I recently did another podcast with Curt Jaimungal, on the topic of unification, which is now available here. As part of this I prepared some slides, which are available here.

The main goal of the slides is to explain the failure of the general paradigm of unification that we have now lived with for 50 years, which involves adding a large number of extra degrees of freedom to the Standard Model. All examples of this paradigm fail due to two factors:

- The lack of any experimental evidence for these new degrees of freedom.
- Whatever you get from new symmetries carried by the extra degrees of freedom is lost by the fact that you have to introduce new ad hoc structure to explain why you don’t see them.

There’s also a bit about the new ideas I’ve been working on, but that’s a separate topic. Over the summer I’ve been making some progress on this, still in the middle of trying to understand exactly what is going on and write it up in a readable way. I’ll try and write one or more blog entries giving some more details of this in the near future.

I just watched the interview, and from my layman pov I thought it was great. Definitely the clearest explanation I’ve seen of your new ideas! My question is: in the presentation you talk about some of the questions unified theories have tried and failed to answer, so how does this approach of explaining wick rotation with imaginary time in Euclidean geometry help to answer these outstanding questions? Is it mainly about the ability to do certain lattice calculations that you alluded to? Or is it that formalizing the wick rotation like this might lead to other unknown future insights and predictions?

Bryan,

I’m afraid I didn’t really explain this here, to explain the ideas carefully is another whole talk. Working out details still in progress, but the basic claim is that when you Wick rotate spinors from Euclidean spacetime to Minkowski, one of the two SU(2)s that makes up rotations in 4d Euclidean space-time becomes the internal SU(2) symmetry of the standard model (NOT the usually expected Minkowski space-time transformations). This gives an explanation of the SU(2) in the SM, and a new avenue for unifying things.

Peter, thanks for the explanation. During the lecture I didn’t know what you meant by “internal symmetries” but now it makes sense. Thanks!

This is a genuine question, not meant as a challenge.

If you identify one of the SU(2)’s going from Euclidean to Lorentzian signature with an internal symmetry, where does fermions of the other handedness come from? In other words, your Wick rotation will generate (say) right-handed fermions. If I understand correctly (and maybe I don’t), instead of generating fermions that transform in a left-handed spinor representation, the Wick rotation will generate fermions that transform in the SU(2) weak gauge group. But we observe states which transform with a left-handed spinor representation (for example, the electron has a mass so it has both left and right handed spinor components). Where do those left-handed states come from in this picture?

Gavin,

Still working on writing up the details of this that would completely answer your question, but here are some things to keep in mind (note, here “right” and “left” are being used to label chirality, not discussing helicity).

1. The way chirality (left vs. right) works is quite different in Euclidean and Minkowski signature. In Euclidean spacetime, there are independent SU(2) groups for each chirality. In Minkowski spacetime there is just one SL(2,C) group.

2. The way chirality works in Minkowski spacetime is that the standard spinor representation of the SL(2,C) group is one chirality, the complex conjugate representation the other chirality. If a particle is right chirality, its antiparticle is left chirality. It’s well-known that when you write the SM in terms of fundamental Weyl fields, you can take the fundamental fields to be all one chirality (say, right, to go with my “spacetime is right-handed” slogan). The left chirality particles are anti-particles of these fundamental fields.

There’s a lot more to say about this, again, exactly how the reconstruction of the Minkowski spacetime spinor fields from the Euclidean spacetime spinor fields works, and what happens to chirality as you do this, is something I’m still sorting out.

Presumably, Peter, your approach circumvents the theorems of Lochlainn O’Raifeartaigh and Coleman-Mandula relating to the impossibility of combining internal symmetries with relativistic symmetries.

Nigel B.,

Those theorems say that in Minkowski spacetime you can only extend spacetime symmetries by symmetries that commute with spacetime symmetries (“internal”). If you extend by symmetries that don’t commute with spacetime symmetries, you will get a trivial theory.

What I’m doing doesn’t violate this, since the Euclidean left SU(2), after Wick rotation, commutes with Minkowski space-time symmetries.

This should be clear from the point of view of my last paper, where, from the complex point of view, encompassing both Euclidean and Minkowski, space-time symmetry is purely right-handed, commuting with the left-handed factor.

Thanks! Looking forward to seeing the details!

Regarding evidence in favor of conventional unification, one could mention the near-unification of the gauge couplings when extrapolated to high energies, and the fact that the generations form SU(5) or SO(10) multiplets. (I sometimes wonder to what extent anomaly cancellation alone, favors ensembles of fields that look like GUT multiplets.)

Mitchell Porter,

That a generation fits nicely into the spin representation of SO(10) may very well be some kind of hint about unification. But the SO(10) symmetry is very badly broken, and this embodies exactly the problem I’m pointing to: whatever positive you get from the new symmetry is overwhelmed by the huge negative of having to introduce all sorts of ad hoc new structures and parameters, just to break the new symmetry down to the SM symmetry, carefully hiding all observable effects of the new symmetry.

On coupling constant unification, same problem. There you have the additional problem of needing a SUSY theory, so you get all the extra negatives of having to do SUSY breaking.

Georgi and Glashow were right to give up on this a long time ago, even though it was their baby. Since that time, things have just gotten worse and worse for this idea every year, as limits on SUSY masses and the proton lifetime get pushed higher and higher.

Dear Peter,

I am a “chiral” theoretical physicist (studying quark matter) and I do not understand physically your statement: “The left chirality particles are anti-particles of these fundamental fields”.

For massive Weyl fermions, the mass mixes chirality and it is not a good quantum number. Very simply put, a left handed fermion for an observer is right handed for another inertial observer if he has the correct speed and this is possible because the fermion does not go at the speed of light. Hence the chirality is not a good quantum number because it is not observer independant. I do not see how your statement about the left chirality of particles being anti-particles is compatible with this physical explanation.

But I am not a mathematician so may be the misunderstanding is purely a matter of physical interpretation of mathematical statement.

Best,

Arno

Arno,

I think there are various problems of terminology here. For me Weyl fermions are massless, so I’m not talking about mass terms, or SM Yukawas. For massive particles helicity is not chirality, have to distinguish the two.

I don’t want to get into this anyway, because what I’m talking about is just exactly the same story that is in every textbook if you just look at it in Minkowski space-time. For what I’m interested in, you have to think about Euclidean space-time spinors. Part of the story is that the way chirality works is quite different in the two cases. In Euclidean space time right and left chirality Weyl spinors are completely independent, while in Minkowski spacetime they are conjugates of each other.

One question for Peter, have you used any mathematical construction so far that wasn’t already published before 1973? In the optimistic scenario that you are on to something remarkable, how sad it would be if it could have all been done 5 decades earlier, just imagine the progress that might have been possible in the intervening period, compared to what we got.

Bertie,

Most of what I’m looking at involves results in math and physics not necessarily pre-1973, but from the 70s and early 80s, before the field reoriented around string theory in 1984-5. In particular, the main work on twistors in Euclidean signature and the relation of this self-dual Yang-Mills began in 1977-78.

One thing I’ve been spending a lot of time looking at is the standard reference about wick rotation of spinor fields, an Osterwalder-Schrader paper from 1973.

peter:

i greatly enjoyed both the recap and the new ideas. i’m not well versed in these areas but i’m trying! 🙂

to ask a vaguely curt-like question and to tie the second half of your talk back to the first a little bit, would it be fair to summarize your approach (as manifested, not necessarily as conceived) as something akin to: “why are we off inventing new things (structures, dofs) which don’t describe the universe when we haven’t actually nailed down what we think we are sure on? and look, when i really try to nail down some of these existing technicalities everyone is hand waving (in this case spinors under wick rotation), things start to happen that seem like exactly what we were missing?”

issa,

Yes, that’s a pretty good summary.

Dear Peter,

On the unification topic, is there something like a yearly progress review that would summarize the successes and failures of the most studied currents, and present the promising new ideas ? (Sorry for the somehow naïve question)

Mathieu,

Unfortunately a yearly progress review of the kind you are asking for would just say that their have been no successes, and no one is interested in discussing the failures. As for promising new ideas, lots of people with often dubious claims of them, but none that have gotten any wide acceptance.

So any idea how SU(3) (QCD) and U(1) (the ”rest” of the electroweak theory) emerge? Why is SU(2) ”special”?

lun,

Some related ideas about SU(3) and U(1) are in the “Twistor Unification” paper I wrote and talks about that. It is is the SU(2) and its chiral nature that has an explanation just from trying to understand Wick rotation for spinors, without getting into the twistor story.

I can’t say anything about physics, but su(2) is pretty special from a mathematical point of view, since it is small, but mighty, and turns up everywhere. ^_^

(PS Peter— I don’t know what happened with commenters’ names all getting a + instead of spaces, but I finally remembered to edit to take it out)