still gets the same answer. ;)

Orion1: Good question. I don't know how the doublet-triplet problem will be solved -- I'm hoping the answers come if or when we figure out how masses work in general. And, yes, it will be fun if we see some X bosons soon.

MTd2: I don't want to try and use preons yet -- they're an additional layer of complication. But, yes, if I get desperate this is a decent idea.

jal: A cool thing about EPE is that, since we're using a linear projection down to 2D, all the particle interactions you see still have to balance.

 

[Orion1]

E6 x su(3)...


[PLAIN]http://home.comcast.net/~lambo1826/physics/038_0003.jpg
SU(4) \times SU(2)_{L} \times SU(2)_R
[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/E6Coxeter.svg/300px-E6Coxeter.svg.png[/URL]
E_6 \times SU(3)

I noticed that the Garrett Lisi E_8 model predicts only two new particles based upon seven charge dimensions, however the Pati–Salam model predicts eight new particles, (three Higgs bosons, one electroweak Higgs boson, one singlet, two mass particles, one sterile neutrino), and the Standard Model predicts only one Higgs boson, none of which has ever been detected in any particle detector experiment.

The next higher superset above the Standard Model must predict these eight new particles, instead of two, in order to mathematically qualify as a Pati–Salam model, should they not?

What is the reason for this discrepancy?

Is the Garrett Lisi E_8 model based upon E_6 \times SU(3) instead of SU(4) \times SU(2)_{L} \times SU(2)_R?

Mathematically these are not the same?. One is the Pati–Salam model and the other is not?

Is this subset correct?
E_8 \supset E_6 \times SU(3)

Does the Garrett Lisi E_8 model break symmetry as this?:
E_8 \rightarrow E_6 \times SU(3) \rightarrow SU(3) \times SU(2) \times U(1)

According to Wikipedia, the \frac{E_6 \times SU(3)}{SP(8)} model predicts two graviton singlets.
[/Color]
Reference:
http://home.comcast.net/~lambo1826/physics/Slansky01.pdf"
http://en.wikipedia.org/wiki/Gauge_theory"
http://en.wikipedia.org/wiki/Standard_Model"
http://en.wikipedia.org/wiki/Pati%E2%80%93Salam_model"
http://en.wikipedia.org/wiki/E6_%28mathematics%29"
https://www.physicsforums.com/showpost.php?p=2997945&postcount=59"

 

[rhody]

The December issue of SciAm finally hits Newstands tomorrow.
For those of us who don't have online subscriptions, the mystery will be over, plan to stop at Barnes and Noble on way home from work to pick up a copy.

Rhody...