# Explicit embedding of gravity+Standard Model in E8 (new Lisi paper)

1. Jun 27, 2010

### marcus

http://arxiv.org/abs/1006.4908
An Explicit Embedding of Gravity and the Standard Model in E8
A. Garrett Lisi
14 pages. For peer review and publication in the "Proceedings of the Conference on Representation Theory and Mathematical Physics."
(Submitted on 25 Jun 2010)
"The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3) acting on a Majorana-Weyl spinor, consistent with GraviGUT unification. This entire structure embeds in the quaternionic real form of the largest exceptional Lie algebra, E8. These embeddings are presented explicitly and their implications discussed."

As I recall there was a conference at Yale last October at which Garrett was invited to present a paper on this topic. I think the Yale 2009 conference was the one referred to here---on Representation Theory and Math Physics.

The way it works out, it seems like this "ToE" predicts a whole bunch of new particles which the LHC can find or not find. In effect, it does what theoretical physics is supposed to do, and is what any proposed new unification model is supposed to be---namely predictive and testable.

Some of what other particle theorists work on these days is not so explicitly predictive, and does not risk rejection by Nature--it's more along the lines of a mathematical pastime--or a "framework" of math with numerous different possible applications. But I don't think Lisi's is the only testable unification on the table. There is one that Hermann Nicolai presented last year---joint work with Kris Meissner---making, as I recall, explicit predictions which could be ruled out (or confirmed) over the next few years at LHC.

Last edited: Jun 27, 2010
2. Jun 27, 2010

### dpackard

How can a classical field theory like GR and a quantum field theory like the SM be unified in a single algebraic structure like E8? I guess this question applies to the GraviGUT step specifically. Is it merely that there is a spin-2 boson in the theory that matches the graviton, as is seen in string theory? I've never really understood how having such a particle really equates to a unification of QM and GR - for instance, how do the interactions of this particle reproduce something like the precession of Mercury's perihelion, or any of the other phenomena that required the GR modification to gravity? Anyone know?

On another note, doesn't this attempt at a TOE maintain the same background dependence issues that LQG people say plague other unification attempts like string theory?

I do like that he responds to Jaques Distler's critiques in this paper, thought I'll be interested to see if Distler himself finds the argument convincing (about how the mirror fermions gain extra mass and thus remain unseen, if I'm reading this correctly).

3. Jun 28, 2010

### tom.stoer

Distler argues that E8 is not large enough to contain three fermion generations and that the existence of mirror fermions / non-chiral matter kills the model. As far as I can see this new paper does not really address these issues.

4. Jun 28, 2010

### MTd2

Last edited by a moderator: Jun 28, 2010
5. Jun 28, 2010

### rhody

Maybe this will be a High Noon moment...

See attached thumbnail...

Good luck to the guy whose name starts with the same first letter as Mr Cooper...

Too bad the original gunfight didn't take place at: 12:18...

Rhody...

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6. Jun 28, 2010

### vacuumcell

Maybe the post-Distler Garrett will be kind enough to discuss here at PF his thinking just as the pre-Distler Garret did.

7. Jun 28, 2010

### marcus

!

Beautiful spot for a workshop on E8 and Lisi's unification idea! Banff. MTd2 thanks for posting the link to the workshop. The organizer is Joe Wolf, which says a lot. I will quote:

Banff International Research Station for Mathematical Innovation and Discovery

Structure and representations of exceptional groups

Objectives

"From Cartan and Killing's original classification of simple Lie groups in the 1890s, these groups have been understood to be of two rather different types the infinite families of classical groups (related to classical linear algebra and geometry); and a finite number of exceptional groups, ranging from the 14-dimensional groups of type G2 to the 248-dimensional groups of type E8. Often it is possible to study all simple Lie groups at once, without reference to the classification; but for many fundamental problems, it is still necessary to treat each simple group separately.

For the classical groups, such case-by-case analysis often leads to arguments by induction on the dimension (as for instance in Gauss's method for solving systems of linear equations). This kind of structure and representation theory for classical groups brings tools from combinatorics (like the Robinson-Schensted algorithm), and leads to many beautiful and powerful results.

For the exceptional groups, such arguments are not available. The groups are not directly connected to classical combinatorics. A typical example of odd phenomena associated to the exceptional groups is the non-integrable almost complex structure on the six-dimensional sphere S6, derived from the group G2. What makes mathematics possible in this world is that there are only finitely many exceptional groups: some questions can be answered one group at a time, by hand or computer calculation.

The same peculiarity makes the possibility of connecting the exceptional groups to physics an extraordinarily appealing one. The geometry of special relativity is governed by the ten-dimensional Lorentz group of the quadratic form of signature (3,1). Mathematically this group is part of a family of Lorentz groups attached to signatures (p,q), for any non-negative integers p and q; there is no obvious mathematical reason to prefer the signature (3,1). A physical theory attached to an exceptional group - best of all, to the largest exceptional groups of type E8 - would have no such mathematical cousins. There is only one E8.

Two years ago Garrett Lisi proposed an extension of the Standard Model in physics, based on the structure of the 248 dimensional exceptional Lie algebra E8. Lisi's paper raises a number of mathematically interesting questions about the structure of E8, for instance this one: the work of Berel and de Siebenthal published in 1949, and Dynkin's work from around 1950, gave a great deal of information on the complex subgroups of complex simple Lie groups. For example, they independently showed that complex E8 contains (up to conjugacy) just one subgroup locally isomorphic to SL(5,C) x SL(5,C). For Lisi's work, one needs to know about _real_ subgroups of _real_ simple groups: which real forms of SL(5) x SL(5) can appear in a particular real form of E8? These are subtle questions, not yet completely understood. A mathematical study of these questions is interesting for its own sake, and may provide some constraints on the structure of the physical theories that can be built using E8.

The goal of this workshop is to introduce mathematicians to these physical ideas, and to describe much of the recent mathematical work on the exceptional Lie groups."

8. Jun 28, 2010

### rhody

This is off topic. I have two co-worker friends who have been to Banff and they both said it was one of the most beautiful places they had ever been to. How does it stack up next to Maui ?
I don't know, haven't been to Banff, but can say that one secret hidden black lava beach on Maui, near Hana (thanks to a mutinuous tour guide back in 2006, hehe)
was the most beautiful unspoiled beach I had ever seen and for the local's sake, hope it stays that way.

Rhody...

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9. Jun 28, 2010

### garrett

Marcus: Thanks for starting the thread.

Rhody: I haven't been to Banff yet either -- I'm curious too.

vacuumcell: Sure, I can answer brief questions here -- preferably focusing on what's in the paper, which I'm happy about.

10. Jun 28, 2010

### marcus

Rhody, it is not only one of the most beautiful spots in N. America judging from this:
http://www.birs.ca/images/birs/publications/birs_brochure_dec09.pdf [Broken]

it is also (according to Joe Wolf) where they regularly have some of the best mathematics workshops in the world. The only comparable venue being Oberwolfach in Europe.
I took a course from Joe Wolf around 1970---it was a lecture/'seminar on Group Reps and QM he taught with a guest expert from Harvard (George Mackey). Wolf was a callow youth at the time, quiet gangly reserved amazingly smart. Now 40 years later, he looks a bit grizzled:
http://math.berkeley.edu/index.php?module=mathfacultyman&MATHFACULTY_MAN_op=sView&MATHFACULTY_id=146
I'll get what he says about the Banff workshops:

==Wolf on Banff==
"The Banff International Research Station plays an important role in North American science. Its programs bring Canadian, Mexican, and U.S. researchers into contact with European and Asian researchers, for scientific programs at the highest level. The only comparable facility in the world is the Mathematisches Forschungsinstitut Oberwolfach in Germany."

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11. Jun 28, 2010

### MTd2

Last edited by a moderator: Apr 25, 2017
12. Jun 28, 2010

### humanino

But have you ever really understood the problem, at all ? Why do you believe there is a problem in unifying GR with QM ?

In fact, it is published and well known : perturbative quantum gravity works fine, it just happens not to be renormalizable. That means, at any finite energy we need to perform loop calculation up to a given order, and fix the parameters using a finite number of experiments. As energy increases and more loops are required, we will get more parameters until our effective theory has more parameters than we have measurements, and then we loose predictivity.

At low energy, we can compute first quantum corrections, and they are well-behaved. For the specific problem of the perihelion, it was first published in
"Quantum Theory of Gravitation vs. Classical Theory"
Iwasaki, Prog. Theor. Phys. 46, 1587 (1971).

For a more recent review, please check
Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses

So please, re-think about it. It was done, it works fine, and it has nothing to do with finding a well-behaved high-energy completion of quantum gravity.

13. Jun 28, 2010

### marcus

MTd2, I see that Tommaso got into playing with E8 using that graphic software Garrett put on line.

Another of the organizers is David Vogan (MIT) who was one of those who analyzed E8.
http://www.boston.com/news/globe/he...07/03/26/his_mind_is_on_the_eighth_dimension/
http://www-math.mit.edu/people/profile?pid=286

I have a different take on things from people like Distler. There are people who like to simplify their lives by declaring "This cannot work! It cannot be the Holy Grail!" and giving half a dozen reasons.
To me, if an idea makes testable predictions and is, at the same time, mathematically interesting, that says a lot. If you have Joe Wolf and David Vogan looking at it, there is probably something there--a scent of game.

The best mathematicians are like dogs that can smell when an idea is fertile. They make their living by having a good intuitive nose for possibilities. Jacques Distler can swear on a stack of Jacksons that something must fail, but he doesn't own the future of physics---we just have to see.

Oberwolfach (the European version of Banff) is where Matilda Marcolli (Caltech) just had that workshop on combining the Noncommutative Geometry Standard Model with LQG (Ncg + Lqg).

Last edited: Jun 29, 2010
14. Jun 29, 2010

### MTd2

Garrett, let me see if I understand what you say. You substitute the concept of chirality by asymmetry of the particles and its mirror image by an existing particle. They are just not seen because they might be very very heavy, right? But the problem is that the other 2 generations are not there and that the triality is just a hint. So, no TOE yet...

Last edited: Jun 29, 2010
15. Jun 29, 2010

### garrett

MTd2: Correct.

16. Jun 29, 2010

### MTd2

Let me see if I get this. Triality does something like this:

C - A - B -> 3 gen

B - C - A -> 2 gen

A - B - C -> 1 gen

| | |

fer mir bos

Triality exchanges the matrix elements. It could be presented by a matrix operator, where i=j you have bosons and for i=/=j you've got bosons. If written in full form, it would be like an operator that fastly exchanges matrixes like CKM.

17. Jun 29, 2010

### garrett

MTd2: Yes, and if you can figure out a way to formulate that concretely and naturally, there might be a prize in it of some sort.

18. Jun 30, 2010

### arivero

Hmm, related to CKM, an important point is that it implies that mass eigenvectors are not charge eigenvectors.

19. Jun 30, 2010

### MTd2

I was staring at the table I made yesterday, and I had this weird idea a few hours ago. Going from left to right, you'd see the list of energy shells from outside from inside.

The third generation would be a "nucleus", formed by fermion and mirror, surrounded by a boson "cloud". This is the heaviest set, due to the proximity of the fermion and anti fermion.

Second generation are two nucleus, "covalently" bound by the boson "cloud".

First generation fermion and mirror are free, but given that the mirror is short lived, you just see the the fermion.

Now, we see that maybe the only thing that Garrett was missing was screaming at his face all the time: the chiral force!

Triality, like the CKM, is the transition probability, this time between binding states.

Last edited: Jun 30, 2010
20. Jun 30, 2010

### BenTheMan

How does this new work evade Distler's no-go theorem?

21. Jun 30, 2010

### MTd2

it doesnt. In my opinion,the only way to reproduce the sm is to calculate the bound states between each particle with its mirror, and see if the allowed states gives away the remaining generations. Other than that, i see no solution to where to hide the mirror particles neither what to do with only one generation of particles. Of course, to accomplish what i described, garrett must show that there exist a kind of chiral force.

22. Jul 1, 2010

### BenTheMan

If this is true, how can it be honestly called an explicit embedding''?

Let me rephrase:

Whenever I give a talk about string theory, I always say If some string theorist tells you he can get the standard model out of string theory, your first question should be What do you mean be Standard Model?' ''.

So I ask: what does Lisi mean by standard model''? Does he mean SU(3)xSU(2)xU(1)? three generations with hierarchical masses? order one top quark yukawa coupling? CKM angles and phases?

If he can't explain these things with E8, the thread title should be changed to say `standard model-like embeddings'', you know, for honesty's sake.

23. Jul 1, 2010

### MTd2

Well, I read his paper, and this new one, at least for me, he seems to be pretty clear that he is clueless about "what he seems to be the standard model", and all your subsequent questions.

In the text he says he got one generation, but he is clueless on how to get all 3. He talks about that the reps of the mono generation SM, the mirror mono generation SM and bosons are extremely similar and works alright, if the SM had only 1 generations. Hints about a certain triality, in a way that mirrors and bosons could be somehow transformed into 2nd and 3rd generation. But, again, this time he was clear in the text, at least for me, that this is an aesthetic argument.

As for him being honest or not, I am waiting him answering if the generations of SM can be built by bound states of a mysterious chiral force.... I mean, I invented this solution in the last post, so it is not something that he wrote. :S

24. Jul 1, 2010

### garrett

Ben: Good point. The abstract makes it clear that it is one generation that is being explicitly embedded in E8 -- I would have added that to the title, but it was getting too long as it was. How to get three generations is still an open question, and I can't even rule out MTd2's wild ideas.

25. Jul 1, 2010

### BenTheMan

Can you estimate the yukawa couplings at all? Or, what sets the yukawas? I'm guessing that the only real free parameter you have floating around is the gauge coupling, so it should come from alpha and factors of pi?