# Is there any news to Garrett Lisi theory?

He's a member here, I'll ping him :) @garrett

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This is why I am asking. It's a long time since anything happened.

Gold Member
Hi MTd2, thanks for asking. A year or so ago I figured out how to generalize Cartan geometry and make sense of the idea of a deforming Lie group. It's turned out to be a very powerful and succinct geometric structure for modeling both GR and the SM, and I've been working on a paper. I gave some more hints about it on the interview jedishrfu linked. I also bought a house here in Maui, built some guest cabins, and have been running it as a micro-science institute, which has been great fun.

mheslep, David Horgan, marcus and 1 other person
Staff Emeritus
Hi, I don't want to launch a hostile discussion, but I am wondering whether you have a simple answer to the first commenter's objection on the Scientific American website: He claims that
It has been known for many years that there is no embedding of the standard model into E8 (http://arxiv.org/abs/0905.2658). This is a mathematical, group-theoretical fact, which Garrett Lisi has made a career out of obscuring. His would-be theory is also precisely the kind of word-level-idea that is ruled out by the no-go theorem of Coleman and Mandula.

Gold Member
Hi stevendaryl, I'm not sure I've ever seen a hostile PF discussion, and I don't think this one qualifies. I replied to some objections, including both of these, in another arxiv paper and in this Sciam post: http://blogs.scientificamerican.com...sm-of-his-proposed-unified-theory-of-physics/
(See items 2 and 4.) In summary, the Coleman-Mandula theorem doesn't apply in this kind of pre-gravitational unification, and the embedding of the SM works for one generation of fermions but embedding three generations is either weird or impossible.

atyy
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Hi MTd2, thanks for asking. A year or so ago I figured out how to generalize Cartan geometry and make sense of the idea of a deforming Lie group. It's turned out to be a very powerful and succinct geometric structure for modeling both GR and the SM, and I've been working on a paper. I gave some more hints about it on the interview jedishrfu linked. I also bought a house here in Maui, built some guest cabins, and have been running it as a micro-science institute, which has been great fun.
Several bits of good news here! I'm looking forward to the paper currently in progress.
I'd love to know if you have any comment to make in passing on this November 2014 paper by Chamseddine Connes Mukhanov:
http://arxiv.org/abs/1411.0977
Geometry and the Quantum: Basics

It seems to be an alternative approach to treating GR and StdMdl particles in the same framework. Is there any (possibly very general) sense in which your work and theirs is converging towards a common physical interpretation of quantum geometry and matter?

Gold Member
Hi Garrett,

Do you have an opinion about the SU(8) papers of Stephen Adler? It looks like he succeded in squezing in the SM, including the three generations, into this group. Opening a path to E(8).

Remark from Stephen: “SU(8) gravity” multiplet has 128 boson and fermion helicity states, and the “SU(8) matter” multiplet has 112 boson and fermion helicity states. These numbers respectively match the numbers of half-integer and integer roots of the exceptional group E(8). Is this a numerical coincidence, or a hint of a deep connection with the E(8) root lattice?".

berlin

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Hi MTd2, thanks for asking. A year or so ago I figured out how to generalize Cartan geometry and make sense of the idea of a deforming Lie group. It's turned out to be a very powerful and succinct geometric structure for modeling both GR and the SM, and I've been working on a paper. I gave some more hints about it on the interview jedishrfu linked. I also bought a house here in Maui, built some guest cabins, and have been running it as a micro-science institute, which has been great fun.
In the blog of the interview, you mention 10 dimensions. Isn't that a bit like string theory?
BTW, are there accommodations in that house for people who have a disability, like me?

Gold Member
Thanks, Marcus. On that CCM paper, I think their approach is great and I'm happy that a whole community of researchers have been working in that direction. With this paper in particular though, it's mightily complex, and I worry that with each step of complexity they're getting further away from good physics. This is often the case with research programs that get popular -- there's a tendency to pile on complications, constructing more and more theory until it becomes a bit of a nightmare. And though I do think this is happening here, at least it hasn't yet gotten as bad as strings.

On the content side, I think I see some of what they're doing, and it is getting closer to my work. Their $M_2(\mathbb{H}) \times M_4(\mathbb{C})$ algebra contains the $su(2) \times su(2) \times su(4)$ Pati-Salam model, and they're presumably getting gravitational degrees of freedom from the rest of $M_2(\mathbb{H})$, though I couldn't see quite how in their paper. If that is what they're doing, then they could embed that algebra in $spin(4,4) \times spin(8)$, add their spinor representation and triality, and be looking squarely at $E_8$.

I do consider them my closest competition. But I'm not especially worried, because my approach is to minimize rather than expand complexity, which is a terrible strategy for building a career but possibly the best for figuring something out.

marcus
Gold Member
Hi Berlin. Stephen Adler has been working in this area for quite a long time. And he does mention that possible connection to $E_8$ at the close of his paper. His approach with $su(5)$ GUT and $su(3)$ family unification via $su(8)$ is very reasonable. I'd like to see gravity included though. One interesting thing to try might be using Bert Kostant's decomposition, $$e8=su(5) \oplus su(5) \oplus (5 \otimes 10) \oplus (10 \otimes \bar{5}) \oplus (\bar{5} \otimes \bar{10}) \oplus (\bar{10} \otimes 5)$$ But I'm more interested in relating the generations via triality.

wabbit
Gold Member
MTd2, is that a troll? ;) It's not at all like string theory. The ten-dimensions are the Cartan geometry description of spacetime from deforming the ten-dimensional Lie group $Spin(1,4)$ while maintaining the structure of a six-dimensional $Spin(1,3)$ subgroup to get four-dimensional spacetime.

I don't know how you are disabled, but the Pacific Science Institute buildings are single-story.

Enrico Fermi
Did you use any Klein geometry as well?Because You used Lie geometry .You used the principal group(G) and a closed lie subgroup(h).

Gold Member
Enrico, yes, the initial Klein geometry decomposition gives de Sitter spacetime, $Spin(1,4)/Spin(1,3)$, which is a symmetric space and subgroup of $Spin(1,4)$. That then deforms as a Cartan geometry to describe spacetime.

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I am paraplegic, I need a wide space in the bathroom. There are norms to follow. This pessage is too thin and it should go all way to the parking lot or whenever a car would leave the person

it should be larger, like 1.5 meter wide and with at most a slight inclination, not more than 5º to not few uncomfortable. And there's the problem of bathrooms.

Gold Member
MTd2, PSI is currently a typical residence, so you'd probably need someone around to help you if you came to visit.

roberto85
Yes, he recently posted this paper 6 days ago:
http://arxiv.org/abs/1506.08073

I would love for a technical discussion to arise from this paper like it did his last one, it was very interesting.

roberto85