Garrett's article in SciAm December issue

[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...