Lisi, Distler, Garibaldi, and chirality

Last August, when I met Lenny Susskind in Prague, he told me that it was OK for Garrett Lisi to propose his revolutionary idea. People decided it wasn't correct, the story ended, and there's no reason to say anything else.



Garrett Lisi organized a surfer dude physics conference in the middle of Prague. The speaker above gave a talk called "How we're chirally correlated with the direction of the wave in Lisi's TOE."

That surely sounds nice except that Lenny must live outside reality if he thinks that this is how the story ended. In reality, the idea of a surfer dude who found a theory of everything started to live its own life. It has never ended.

In the media, the surfer dude has been more frequently discussed than Susskind, Witten, and Maldacena combined ;-), his "theory of everything" is continued to be mentioned by popular magazines as a leading contender for a unifying theory - on par with string theory - and pretty much everyone who is interested in physics but who lives outside a top high-energy physics theory group is influenced by a powerful, huge, omnipresent hype surrounding this piece of crap.




The undergraduates are being brainwashed by this - and similar - new kinds of science and those who are not are being increasingly marginalized. The discipline is dying under the external pressure. The inflow of new people is being diluted every year.

One year ago, Jacques Distler and Skip Garibaldi submitted a paper,

There is no "Theory of Everything" inside E8,

that was addressed to mathematicians. They decided to accept Lisi's rules of the game, ignore issues such as the correct statistics, spin, diffeomorphism symmetry, renormalizability of gravity, and so on, and just figure out whether they can get the right representations for the particles using Lisi's kindergarten method.

Of course, the answer is that you can't get them, either. There's no reason why this - not too constraining, but still nontrivial - condition should hold if there doesn't exist a single reason to think that Lisi's writing makes any sense as a theory of physics.

One can enumerate some basic features of the fundamental forces and matter species as we know them and check whether Lisi's theory can agree with them:

1. correct gauge group for non-gravitational forces
2. correct representations for fermions in one generation
3. presence of gravity, a force built on the bulk diffeomorphism group
4. chirality (left-right asymmetry) of the electroweak interaction
5. gauge coupling unification (non-gravitational)
6. gauge coupling unification (gravitational)
7. natural occurrence of several (or three) generations
8. renormalizability of non-gravitational forces
9. renormalizability including gravity
10. solution to the hierarchy problem
11. existence of a dark matter candidate
12. solution to the cosmological constant problem.

Lisi's score (if I overlook some possible problems) is

1. PASS
2. PASS
3. FAIL
4. FAIL
5. FAIL
6. FAIL
7. FAIL
8. FAIL
9. FAIL
10. FAIL
11. FAIL
12. FAIL
13. FAIL
14. FAIL

The first two conditions were satisfied because Lisi essentially "borrowed" them from the Grand Unified Theories (GUTs), more precisely from those that are embedded in the E8 as they have been embedded in the E8 x E8 heterotic string since 1985.

Well, he doesn't do it quite right, so that his physics doesn't quite work, but if he had copied the standard grand unification, it would work. Let's say a few words about the character of the failures of Lisi's theory in most criteria relevant for a unifying theory:

1. the Standard Model group can be embedded into an E8: that's how it has worked for 25 years, since the discovery of heterotic strings and the 4D heterotic paper by Candelas, Horowitz, Strominger, and Witten that introduced the Calabi-Yaus to string theory
2. the representations under the gauge group for the fermions can come out realistically: that's been known for 35 years because only the grand unified subgroup becomes relevant
3. gravity can't emerge from such a purely Yang-Mills theory in the bulk because its gauge symmetry, the diffeomorphism group, isn't a subset of a normal Yang-Mills group, and the local Lorentz symmetry simply isn't enough as a replacement because it doesn't act on positions in spacetime and can't remove the unphysical polarizations of the graviton
4. chirality can't emerge from an E8 field theory because E8 doesn't have any complex representations, so it can't be used as a grand unified group in normal field theory; E8 has to be broken before you get to field theory (in string theory, it's broken by some gauge configuration on the Calabi-Yau); this point would be enough to replace the paper by Distler and Garibaldi
5. gauge coupling unification isn't discussed by Lisi because he never gets beyond naive classical Lagrangians at all; he only wants to write a naive classical theory and look at people celebrating a theory of everything; at any rate, the unification doesn't work well without SUSY so the forces can't really unify anywhere
6. gravity doesn't unify at all - a wrong scale, no extra dimensions etc. make it impossible; let me also say that it is ludicrous to think that he unifies bosons and fermions via a symmetry that only has bosonic generators, that's simply not possible
7. multiple generations can't really emerge from Lisi's starting point; I could add that he can't say anything new or convincing about the masses and couplings of the Standard Model, either
8. renormalizability is not discussed because it's too "quantum" for Lisi but as long as he wants to believe that his theory includes gravity, the renormalizability is broken for the gauge group dynamics, too
9. renormalizability including gravity doesn't work, because he wants to get an ordinary GR - which he doesn't; but even if he did, he wouldn't make any progress in removing its deadly divergences; so he's not even trying to address any of the problems of quantum gravity
10. no SUSY and no other candidate to explain the lightness of the Higgs; he really didn't get to the real physics yet (e.g. the hierarchy problem)
11. no dark matter candidate; Lisi's is a typical theory that tries to be "minimal" and that tries to predict nothing new (it assumes that nothing new exists), except that in this case, it is "too minimal" and contradicts the astrophysical observations of dark matter
12. of course, no solution to the cosmological constant problem (why it's so small but nonzero) is presented, either: but some serious theories - and I really mean string theory only (which is the only approach that can pass the previous points) - may get a "FAIL" for this point, too, depending on whether or not the grader would believe the anthropic principle

To summarize, Lisi got excited because he (incorrectly) understood some points about the grand unification and the role of E8 in heterotic string theory. He must have been on crack to get excited at this point.

Now, instead of being happy that Garibaldi and Distler wrote an appendix to his crackpot paper, he is unsatisfied. In this memorandum, he disagrees with Distler's and Garibaldi's trivial statement:

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.

Lisi writes that it's not true, it's politically incorrect, it's misleading, and all this complete crap. In other words, Lisi wants to obscure the fundamental difference between chiral (left-right asymmetric) and non-chiral (left-right symmetric) theories because his theory not only predicts the wrong things but he even doesn't want to study basic parts of particle physics such as chirality. He writes a lot of obscure nonsense about "mirror fermions" that can get massive and disappear from the theory.

But they can't.

If your theory is left-right (or at least CP) symmetric at very short distances, it will stay left-right symmetric forever, as you approach longer distances. Well, you could think about a slight breaking of the left-right symmetry breaking in the ultraviolet that would get enhanced at longer distances, by spontaneous symmetry breaking.

But you will find out that it's impossible to give the "undesired" mirror fermions high masses. You can't give them ordinary masses because they carry nonzero hypercharge (among other quantum numbers), so that the squared fermionic fields are not neutral and their presence in the Lagrangian would break the symmetry.

You can't write "fermion times fermion conjugate" either because the complex conjugate fermion has the opposite chirality which can't be contracted with the original spinor to produce a scalar. To summarize, you would need another copy of the Higgs multiplet as well - a mirror Higgs. The mirror Higgs would be much heavier than the normal Higgs.

Such a theory would be possible in principle except that it would be much more fine-tuned than the normal chiral Standard Model: you would have to protect all the "mirror" objects from combining into much more massive pairs. Moreover, it can't be embedded in Lisi's "single group fits all", anyway, not even according to his own sloppy rules.

Unlike supersymmetry, such a doubling of the field content is completely unsubstantiated. It brings no advantages to the model - just disadvantages. Things get more fine-tuned, not less fine-tuned, and so on. It can be studied but theories of this kind actually don't end up being "grand unified".

Incidentally, it seems that Jacques Distler himself is confused about chirality, too. He criticized Nathan Berkovits' pure spinor formalism because it's not immediately clear how to formulate the reality projections on the pure spinors in the Minkowski signature of spacetime - Nathan likes to talk about the spinors in the Euclidean 10D spacetime.

But such things are never a problem. If a machinery can be defined in one signature and extrapolated to another signature so that the desired reality and unitarity conditions are satisfied, things are just OK.

In particular, Jacques seems to be confused about the behavior of the reality conditions under the Wick rotation. The spinors change their type and he thinks that it inevitably doubles the degrees of freedom, and so on. But the real total number of degrees of freedom is never changed.

It's just that the reality condition - constraining a priori complex fields - may get an extra time reversal in the Euclidean spacetime so it becomes non-local, if you wish. While the condition may be

Field (x,y,z,t) = Field^* (x,y,z,t),

the corresponding condition in the Euclidean spacetime with "t_E = it" says

Field (x,y,z,t_E) = Field^* (x,y,z,-t_E).

The extra sign arises because the fields at time different from "t=0" can be obtained by the conjugation with the evolution operator "exp(iHt)", but the Hermitean conjugation of the evolution operator behaves differently for real "t" or imaginary "t" (i.e. real "t_E").

While for real "t", the Hermitean conjugate of "exp(iHt)" gives "exp(-iHt)", for imaginary "t", the exponential is actually self-adjoint. This is why the reality conditions in the Euclidean spacetime differ from those in the Minkowski spacetime by an extra time reversal. So the number of "real" components of fields at a given point may change but the total number of reality constraints, and therefore the total number of "degrees of freedom in the whole spacetime", doesn't change.

After all, all the fields and other objects are just continuations of the same objects to complex values of time, so you can't possibly change the total number of degrees of freedom.