I’ve been finding recently that an increasing serious problems with blogs is that there are too many good ones with material worth reading. I’ve learned quite a lot recently from many well-informed blog postings, but the sheer number of these makes it hard to find the time for other things one should be doing.

I’ll violate my usual rule of sticking to math and physics and report that my brother Steve is joining me in the family blogging business by being involved as Publisher in a new venture that just launched this week called Xconomy. Basically it’s a blog based up in Cambridge, with offices in Kendall Square, devoted to news about what they call the “exponential economy”, that part of the economy responsible for what is perhaps too optimistically described as exponential growth in certain areas. They’re focusing on events and news relevant to new technology, especially bio-technology, businesses in the Boston area. For some interesting blog postings by their CEO Bob Buderi about what it’s like to start up this sort of business, see here and here. For a nice posting about Doc Edgerton, see here.

Back to physics and math, over at Backreaction there’s an excellent posting on the GZK cutoff and high energy cosmic ray experiments, and a report from Loops 07 sent in via Blackberry by Sabine Hossenfelder.

An American Physics Student in England tells about a recent conference on Heavy Flavour Physics, giving a very nice overview of what is going on in that field.

The latest This Week’s Finds in Mathematical Physics from John Baez is out (available here, blog entry and comments here). It’s a wonderful description of the various mathematical patterns that the standard model particles fit into. Most well known is what happens in SU(5) and SO(10) GUTs, where one can fit the fermion quantum numbers into something that can equivalently be described as the spinor representation in d=10, or the exterior algebra $\Lambda ^* (\mathbf C ^5)$. John goes on to explain various possible connections to the exceptional groups, including a recent idea from Garrett Lisi about how to use E_{8} to get three generations.

The blog entry comments discuss two recent papers by Chamseddine and Connes about their non-commutative algebra approach to this question of mathematically characterizing the SM degrees of freedom. The papers are on the arXiv, entitled A Dress for SM the Beggar, and Why the Standard Model. Because of these papers and Witten’s recent one, John seems to be getting a bit more optimistic about physics, writing “I get the feeling that theoretical physics may not be quite so stagnant after all!”

All sorts of interesting stuff at the Secret Blogging Seminar, including yet more about Connes: a “review” by A. J. Tolland of the first quarter of the new book by Connes and Marcolli (available here), which A. J. claims has the title *Noncommutative Geometry, Quantum Fields, Kitchen Sinks and Motives*. Like the earlier fat book on non-commutative geometry by Connes, it’s an amazing document, ranging widely over physics and mathematics, covering ground from QFT to the Riemann hypothesis, at a level varying from expository sections on well-known subjects to more speculative research-level discussions. I’ve just started looking at it, may bring along a copy for summer vacation reading when I head up to a lake in New Hampshire tomorrow.

Other interesting things at the same blog include reports (here and here) from Ben Webster about talks by Sergei Gukov on categorification and gauge theory (about which he has a new expository paper here), as well as about an earlier talk by Gukov on Arithmetic Topology and Gauge Theory.

Also worth reading are posts from Ben Webster about centers of blocks of category O, various comment section discussions with David Ben-Zvi at both this blog and the n-category cafe, and a series of postings by David Speyer about quadratic reciprocity and geometric class field theory (I’m running out of energy to provide links…).

From Ben-Zvi (who could run a really great blog if he chose to…) there are notes from the recent conference at Northwestern on non-commutative geometry. These include an intriguing lecture by Beilinson, as well as lectures by Nadler and Ben-Zvi himself about their recent work which connects geometric Langlands with questions about more conventional representation theory using striking ideas about how to handle loop spaces. They have a recent paper about this, which has been very high on my list of things I wish I understood better ever since David gave an inspiring talk about this here a couple months ago.

Finally, one more thing definitely worth looking at in light of Witten’s new work: an expository and historical article by Jim Lepowsky about the story of the relation of vertex operator algebras and the monster group. He explains what is so remarkable about the specific vertex operator algebra that Witten is connecting to 3d gravity on AdS, including the ways in which it is conjecturally uniquely the “smallest” such structure in a specific sense.

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Mathematicians are wonderfully nonlinear complex systems — one little perturbation and good stuff flies in all directions!

Although relating the three fermion generations to E8 triality got John interested, I’m actually assigning ALL standard model and gravitational fields to elements of Lie(E8). There’s a link to this description in TWF, but here it is directly:

Deferential Geometry

The above site (my research wiki) has a one paragraph summary and a link to a talk (slides and practice audio) I just gave here in Morelia. In five words… “everything in an E8 connection.” This includes putting the gravitational spin connection and frame together in this connection too, which should be looking like a familiar thing to do right now… ðŸ˜‰

Oops, bad link. This one should work:

Deferential Geometry

Hi Peter,

Thanks for the link. What I didn’t write in the post is that there’s some preliminary data from Pierre Auger which apparently confirms the presence of the cut-off – I expect it will be presented at that Cosmic Ray conference next week. Also, I have a second post about the Loops 2007 with some photos, but admittedly little content. I hope the slides to the talks will be on the website soon. E.g. Fotini’s talk (about non-locality) was very interesting, and so was Garrett’s ðŸ™‚

The conference closed today with a discussion session (moderated by Carlo Rovelli) where everybody was asked to give the most optimistic prediction what he/she will be talking about at the Loops 2017 – and what the probability is for that to actually happen. It was very interesting (much of it based on what the phenomenology will hopefully teach us in the soon future). It was recorded and I hope the audios will be available on the websites as well.

Best,

B.

Hi Bee,

Can you tip us off on the the cut-off energy seen? Is it exactly the GZK prediction?

Cheers,

Kris

Regarding the use of the word ‘exponential’: Any increasing function on a finite interval grows faster than a non-trivial exponential function. So I would say the use of the word above is not so much optimistic as it is next to meaningless.

Bee: various Auger talks at ICRC 2007 already appeared on astro-ph, including some energy spectra. For example see arXiv:0706.2096

Hi Garrett.

I just saw your great wiki and started to have a look into E8: the idea of unifying all in a single connection is really nice.

I just wonder if you can really avoid the problem of mirror fermions. For example the Cl_7 model of Trayling suffers (at least to me) of that problem: there is a duplication of the fermions, since the (algebraic) spinor has 8×8 complex = 128 real components, that is twice the components of a SM family, 16×2 complex=64 real. (and antiparticles are usually already taken care by the 16 weyl fermions of the SM)…

Cheers,

Fabrizio Nesti

Hi Fabrizio,

This is a good question. Before I answer it, let me tell the story of how the connection came together. I was working mostly with GR and spinors using Clifford algebra, when I saw Trayling’s nice description in Cl(7). But his model made more sense to me in Cl(1,7), and after playing with it a bit I was able to combine Trayling’s description with the spin connection and frame of GR, with the Higgs entering in a nice way. But this only had one generation of fermions. When I saw E8, it matched this exact structure, along with two more blocks of fermions. This made me very happy, so I’ve been telling people about it, even though there’s still some things to figure out.

Now, your question. Trayling solves it by either dropping the “mirror” fermions, or including them as anti-fermions. Without looking at the big picture, there’s no good reason to do one or the other. But in the big picture it’s more clear what’s going on. If we start with the compact real form of E8, there are no mirror fermions — each fermion block has the correct number of real degrees of freedom. But the real form has SO(4) as a subgroup, whereas we want SO(1,3) — the Lorentz group, with the corresponding action on the blocks of spinors. To fix this, we could start with a complex form of E8, such as would be built from complex Cl(8) bivectors — but this has twice the desired degrees of freedom for all particles, kind of like supersymmetry. This would include the “mirror” fermion problem you describe. Instead, we use a real form of complex E8, built from a complex representation of Cl(1,7). This has the same degrees of freedom as compact E8, with no mirror fermions, and has the Lorentz group as a subgroup.

Now, I don’t know WHY it’s right to start with this real form of complex E8, other than because it works. The answer to this will have to come from whatever even big picture emerges. ðŸ™‚

I hope this answers your question, but here’s some more nitty-gritty detail. If you look at the big matrix, each generation of fermions is a 4×4 block, with each entry a 2×2 block representing a Weyl spinor. Each of these Weyl spinors has 4 real degrees of freedom, which can be reassembled into a column of two complex numbers — the way we usually work with them.

Best,

Garrett

For those who are interested:

Geometrically Engineering the Standard Model: Locally Unfolding Three Families out of $E_8$

http://arxiv.org/abs/0704.0445

Âµ is a nice letter

Hi Garrett,

yes, that is what I was asking. One must have a sort of reality condition on the Cl_7 (or Cl_1,7) spinors, but this puzzled me, since spinors always carry a complex representation… On the other hand, mirror fermions can not be decoupled by making them heavy, because chiral fermions can not have a gauge invariant mass term.

Incidentally, this is what led me to consider that Cl_4 is actually enough, if one considers everything in LR-symmetric way: you can unify just isospin with gravity, and strong interactions are just internal geometrical symmetries (my 0706.3304). This approach also leads back to Peter Woit’s inspiring NPB paper of 1988, where he introduced spinors on a 4-dim complex spacetime, and our world is a real section of that…

If now in E8 one can fit the fermions in the (OxO)3 part of the gauge field (64×3 real fields) I expect that doubling is no longer a problem because one can use the would-be mirror family (S8-) as the second generation… (and the vector (V8) as the third).

If this works (e.g. strong spinor charges, triality.. work well) it is really nice!

Fabrizio

Hi Garrett.

I just saw your great wiki and started to have a look into E8: the idea of unifying all in a single connection is really nice.

I just wonder if you can really avoid the problem of mirror fermions. For example the Cl_7 model of Trayling suffers (at least to me) of that problem: there is a duplication of the fermions, since the (algebraic) spinor has 8Ã—8 complex = 128 real components, that is twice the components of a SM family, 16Ã—2 complex=64 real. (and antiparticles are usually already taken care by the 16 weyl fermions of the SM)â€¦

Hello Peter:

I finished your ‘Not Even Wrong’ and Lee Smolin’s ‘The Trouble with Physics’ a few weeks ago. I posted a review on my new blog that you might like to check out:

Review

I am a systems theorist by training, not a physicist, so I hope I haven’t gone too far out on a limb in my assessment of the debate. Thanks for a great read, you’ve done the planet a service with this book (and this blog)! I spent several weekends ploughing through both books and it was very rewarding, if exhausting, work. I think my comprehension was between 10-50% through most of the read, but even that left me feeling illuminated.

Don’t believe everything you read. Check out the various reviews of Lee’s book on cosmic variance, for example.

More good stuff:

Interesting read… but… is it just me or is it very unusual finding a purely phenomenological paper coauthored by N.Seiberg? Are the winds changing in high energy physics?

Here is the promised update:

GZK cutoff confirmed

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