## Lisi’s *Exceptionally Simple TOE*

Update below.

Here’s my reaction to Garrett Lisi’s *An Exceptionally Simple Theory of Everything*.

Generally Lisi seems long on math and short on physics. The math part really does seem pretty cool—he fits all the known elementary particles, including what you’d need for gravity, into one nice structure, an E8 connection, without much room left over, all in what does look like a nice way. But the physics part seems sketchy and ad hoc, and in at least one respect very very odd.

So, what’s going on here? Lisi’s theory, except for the very very odd bit I’ll get to, is reminiscent of the GUTs of the 70’s and 80’s. Those attempted to combine all the known particles into one framework, the framework being determined by a symmetry group. (Well, they didn’t include gravity; “grand” was frankly a bit presumptous.) In those theories the fermions that make up matter—quarks and electrons and whatnot—live in representations of the symmetry groups, while the bosons that mediate the fundamental forces—photons, W’s and Z’s, gluons—are components of a “connection,” and hence live in the adjoint representation of the group. In Lisi’s theory, *everything*, bosons and fermions alike, live in the connection. There are no other representations of the group involved.

And that’s where the weirdness comes in. In his theory, at some basic level bosons and fermions are the same thing, but he doesn’t explain how that works, and he *really* needs to (he makes one cavalier statement about it: “These Grassman fields may be considered ghosts of former gauge fields, or accepted a priori as parts of this superconnection.”) Of course, supersymmetric theories also have bosons and fermions on the same footing, but they work for it. (They also run into problems with experimental evidence, as the superpartners required by supersymmetry have never been observed, but that’s not important here.) On the other hand, it really *is* interesting that in Lisi’s decomposition of E8, the bosons and fermions all live in the proper representation of gravitational SO(3, 1).

I think Lisi does have more of an explanation of the boson/fermion problem than he discusses in this paper. I’d love to see it in detail! The direction I’d look in is the possiblity that the integer-spin fermions and half-integer-spin bosons are suppressed at some “dynamical” level, essentially by the spin-statistics theorem.

The vagueness on bosons and fermions is really just the most egregious example of the general ad hoc-ness of the Lisi’s physics. One problem that any unified theory based on symmetry has to solve is how the symmetry is broken down to what we observe. This Lisi does not attempt to do (as he pretty much acknowledges). He does fit Higgs particles, which are in more standard models exactly because of the need to break symmetries, into his E8 model, but those can’t have anything to do with breaking the E8 symmetry itself (although I presume they can serve their usual function, breaking electroweak SU(2)×U(1), once the symmetry is broken that far).

Actually, the niceness of how everything fits into E8 isn’t completely finished. Most glaringly, he tries to relate triality (the enlarged symmetries of SO(8), which are present here as well) to the three generations of electrons/neutrinos and of quarks. But (as he acknowledges) he hasn’t really worked that out. It could just as easily be a coincidence, in that they all involve the number “3,” as real physics. In general the whole thing could be more coincidence than real physics—this sort of work can veer dangerously close to numerology. In fairness, string theorists do a lot of that too.

Lisi’s discussion of dynamics is, to say the least, sketchy, and as far as I can tell ad hoc. I’m also unsatisfied by his discussion of the topology of spacetime. He says that “[de Sitter spacetime] should be considered the background spacetime for particle interactions in this theory,” but I’m not sure there whether he means that he really does think de Sitter space is the the actual topology of spacetime, or whether he means only that it would work for perturbative calculations. Indeed I don’t see any indication of what he really intends the theory to be at all—does he mean to be working the same perturbative footing that is all other QFTs really have? If so, what about renormalizability, a major and essential problem with QFTs including gravity? Or does he intend something non-perturbative?

So, my overall conclusion is that Lisi does not have an actual Theory of Everything. But what he does have is pretty neat, whether it turns out to be a hint of The Real Theory of Everything, or just a big coincidence.

UPDATE. I’ve now read a previous paper of Lisi’s, and it does make things clearer. Most importantly he talks at length of how he gets fermions out of BRST gauge fixing. I need to digest it more, and I’m not sure I’ll believe it once I do, but it’s certainly something. I’ve forgotten everything I once knew about BRST ghosts, but I’m pretty sure that in more ordinary settings they do not manifest themselves as real particles; they’re more of a bookkeeping device to take care of the artifacts of gauge-fixing. But I’m keeping an open mind.