Here's a note to describe, for those interested, what is going on in the "refutation" of E8 theory by Jacques Distler and Skip Garibaldi.
In a paper I posted to the arxiv in 2007, I proposed that the algebraic elements representing all know forces in physics (gravity, the strong force, the weak force, and electromagnetism) and the algebraic elements representing one generation of fermions (electrons, neutrinos, and up and down quarks) can be identified with algebraic elements of the E8 Lie algebra. For me, this was a very exciting discovery. In this sense "everything" is in E8 -- a remarkable unification of all forces and at least one generation of fermions. Now, in physics we know there are also second and third generation copies of the fermions, which relate to the forces in the same way as the first generation fermions. Algebraically, as far as we know, these particles are identical to their first generation partners. Other than having larger masses, a muon and tau interact just like an electron. Back in 2007, I suggested how these second and third generation particles might be related to other algebraic elements in E8 by triality, but stated that this relation could not work in the conventional way. Specifically, in my paper it says "When considered as independent fields with E8 quantum numbers, irrespective of this triality relationship, the second and third generation of fields do not have correct charges and spins."
What Garibaldi and Distler did was to prove that fitting the second and third generation fermions in E8 can't work in the conventional way. To this I say: yes, and that's what I said in my paper. They also prove that when one puts the first generation fermions in E8, and examines some of the other elements of E8 in a conventional way, some are mirror fermions, matched to the first generation but with opposite charges -- fermions and their mirrors making a "non-chiral" set. Except, they don't say it quite that way. What they say is "it is impossible to obtain even the 1-generation Standard Model." I consider that to be an extremely misleading statement. Their justification for saying it, and for their title, "There is no 'Theory of Everything' inside E8," is to state (buried in a footnote) that mirror fermions make a theory unviable. Specifically, they claim "Whatever intricacies a quantum field theory may possess at high energies, if it is non-chiral, there is no known mechanism by which it could reduce to a chiral theory at low energies." But that statement, crucial to their argument, is just not true. There are many theoretical models which include mirror fermions, and people have worked on ways to deal with them, giving the mirror fermions large masses. Since there is currently no good explanation for why the three generations of fermions exist, or why they have the masses they do, it is incorrect of Distler and Garibaldi to claim that mirror fermions with large masses cannot exist.
Distler and Garibaldi are trumpeting that they have proved E8 unification can't work, and they're doing their best to discredit the theory. To this challenge, I have only one question in response: Do the fields of gravitational and standard model forces acting on a generation of fermions match a subset of algebraic elements of E8, or do they not?
Regardless of this theorist squabbling, the real excitement in particle physics right now is that the LHC is beginning high energy collisions! Personally, I'm hoping they're going to see some particles consistent with unification, such as a Z', multiple Higgs, or -- who knows -- even some mirror fermions. We live in interesting times.
-Garrett