From a recent interview:
--Here at SciAm we never jumped on the bandwagon regarding your E8 theory,
I had kind of wondered about that, since the representation theory involved has a visually appealing aspect that would probably make for a good SciAm article. But I certainly appreciate and commend conservatism, especially since some of the media response went overboard.
--but I _am_ doing a short "second day" story (more like "second month" at this stage) briefly assessing where things stand now that the shouting has died down.
OK, great, I'll help out however I can.
--Mainly I just need to confirm that I have the right impression (from following various threads online, such as the PhysicsForums thread) about what you are doing with regard to the theory. Namely, you continue working on it to try to overcome the various problems that were pointed out (some of which you had already mentioned in your preprint as being areas needing further research).
Yes, that's correct. The largest problem is the description of the second and third generation fermions, and this was discussed extensively in the paper.
One thing I could have done a better job of, but will try to remedy as things develop, is describing the fact that this general technique of describing all fields of the standard model (bosons and fermions) using one connection does work to describe what we currently know. It is only the fit to E8 that is rather tenuous at this point -- but this fit to E8 was such an exciting possibility that I ran with it in this paper.
--Also, do you have any real collaborators at this point?
I prefer to work on my own, although I've certainly been communicating with a great number more people. It's been so long since I've worked with a collaborator, I'm not sure I remember how. But I have been talking with people as they've worked through the paper and used parts of it to pursue their own ideas, which has been good.
--Have you been invited to give talks anywhere recently?
Yes. My earliest upcoming talks will be at the TED conference on Feb 28, then I'll be talking with physicists at UC Davis on March 7.
--About the problems... I know from the beginning you've been saying that the issue of getting all three generations of fermions "needs further research."
Yep, right now there are just many interesting clues.
--About Distler's claims that even one copy of the proper chiral representation does not sit inside E8 as it needs to, I understand your position is: you're not sure if Distler is right in his claims
Yes, I think he may be making a mistake in his choice of complex structure when he uses conjugation to replace right-chiral fields with anti-left-chiral fields in describing the standard model. It's a subtle calculation, and it's possible that either of us could be confused on this point. I prefer to work through these things slowly and carefully before enjoining arguments though.
--even if he is, using the complex form of E8 instead of the real will, without any doubt, fix the problem.
Yes. If you read his argument, he's unhappy with the way the real spinors in E8 are being twisted in this theory to build complex spinors. If you start with complex spinors in complex E8, there's no problem -- at least not for the first generation. But at this point I'd prefer to stick with a real form of E8 if possible.
--I have to say the issue that bothers me the most is the fundamental one of mixing fermions and bosons so closely together without having some kind of superalgebra.
Ah. There is actually a large but unfortunately somewhat byzantine literature on this construction -- it's part of the BRST formulation.
But the mathematics of this construction are rock solid. The place I first learned about it was in this review paper:
http://arxiv.org/abs/hep-th/0201124
where, on page 70, it's defined and described as a "generalized connection":
w = A C
in which A is a 1-form and C is a Grassmann valued field, both valued in parts of a Lie algebra.
Using the algebraic structure of the exceptional groups, the C can be a spinor field algebraically. Unlike in supersymmetry, these A and C never mix -- so they can have different units without difficulty. The main advantage of formally adding them is for the distributive property in the Lie bracket -- giving an expression referred to as "The Russian Formula." (Have a quick look at page 70 of the above reference).
For a more mathematical description of this kind of BRST extended connection, this recent math paper is typical:
http://arxiv.org/abs/0710.5698
Unfortunately, this sort of BRST symmetry is less familiar to people than supersymmetry, even though it plays an essential role in QFT.
You might have noticed that Peter Woit also likes the idea of possibly interpreting these "ghost" fields, C, as fermions.
I can go into more detail if you're still not happy with this formal addition of A and C -- it's bothered other people as well, but I'm quite confident in this aspect of the theory.
--In any case, I look forward to your reply.
Sure, let me know if you have other questions. Good luck with the writing.